diff --git a/2016/12/itext-pdf/index.html b/2016/12/itext-pdf/index.html
index 24e436c5..3e24e297 100644
--- a/2016/12/itext-pdf/index.html
+++ b/2016/12/itext-pdf/index.html
@@ -32,9 +32,9 @@
 <meta property="article:published_time" content="2016-12-23T14:59:09.000Z">
 <meta property="article:modified_time" content="2023-12-04T15:12:41.466Z">
 <meta property="article:author" content="nullwy">
-<meta property="article:tag" content="Java">
 <meta property="article:tag" content="工具">
 <meta property="article:tag" content="代码">
+<meta property="article:tag" content="Java">
 <meta name="twitter:card" content="summary">
 
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@@ -330,9 +330,9 @@ <h1 class="post-title" itemprop="name headline">
 
       <footer class="post-footer">
           <div class="post-tags">
-              <a href="/tags/Java/" rel="tag"># Java</a>
               <a href="/tags/%E5%B7%A5%E5%85%B7/" rel="tag"># 工具</a>
               <a href="/tags/%E4%BB%A3%E7%A0%81/" rel="tag"># 代码</a>
+              <a href="/tags/Java/" rel="tag"># Java</a>
           </div>
 
         
diff --git a/atom.xml b/atom.xml
index 5dc19b65..9c91813a 100644
--- a/atom.xml
+++ b/atom.xml
@@ -564,12 +564,12 @@
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-    <category term="Java" scheme="https://nullwy.me/tags/Java/"/>
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     <category term="代码" scheme="https://nullwy.me/tags/%E4%BB%A3%E7%A0%81/"/>
     
+    <category term="Java" scheme="https://nullwy.me/tags/Java/"/>
+    
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diff --git a/css/main.css b/css/main.css
index b7e8bbf7..94902a84 100644
--- a/css/main.css
+++ b/css/main.css
@@ -1190,7 +1190,7 @@ pre .javascript .function {
 }
 .links-of-author a::before,
 .links-of-author span.exturl::before {
-  background: #98ff32;
+  background: #79a718;
   border-radius: 50%;
   content: ' ';
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diff --git a/search.xml b/search.xml
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+++ b/search.xml
@@ -230,6 +230,204 @@ What resources exist for Database performance-tuning? <a href="http://stackoverf
         <tag>CS</tag>
       </tags>
   </entry>
+  <entry>
+    <title>Elastic Stack 日志分析平台搭建笔记</title>
+    <url>/2019/01/elastic-stack/</url>
+    <content><![CDATA[<p>Elastic Stack（旧称 ELK Stack）是最受欢迎的开源日志平台 [ <a href="https://www.elastic.co/cn/solutions/logging">ref</a> ]。Elastic Stack 由 Elasticsearch、Logstash、Kibana 和 Beats 四个组件组成：</p>
+<ul>
+<li><a href="https://www.elastic.co/cn/products/beats">Beats</a>，是轻量型采集器的平台，从边缘机器向 Logstash 和 Elasticsearch 发送数据。</li>
+<li><a href="https://www.elastic.co/cn/products/logstash">Logstash</a>，集中、转换和存储数据，是动态数据收集管道，拥有可扩展的插件生态系统，能够与 Elasticsearch 产生强大的协同作用。</li>
+<li><a href="https://www.elastic.co/cn/products/elasticsearch">Elasticsearch</a>，搜索、分析和存储您的数据，是基于 JSON 的分布式搜索和分析引擎，专为实现水平扩展、高可靠性和管理便捷性而设计。</li>
+<li><a href="https://www.elastic.co/cn/products/kibana">Kibana</a>，实现数据可视化，导览 Elastic Stack。能够以图表的形式呈现数据，并且具有可扩展的用户界面，供您全方位配置和管理 Elastic Stack。</li>
+</ul>
+<span id="more"></span>
+<p>Elastic Stack 是逐步发展而来的，一开始只有 Elasticsearch，专注做搜索引擎，2013 年 1 月 Kibana 及其作者 Rashid Khan <a href="https://www.elastic.co/blog/welcome-drew-rashid">加入</a> Elasticsearch 公司，同年 8 月 Logstash 及作者 Jordan Sissel 也<a href="https://www.elastic.co/blog/welcome-jordan-logstash">加入</a>，原本的非官方的 ELK Stack，正式成为官方用语。2015 年 3 月，旧金山举行的第 1 届 Elastic{ON} 大会上，Elasticsearch 公司改名为 Elastic。两个月后，Packetbeat 项目也<a href="https://www.elastic.co/blog/welcome-packetbeat-tudor-monica">加入</a> Elastic，Packetbeat 和 Filebeat（之前叫做 <a href="https://github.com/elastic/logstash-forwarder">Logstash-forwarder</a>，由 Logstash 作者 Jordan Sissel 开发）项目被整合改造为 Beats。加上 Beats 以后，官方不知道如何将 “B” 和 E-L-K 组合在一起（用过 ELKB 或 BELK），ELK Stack 于是改名为 Elastic Stack，并在 2016 年 10 月正式发布 Elastic Stack 5.0 [ <a href="https://www.elastic.co/cn/about/history-of-elasticsearch">ref1</a>, <a href="https://www.elastic.co/elk-stack">ref2</a>, <a href="https://www.elastic.co/cn/blog/elastic-stack-5-0-0-released">ref3</a> ]。</p>
+<h1 id="使用-Logstash">使用 Logstash</h1>
+<p>Logstash（<a href="https://www.elastic.co/cn/products/logstash">home</a>, <a href="https://github.com/elastic/logstash">github</a>）最初是来自 Dreamhost 运维工程师 Jordan Sissel 的开源项目，是管理事件和日志的工具，能够用于采集数据，转换数据，然后将数据发送到您最喜欢的“存储库”中（比如 Elasticsearch）。Logstash 使用 JRuby 开发，2011 年 5 月发布 1.0 版本。2013 年 8 月 Jordan Sissel 带着 Logstash 加入 Elasticsearch 公司，Logstash 成为 Elastic Stack 一员。</p>
+<p>在 Ubuntu 下<a href="https://www.elastic.co/guide/en/logstash/6.5/installing-logstash.html">安装</a>、<a href="https://www.elastic.co/guide/en/logstash/6.5/running-logstash.html">启动</a> Logstash 可以使用下面命令：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo apt-get install logstash                <span class="comment"># 安装 logstash</span></span><br><span class="line">$ sudo systemctl start logstash.service        <span class="comment"># 系统服务方式启动 logstash</span></span><br><span class="line">$ /usr/share/logstash/bin/logstash --version   <span class="comment"># 查看 logstash 版本</span></span><br><span class="line">logstash 6.5.4</span><br><span class="line">$ sudo vim /etc/logstash/logstash.yml          <span class="comment"># 查看默认 logstash.yml</span></span><br><span class="line">$ sudo vim /etc/logstash/logstash-sample.conf  <span class="comment"># 查看示例 logstash-sample.conf</span></span><br></pre></td></tr></table></figure>
+<p>安装完成后，二进制文件在 <code>/usr/share/logstash/bin</code> 目录下，配置文件位于 <code>/etc/logstash</code> 目录，日志输出位于 <code>/var/log/logstash</code> 目录，其他详细的目录位置的分布情况，可以阅读<a href="https://www.elastic.co/guide/en/logstash/6.5/dir-layout.html">官方文档</a>。</p>
+<h2 id="最简单的示例">最简单的示例</h2>
+<p>Logstash 管道（pipeline）由 <code>input</code>、<code>filter</code> 和 <code>output</code> 三个元素组成，其中 <code>input</code> 和 <code>output</code> 必须设置，而 <code>filter</code> 可选。<code>input</code> 插件从数据源中消费数据，<code>filter</code> 插件按指定方式修改数据，<code>output</code> 插件将数据写入特定目标中 [ <a href="https://www.elastic.co/guide/en/logstash/6.5/first-event.html">doc</a> ]。</p>
+<img width="600" alt="Logstash 管道" title="Logstash 管道" src="https://static.nullwy.me/basic_logstash_pipeline.png">
+<p>现在来试试 Logstash 下 Hello Wolrd 级别的示例，运行下面命令：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -e <span class="string">&#x27;input &#123; stdin &#123; &#125; &#125; output &#123; stdout &#123;&#125; &#125;&#x27;</span></span><br></pre></td></tr></table></figure>
+<p><code>-e</code> 选项能够使 Logstash 直接在<a href="https://www.elastic.co/guide/en/logstash/6.5/running-logstash-command-line.html">命令行</a>中设置管道配置。示例中 <code>input</code> 插件为 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-inputs-stdin.html">stdin</a> （标准输入），<code>output</code> 插件是 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-outputs-stdout.html">stdout</a> （标准输出）。若在控制台输入 <code>hello world</code>，相应的控制台将输出：</p>
+<figure class="highlight json"><table><tr><td class="code"><pre><span class="line"><span class="punctuation">&#123;</span></span><br><span class="line">      <span class="string">&quot;@version&quot;</span> =&gt; <span class="string">&quot;1&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;host&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;@timestamp&quot;</span> =&gt; <span class="number">2019</span><span class="number">-01</span><span class="number">-12</span>T05<span class="punctuation">:</span><span class="number">52</span><span class="punctuation">:</span><span class="number">56.291</span>Z<span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;message&quot;</span> =&gt; <span class="string">&quot;hello world&quot;</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
+<p>值得注意的是，输出内容编码格式默认为 <code>rubydebug</code>，使用 Ruby 的 &quot;<a href="https://github.com/awesome-print/awesome_print">awesome_print</a>&quot; 库打印。另外，响应输出 <code>@timestamp</code> 字段的值为 <code>2019-01-12T05:52:56.291Z</code>，这是 <a href="https://en.wikipedia.org/wiki/ISO_8601">ISO 8601</a> 时间格式，时区是 0（zero），和北京时间相差 8 个小时。</p>
+<p>输出内容编码格式，可以通过 <code>codec</code> 指令指定。除了默认的 <code>rubydebug</code> 外，官方还支持其他 20 多种编码格式，参见 <a href="https://www.elastic.co/guide/en/logstash/6.5/codec-plugins.html">doc</a>。若把编码格式改为 <code>json</code>，即 <code>stdout &#123; codec =&gt; json &#125;</code>，输出结果将变成：</p>
+<figure class="highlight json"><table><tr><td class="code"><pre><span class="line"><span class="punctuation">&#123;</span><span class="attr">&quot;message&quot;</span><span class="punctuation">:</span><span class="string">&quot;hello world&quot;</span><span class="punctuation">,</span><span class="attr">&quot;@version&quot;</span><span class="punctuation">:</span><span class="string">&quot;1&quot;</span><span class="punctuation">,</span><span class="attr">&quot;@timestamp&quot;</span><span class="punctuation">:</span><span class="string">&quot;2019-01-12T05:52:56.291Z&quot;</span><span class="punctuation">,</span><span class="attr">&quot;host&quot;</span><span class="punctuation">:</span><span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
+<p>管道配置也可以保存到文件中，以 <code>*.conf</code> 作为文件后缀，比如保存为 <code>test-stdin-stdout.conf</code>：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line">  stdin &#123; &#125;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  stdout &#123; &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>启动 logstash 时，<code>-f</code> 选项用于指定管道配置文件的路径：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -f ~/test-stdin-stdout.conf</span><br></pre></td></tr></table></figure>
+<p>默认情况下，在启动 logstash 后，若再修改管道配置文件，新的修改需要重启 logstash 才能加载生效。在开发调试时，不太方便。解决这个问题，可以使用 <code>-r</code> 命令行<a href="https://www.elastic.co/guide/en/logstash/6.5/running-logstash-command-line.html">选项</a>。开启这个选项后，只要确定配置文件已经发生变更，便会自动重新加载配置文件。</p>
+<h2 id="file-输入插件">file 输入插件</h2>
+<p>上文日志是控制台输入的，但真实情况日志在日志文件中，要想使用 Logstash 读取日志文件，官方提供了 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-inputs-file.html">file</a> 输入插件。管道配置文件示例 <code>test-file-stdout.conf</code>，如下：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line"> file &#123;</span><br><span class="line">   path =&gt; [&quot;/home/yulewei/test.log&quot;]</span><br><span class="line">   sincedb_path =&gt; &quot;/dev/null&quot;</span><br><span class="line">   start_position =&gt; &quot;beginning&quot;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">filter &#123;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  stdout &#123;</span><br><span class="line">    codec =&gt; rubydebug</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>启动 Logstash：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-file-stdout.conf</span><br></pre></td></tr></table></figure>
+<p>配置文件中的 <code>path</code> 指令用于指定日志文件的路径。<code>start_position</code> 指令设置 Logstash 启动时读取日志文件的位置，可以设置为 <code>beginning</code> 或者 <code>end</code>，默认是 <code>end</code>，即文件末尾。</p>
+<p>为了跟踪每个输入文件中已处理了哪些数据，Logstash 文件输入插件会使用名为 sincedb 的文件来记录现有位置。由于我们的配置用于开发，所以我们希望能够重复读取文件，并进而希望禁用 sincedb 文件。在 Linux 系统上，将 <code>sincedb_path</code> 指令设置为 “/dev/null” 即可禁用。若没有禁用，默认保存的 sincedb 文件将在 <code>/usr/share/logstash/data/plugins/inputs/file/</code> 目录下。</p>
+<h2 id="grok-过滤插件">grok 过滤插件</h2>
+<p>上文的例子，做的核心事情就是把日志行转换到 <code>message</code> 字段，并附加某些元数据，如 <code>@timestamp</code>。如果要想解析自己的日志，把非结构化日志转换结构换日志，有两个过滤器特别常用：<a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-filters-dissect.html">dissect</a> 会根据分界符来解析日志，而 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-filters-grok.html">grok</a> 则会根据正则表达式匹配来运行。</p>
+<p>如果数据结构定义非常完善，dissect 过滤插件的运行效果非常好，而且运行速度非常快捷高效。同时，其也更加容易上手，对于不熟悉正则表达式的用户而言，更是如此。通常而言，grok 的功能更加强大，而且可以处理各种各样的数据。然而，正则表达式匹配会耗费更多资源，而且速度也会慢一些，如果未能正确进行优化的话，尤为如此。</p>
+<p>现在先来看下 grok 过滤插件。grok 模式的基本语法是 <code>%&#123;SYNTAX:SEMANTIC&#125;</code>，<code>SYNTAX</code> 是用于匹配数据的模式（或正则表达式）名称，<code>SEMANTIC</code> 是标识符或字段名称。Logstash 提供了超过 120 种默认的 grok 模式，全部预定义的模式可以在 <a href="https://github.com/logstash-plugins/logstash-patterns-core/tree/master/patterns">github</a> 上找到。典型的预定义模式（非完整列表）[ <a href="https://github.com/logstash-plugins/logstash-patterns-core/blob/v4.1.2/patterns/grok-patterns">github</a> ]：</p>
+<ul>
+<li>WORD - 匹配单个词汇的模式</li>
+<li>NUMBER - 匹配整数或浮点数（正值或负值均可）的模式</li>
+<li>POSINT - 匹配正整数的模式</li>
+<li>EMAILADDRESS - 邮箱地址</li>
+<li>IP - 匹配 IPv4 或 IPv6 IP 地址的模式</li>
+<li>URI - URI 地址</li>
+<li>TIMESTAMP_ISO8601 - <a href="https://en.wikipedia.org/wiki/ISO_8601">ISO8601</a> 格式的时间</li>
+<li>NOTSPACE - 匹配非空格的任何内容的格式</li>
+<li>SPACE - 匹配任何数量的连续空格的模式</li>
+<li>DATA - 匹配任何数据类型的限定数量的模式</li>
+<li>GREEDYDATA - 匹配剩余所有数据的格式</li>
+</ul>
+<p>比如，<code>3.44</code> 可以使用 <code>NUMBER</code> 模式进行匹配，<code>192.168.2.104</code> 可以使用 <code>IP</code> 模式。<code>%&#123;NUMBER:num&#125; %&#123;IP:client&#125;</code> 模式，将会用 <code>NUMBER</code> 模式把 <code>3.44</code> 识别为 <code>num</code> 字段，用 <code>IP</code> 模式把 <code>192.168.2.104</code> 识别为 <code>client</code> 字段。默认情况识别获得的字段值是字符串类型，grok 插件支持把类型转换为 <code>int</code> 或 <code>float</code>。要想把 <code>3.44</code> 转换为浮点数，可以使用 <code>%&#123;NUMBER:num:float&#125;</code>。</p>
+<p>假设有如下日志内容：</p>
+<figure class="highlight txt"><table><tr><td class="code"><pre><span class="line">Will, yulewei@gmail.com, 42, 1024, 3.14</span><br></pre></td></tr></table></figure>
+<p>grok 匹配表达式可以写成这样：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">%&#123;WORD:name&#125;, %&#123;EMAILADDRESS:email&#125;, %&#123;NUMBER:num1&#125;, %&#123;NUMBER:num2:int&#125;, %&#123;NUMBER:pi:float&#125;</span><br></pre></td></tr></table></figure>
+<p>即，在这一行日志中依次提取出，<code>name</code>、<code>email</code>、<code>num1</code>、<code>num2</code> 和 <code>pi</code> 字段。完整的 <code>filter</code> 过滤器配置的写法：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">filter &#123;</span><br><span class="line">  grok &#123;</span><br><span class="line">    match =&gt; &#123; &quot;message&quot; =&gt; &quot;%&#123;WORD:name&#125;, %&#123;EMAILADDRESS:email&#125;, %&#123;NUMBER:num1&#125;, %&#123;NUMBER:num2:int&#125;, %&#123;NUMBER:pi:float&#125;&quot; &#125;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>启动 logstash：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-file-grok-stdout.conf</span><br></pre></td></tr></table></figure>
+<p>控制台将输出：</p>
+<figure class="highlight json"><table><tr><td class="code"><pre><span class="line"><span class="punctuation">&#123;</span></span><br><span class="line">      <span class="string">&quot;@version&quot;</span> =&gt; <span class="string">&quot;1&quot;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;message&quot;</span> =&gt; <span class="string">&quot;Will, yulewei@gmail.com, 42, 1024, 3.14&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;num1&quot;</span> =&gt; <span class="string">&quot;42&quot;</span><span class="punctuation">,</span></span><br><span class="line">            <span class="string">&quot;pi&quot;</span> =&gt; <span class="number">3.14</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;@timestamp&quot;</span> =&gt; <span class="number">2019</span><span class="number">-01</span><span class="number">-12</span>T08<span class="punctuation">:</span><span class="number">12</span><span class="punctuation">:</span><span class="number">49.581</span>Z<span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;path&quot;</span> =&gt; <span class="string">&quot;/home/yulewei/test-grok.log&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;host&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;email&quot;</span> =&gt; <span class="string">&quot;yulewei@gmail.com&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;name&quot;</span> =&gt; <span class="string">&quot;Will&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;num2&quot;</span> =&gt; <span class="number">1024</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
+<p>Logstash 提供了超过 120 种默认的 grok 模式，基本上满足大多数使用场景。若没有符合要求的预定义的模式，可以使用 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-filters-grok.html#_regular_expressions">Oniguruma</a> 语法指定正则表达式：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">(?&lt;field_name&gt;the pattern here)</span><br></pre></td></tr></table></figure>
+<p>上文中的 <code>%&#123;WORD:name&#125;</code> 和 <code>%&#123;EMAILADDRESS:email&#125;</code>，等价的正则表达式的写法如下 [ <a href="https://github.com/logstash-plugins/logstash-patterns-core/blob/v4.1.2/patterns/grok-patterns">ref1</a>, <a href="https://stackoverflow.com/a/8829363">ref2</a> ]：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">(?&lt;name&gt;\w+)</span><br><span class="line">(?&lt;email&gt;[a-zA-Z][a-zA-Z0-9_.+-=:]+@[0-9A-Za-z][0-9A-Za-z-]&#123;0,62&#125;\.[0-9A-Za-z][0-9A-Za-z-]&#123;0,62&#125;)</span><br></pre></td></tr></table></figure>
+<p>调试 grok 匹配表达式容易出错，官方提供可视化的 <a href="https://www.elastic.co/guide/en/kibana/6.5/grokdebugger-getting-started.html">Grok Debugger</a> 工具，提高调试效率。</p>
+<img width="800" alt="Grok Debugger" title="Grok Debugger" src="https://static.nullwy.me/kibana-grokdebugger.png">
+<h3 id="解析-http-服务器日志">解析 http 服务器日志</h3>
+<p>现在来看下，真实的日志解析案例，使用 grok 过滤插件解析 http 服务器日志。通用日志格式（<a href="https://en.wikipedia.org/wiki/Common_Log_Format">Common Log Format</a>），是 http 服务器的标准的日志格式。对通用日志格式扩展，加上额外的 referer 和 user-agent 字段，称为组合日志格式（Combined Log Format）。两种日志格式包含的字段如下：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line"># 通用日志格式</span><br><span class="line">%remote-host %ident %authuser %timestamp &quot;%request&quot; %status %bytes</span><br><span class="line"># 组合日志格式</span><br><span class="line">%remote-host %ident %authuser %timestamp &quot;%request&quot; %status %bytes &quot;%referer&quot; &quot;%user-agent&quot;</span><br></pre></td></tr></table></figure>
+<p><a href="https://httpd.apache.org/docs/2.4/logs.html#accesslog">Apache</a> 和 <a href="https://nginx.org/en/docs/http/ngx_http_log_module.html#log_format">Nginx</a> 服务器默认的日志格式，采用的就是通用日志格式或者组合日志格式。解析这两种日志格式，Logstash 提供预定义模式 <a href="https://github.com/logstash-plugins/logstash-patterns-core/blob/v4.1.2/patterns/httpd#L14">COMMONAPACHELOG</a> 和 <a href="https://github.com/logstash-plugins/logstash-patterns-core/blob/v4.1.2/patterns/httpd#L15">COMBINEDAPACHELOG</a>。</p>
+<p>典型的 nginx 日志例子：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">192.168.2.104 - - [13/Jan/2019:02:01:15 +0800] &quot;GET /images/avatar.png HTTP/1.1&quot; 200 266975 &quot;-&quot; &quot;Mozilla/5.0 (Macintosh; Intel Mac OS X 10.13; rv:64.0) Gecko/20100101 Firefox/64.0&quot;</span><br></pre></td></tr></table></figure>
+<p>管道配置文件示例 <code>test-file-grokhttp-stdout.conf</code>，如下：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line">  file &#123;</span><br><span class="line">    path =&gt; [&quot;/var/log/nginx/access.log&quot;]</span><br><span class="line">    sincedb_path =&gt; &quot;/dev/null&quot;</span><br><span class="line">    start_position =&gt; &quot;beginning&quot;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">filter &#123;</span><br><span class="line">  grok &#123;</span><br><span class="line">    match =&gt; &#123; &quot;message&quot; =&gt; &quot;%&#123;COMBINEDAPACHELOG&#125;&quot; &#125;</span><br><span class="line">    remove_field =&gt; [&quot;message&quot;]</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  stdout &#123; &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>示例中使用了 grok 的预定义模式 <a href="https://github.com/logstash-plugins/logstash-patterns-core/blob/v4.1.2/patterns/httpd#L15">COMBINEDAPACHELOG</a>。另外，<code>remove_field</code> <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-filters-grok.html#plugins-filters-grok-remove_field">指令</a>用于把输出事件中某字段删除，示例中是 <code>message</code> 字段。</p>
+<p>启动 logstash：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-file-grokhttp-stdout.conf</span><br></pre></td></tr></table></figure>
+<p>解析获得的结构化数据，如下：</p>
+<figure class="highlight json"><table><tr><td class="code"><pre><span class="line"><span class="punctuation">&#123;</span></span><br><span class="line">           <span class="string">&quot;auth&quot;</span> =&gt; <span class="string">&quot;-&quot;</span><span class="punctuation">,</span></span><br><span class="line">           <span class="string">&quot;host&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">,</span></span><br><span class="line">           <span class="string">&quot;verb&quot;</span> =&gt; <span class="string">&quot;GET&quot;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;clientip&quot;</span> =&gt; <span class="string">&quot;192.168.2.104&quot;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;@version&quot;</span> =&gt; <span class="string">&quot;1&quot;</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;httpversion&quot;</span> =&gt; <span class="string">&quot;1.1&quot;</span><span class="punctuation">,</span></span><br><span class="line">     <span class="string">&quot;@timestamp&quot;</span> =&gt; <span class="number">2019</span><span class="number">-01</span><span class="number">-13</span>T13<span class="punctuation">:</span><span class="number">35</span><span class="punctuation">:</span><span class="number">52.983</span>Z<span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;bytes&quot;</span> =&gt; <span class="string">&quot;266975&quot;</span><span class="punctuation">,</span></span><br><span class="line">      <span class="string">&quot;timestamp&quot;</span> =&gt; <span class="string">&quot;13/Jan/2019:02:01:15 +0800&quot;</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;request&quot;</span> =&gt; <span class="string">&quot;/images/avatar.png&quot;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;response&quot;</span> =&gt; <span class="string">&quot;200&quot;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;referrer&quot;</span> =&gt; <span class="string">&quot;\&quot;-\&quot;&quot;</span><span class="punctuation">,</span></span><br><span class="line">           <span class="string">&quot;path&quot;</span> =&gt; <span class="string">&quot;/var/log/nginx/access.log&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;agent&quot;</span> =&gt; <span class="string">&quot;\&quot;Mozilla/5.0 (Macintosh; Intel Mac OS X 10.13; rv:64.0) Gecko/20100101 Firefox/64.0\&quot;&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;ident&quot;</span> =&gt; <span class="string">&quot;-&quot;</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
+<h2 id="dissect-过滤插件">dissect 过滤插件</h2>
+<p>和 grok 过滤插件使用正则表达式提取字段不同，dissect 过滤插件使用分界符切割来提取字段。由于没有使用正则表达式，运行速度相对 grok 快很多。使用 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-filters-dissect.html">dissect</a> 过滤插件时，需要指明提取字段的顺序，还要指明这些字段之间的分界符。过滤插件会对数据进行单次传输，并匹配模式中的分界符。同时，过滤插件还会将分界符之间的数据分配至指定字段。过滤插件不会对所提取数据的格式进行验证。</p>
+<p>现在看下示例，<code>test-dissect.log</code> 文件内容如下：</p>
+<figure class="highlight txt"><table><tr><td class="code"><pre><span class="line">Will, yulewei@gmail.com, 42, 1024, 3.14</span><br></pre></td></tr></table></figure>
+<p>dissect 匹配规则可以写成这样：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">%&#123;name&#125;, %&#123;email&#125;, %&#123;num1&#125;, %&#123;num2&#125;, %&#123;num3&#125;</span><br></pre></td></tr></table></figure>
+<p>完整的配置文件，<code>test-file-dissect-stdout.conf</code>：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line"> file &#123;</span><br><span class="line">   path =&gt; [&quot;/home/yulewei/test-dissect.log&quot;]</span><br><span class="line">   sincedb_path =&gt; &quot;/dev/null&quot;</span><br><span class="line">   start_position =&gt; &quot;beginning&quot;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">filter &#123;</span><br><span class="line">  dissect &#123;</span><br><span class="line">    mapping =&gt; &#123;</span><br><span class="line">      &quot;message&quot; =&gt; &quot;%&#123;name&#125;, %&#123;email&#125;, %&#123;num1&#125;, %&#123;num2&#125;, %&#123;num3&#125;&quot;</span><br><span class="line">    &#125;</span><br><span class="line">    convert_datatype =&gt; &#123;</span><br><span class="line">      &quot;num2&quot; =&gt; &quot;int&quot;</span><br><span class="line">      &quot;num3&quot; =&gt; &quot;float&quot;</span><br><span class="line">    &#125;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  stdout &#123; &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>和 grok 插件一样，默认提取的字段是字符串类型。配置文件中的 <code>convert_datatype</code> 指令用于将类型转为 <code>int</code> 或 <code>float</code>。</p>
+<p>启动 logstash：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-file-dissect-stdout.conf</span><br></pre></td></tr></table></figure>
+<p>输出结果：</p>
+<figure class="highlight json"><table><tr><td class="code"><pre><span class="line"><span class="punctuation">&#123;</span></span><br><span class="line">          <span class="string">&quot;host&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;num1&quot;</span> =&gt; <span class="string">&quot;42&quot;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;message&quot;</span> =&gt; <span class="string">&quot;Will, yulewei@gmail.com, 42, 1024, 3.14&quot;</span><span class="punctuation">,</span></span><br><span class="line">      <span class="string">&quot;@version&quot;</span> =&gt; <span class="string">&quot;1&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;name&quot;</span> =&gt; <span class="string">&quot;Will&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;num2&quot;</span> =&gt; <span class="number">1024</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;@timestamp&quot;</span> =&gt; <span class="number">2019</span><span class="number">-01</span><span class="number">-13</span>T13<span class="punctuation">:</span><span class="number">32</span><span class="punctuation">:</span><span class="number">10.900</span>Z<span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;path&quot;</span> =&gt; <span class="string">&quot;/home/yulewei/test-dissect.log&quot;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;email&quot;</span> =&gt; <span class="string">&quot;yulewei@gmail.com&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;num3&quot;</span> =&gt; <span class="number">3.14</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
+<h1 id="输出到-Elasticsearch">输出到 Elasticsearch</h1>
+<p>上文举的例子全部都是，输出控制台，使用 <code>stdout</code> 输出插件，没有实用价值。Elastic Stack 的核心其实是 Elasticsearch，使用Elasticsearch 搜索和分析日志。想要将数据发送到 Elasticsearch，可以使用 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-outputs-elasticsearch.html">elasticsearch</a> 输出插件。</p>
+<h2 id="安装-Elasticsearch">安装 Elasticsearch</h2>
+<p>如果没有安装 Elasticsearch，参考<a href="https://www.elastic.co/guide/en/elasticsearch/reference/6.5/deb.html">官方文档</a>按步骤安装。唯一要注意的是，在执行 <code>apt install</code> 命令前，必须先添加 elastic 的软件源地址，否则无法正常启动。核心命令如下：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo apt-get install elasticsearch           <span class="comment"># 安装 elasticsearch</span></span><br><span class="line">$ sudo systemctl start elasticsearch.service   <span class="comment"># 系统服务方式启动 elasticsearch</span></span><br><span class="line">$ curl http://localhost:9200/                  <span class="comment"># 用 rest 接口查看 elasticsearch</span></span><br><span class="line">&#123;</span><br><span class="line">  <span class="string">&quot;name&quot;</span> : <span class="string">&quot;1t9JXt5&quot;</span>,</span><br><span class="line">  <span class="string">&quot;cluster_name&quot;</span> : <span class="string">&quot;elasticsearch&quot;</span>,</span><br><span class="line">  <span class="string">&quot;cluster_uuid&quot;</span> : <span class="string">&quot;yQgVsvupSqGCGQbwqnanIg&quot;</span>,</span><br><span class="line">  <span class="string">&quot;version&quot;</span> : &#123;</span><br><span class="line">    <span class="string">&quot;number&quot;</span> : <span class="string">&quot;6.5.4&quot;</span>,</span><br><span class="line">    <span class="string">&quot;build_flavor&quot;</span> : <span class="string">&quot;default&quot;</span>,</span><br><span class="line">    <span class="string">&quot;build_type&quot;</span> : <span class="string">&quot;deb&quot;</span>,</span><br><span class="line">    <span class="string">&quot;build_hash&quot;</span> : <span class="string">&quot;d2ef93d&quot;</span>,</span><br><span class="line">    <span class="string">&quot;build_date&quot;</span> : <span class="string">&quot;2018-12-17T21:17:40.758843Z&quot;</span>,</span><br><span class="line">    <span class="string">&quot;build_snapshot&quot;</span> : <span class="literal">false</span>,</span><br><span class="line">    <span class="string">&quot;lucene_version&quot;</span> : <span class="string">&quot;7.5.0&quot;</span>,</span><br><span class="line">    <span class="string">&quot;minimum_wire_compatibility_version&quot;</span> : <span class="string">&quot;5.6.0&quot;</span>,</span><br><span class="line">    <span class="string">&quot;minimum_index_compatibility_version&quot;</span> : <span class="string">&quot;5.0.0&quot;</span></span><br><span class="line">  &#125;,</span><br><span class="line">  <span class="string">&quot;tagline&quot;</span> : <span class="string">&quot;You Know, for Search&quot;</span></span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>默认情况下 elasticsearch 服务器绑定的 ip 地址是回环地址 <code>127.0.0.1</code>，若想绑定特定 ip 地址，可以修改 <code>/etc/elasticsearch/elasticsearch.yml</code> 配置文件中的 <a href="https://www.elastic.co/guide/en/elasticsearch/reference/6.5/network.host.html">network.host</a> 选项：</p>
+<figure class="highlight yml"><table><tr><td class="code"><pre><span class="line"><span class="attr">network.host:</span> <span class="number">192.168</span><span class="number">.2</span><span class="number">.109</span></span><br></pre></td></tr></table></figure>
+<p>修改完成并重启后，elasticsearch 服务器访问地址从 <code>http://localhost:9200/</code> 变成 <code>http://192.168.2.109:9200/</code>。</p>
+<h2 id="输出到-Elasticsearch-v2">输出到 Elasticsearch</h2>
+<p>现在来看下 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-outputs-elasticsearch.html">elasticsearch</a> 输出插件。示例，<code>test-file-elasticsearch.conf</code>：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line"> file &#123;</span><br><span class="line">   path =&gt; [&quot;/home/yulewei/test.log&quot;]</span><br><span class="line">   sincedb_path =&gt; &quot;/dev/null&quot;</span><br><span class="line">   start_position =&gt; &quot;beginning&quot;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  elasticsearch &#123;</span><br><span class="line">    hosts =&gt; [&quot;http://192.168.2.109:9200&quot;]</span><br><span class="line">    index =&gt; &quot;logstash-%&#123;+YYYY.MM.dd&#125;&quot;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>示例的 <code>elasticsearch</code> 输出插件使用了 <code>hosts</code> 和 <code>index</code> 指令。<code>hosts</code> 指令，用于指定 elasticsearch 服务器的地址。而 <code>index</code> 指令，用于指定 elasticsearch 索引的名称模式，该指令默认值为 <code>logstash-%&#123;+YYYY.MM.dd&#125;</code>。在字符串内部的 <code>%&#123;...&#125;</code>，是 Logstash 字符串插值语法，官方称之为 <code>sprintf format</code> [ <a href="https://www.elastic.co/guide/en/logstash/6.5/event-dependent-configuration.html">doc</a> ]。<code>+YYYY.MM.dd</code>，用于指定 <code>@timestamp</code> 的格式化的格式。<code>logstash-%&#123;+YYYY.MM.dd&#125;</code>，格式化后最终生成的值可能将是 <code>logstash-2019.01.13</code>。</p>
+<p>启动 logstash：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-file-elasticsearch.conf</span><br></pre></td></tr></table></figure>
+<p>查看在 elasticsearch 上新创建的 <code>logstash-*</code> 索引以及从 logstash 同步过来的日志数据：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ curl http://192.168.2.109:9200/_cat/indices</span><br><span class="line">yellow open logstash-2019.01.13       tFjc5xL_QYeNw4oqe4odeg 5 1     3 0 15.5kb 15.5kb</span><br><span class="line">$ curl <span class="string">&#x27;http://192.168.2.109:9200/logstash-*/_search?pretty&#x27;</span> -H <span class="string">&#x27;Content-Type: application/json&#x27;</span> -d<span class="string">&#x27;&#123;&quot;size&quot;: 1&#125;&#x27;</span></span><br><span class="line">&#123;</span><br><span class="line">  <span class="string">&quot;took&quot;</span> : 0,</span><br><span class="line">  <span class="string">&quot;timed_out&quot;</span> : <span class="literal">false</span>,</span><br><span class="line">  <span class="string">&quot;_shards&quot;</span> : &#123;</span><br><span class="line">    <span class="string">&quot;total&quot;</span> : 5,</span><br><span class="line">    <span class="string">&quot;successful&quot;</span> : 5,</span><br><span class="line">    <span class="string">&quot;skipped&quot;</span> : 0,</span><br><span class="line">    <span class="string">&quot;failed&quot;</span> : 0</span><br><span class="line">  &#125;,</span><br><span class="line">  <span class="string">&quot;hits&quot;</span> : &#123;</span><br><span class="line">    <span class="string">&quot;total&quot;</span> : 3,</span><br><span class="line">    <span class="string">&quot;max_score&quot;</span> : 1.0,</span><br><span class="line">    <span class="string">&quot;hits&quot;</span> : [</span><br><span class="line">      &#123;</span><br><span class="line">        <span class="string">&quot;_index&quot;</span> : <span class="string">&quot;logstash-2019.01.13&quot;</span>,</span><br><span class="line">        <span class="string">&quot;_type&quot;</span> : <span class="string">&quot;doc&quot;</span>,</span><br><span class="line">        <span class="string">&quot;_id&quot;</span> : <span class="string">&quot;RUHNRWgBLIBntI4FV8Rf&quot;</span>,</span><br><span class="line">        <span class="string">&quot;_score&quot;</span> : 1.0,</span><br><span class="line">        <span class="string">&quot;_source&quot;</span> : &#123;</span><br><span class="line">          <span class="string">&quot;path&quot;</span> : <span class="string">&quot;/home/yulewei/test.log&quot;</span>,</span><br><span class="line">          <span class="string">&quot;@timestamp&quot;</span> : <span class="string">&quot;2019-01-13T06:01:51.303Z&quot;</span>,</span><br><span class="line">          <span class="string">&quot;@version&quot;</span> : <span class="string">&quot;1&quot;</span>,</span><br><span class="line">          <span class="string">&quot;host&quot;</span> : <span class="string">&quot;ubuntu109&quot;</span>,</span><br><span class="line">          <span class="string">&quot;message&quot;</span> : <span class="string">&quot;hello world&quot;</span></span><br><span class="line">        &#125;</span><br><span class="line">      &#125;</span><br><span class="line">    ]</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>可以看到，新的索引名为 <code>logstash-2019.01.13</code>。同步过来的日志记录全部有 5 条，第 1 条日志的 <code>message</code> 内容是 <code>hello world</code>。</p>
+<h2 id="使用-Kibana">使用 Kibana</h2>
+<p>Kibana，能够对 Elasticsearch 中的数据进行可视化，是 Elastic Stack 的窗口。在 Ubuntu 下<a href="https://www.elastic.co/guide/en/kibana/6.5/deb.html">安装</a> Kibana 可以使用下面命令：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo apt-get install kibana          <span class="comment"># 安装 kibana，当前最新版为 6.5.4</span></span><br><span class="line">$ sudo systemctl start kibana.service  <span class="comment"># 系统服务方式启动 kibana</span></span><br></pre></td></tr></table></figure>
+<p>默认配置下，kibana 服务访问地址是 <code>http://localhost:5601/</code>，连接的 elasticsearch 地址是 <code>http://localhost:9200</code>，这两个配置分别由 <code>server.host</code> 和 <code>elasticsearch.url</code> 控制 [ <a href="https://www.elastic.co/guide/en/kibana/6.5/settings.html">doc</a> ]。上文尝试过把 elasticsearch 服务 ip 地址绑定到 <code>192.168.2.109</code>。现在来试下绑定 ip 地址到 kibana，编辑配置文件 <code>/etc/kibana/kibana.yml</code>，修改为：</p>
+<figure class="highlight yml"><table><tr><td class="code"><pre><span class="line"><span class="attr">server.host:</span> <span class="string">&quot;192.168.2.109&quot;</span></span><br><span class="line"><span class="attr">elasticsearch.url:</span> <span class="string">&quot;http://192.168.2.109:9200&quot;</span></span><br></pre></td></tr></table></figure>
+<p>使用 <code>sudo systemctl restart kibana.service</code> 重启后，kibana 服务访问地址变成 <code>http://192.168.2.109:5601/</code>。</p>
+<p>elasticsearch 服务器上存在索引 <code>logstash-2019.01.13</code>，要想把这个索引导入到 kibana，参考官方<a href="https://www.elastic.co/guide/en/kibana/6.5/tutorial-define-index.html">教程</a>即可。点击 <code>Management</code> 菜单，然后创建索引模式（index pattern）。索引模式可以直接为 <code>logstash-2019.01.13</code>，这样匹配单个索引。若要匹配多个时间的 logstash 索引，可以使用通配符 <code>*</code>，比如 <code>logstash-*</code>。如果要匹配全部 2019 年 01 月的索引，可以写成 <code>logstash-2019.01*</code>。完成索引模式定义后，便可以在 <code>Discover</code> 菜单下查看索引，如图：</p>
+<img width="800" alt="Kibana" title="Kibana" src="https://static.nullwy.me/logstash-kibana.png">
+<h1 id="使用-Filebeat">使用 Filebeat</h1>
+<p>Filebeat，轻量型日志采集器 [ <a href="https://www.elastic.co/cn/products/beats/filebeat">home</a> ]。其前身是由 Logstash 作者 Jordan Sissel 开发的 <a href="https://github.com/elastic/logstash-forwarder">Logstash Forwarder</a>。Logstash Forwarder 项目因为和收购过来的 Packetbeat 项目功能相近，并且都是 Go 语言开发，就一起被整合改造为 Beats [ <a href="https://www.elastic.co/blog/beats-1-0-0">ref</a> ]。</p>
+<p>我们知道，Logstash 使用 JRuby 开发，运行依赖 JVM，会消耗较多的系统资源。为了减少系统资源（CPU、内存和网络）的使用，Logstash Forwarder 改用 Go 语言开发。另外，在功能上也做了精简，只做单一的数据传输，不像 Logstash 有数据过滤能力。Logstash 类似于功能多样的“瑞士军刀”，能提供从多个数据源加载数据的功能，使用各种强大的插件来处理日志，并提供将多个来源的输出数据进行存储的功能。简而言之，Logstash 提供数据 ETL（数据的提取、变换和加载）的功能；而 Beats 是轻量级的数据传输工具，能将数据传输到 Logstash 或 Elasticsearch 中，其间没有对数据进行任何转换 [ <a href="https://book.douban.com/subject/30326542/">Gupta2017</a> ]。Filebeat 和 Logstash 的关系如下图所示 [ <a href="https://logz.io/blog/filebeat-vs-logstash/">logz.io</a> ]：</p>
+<img width="600" alt="Filebeat 和 Logstash 的关系" title="Filebeat 和 Logstash 的关系" src="https://static.nullwy.me/filebeat-and-logstash.png">
+<p>安装 filebeat 很简单，参考<a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/setup-repositories.html">官方文档</a>即可，核心命令如下：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo apt-get install filebeat           <span class="comment"># 安装 filebeat</span></span><br><span class="line">$ filebeat version                        <span class="comment"># 查看 filebeat 版本</span></span><br><span class="line">filebeat version 6.5.4 (amd64), libbeat 6.5.4 [bd8922f1c7e93d12b07e0b3f7d349e17107f7826 built 2018-12-17 20:22:29 +0000 UTC]</span><br><span class="line">$ sudo systemctl start filebeat.service   <span class="comment"># 系统服务方式启动 filebeat</span></span><br></pre></td></tr></table></figure>
+<h2 id="输出到-Elasticsearch-v3">输出到 Elasticsearch</h2>
+<p>修改 filebeat 配置文件 /etc/filebeat/<a href="https://github.com/elastic/beats/blob/6.5/filebeat/filebeat.yml">filebeat.yml</a>，示例如下：</p>
+<figure class="highlight yml"><table><tr><td class="code"><pre><span class="line"><span class="attr">filebeat.inputs:</span></span><br><span class="line"><span class="bullet">-</span> <span class="attr">type:</span> <span class="string">log</span></span><br><span class="line">  <span class="attr">paths:</span></span><br><span class="line">    <span class="bullet">-</span> <span class="string">/home/yulewei/test.log</span></span><br><span class="line"></span><br><span class="line"><span class="attr">output.elasticsearch:</span></span><br><span class="line">  <span class="attr">hosts:</span> [<span class="string">&quot;192.168.2.109:9200&quot;</span>]</span><br></pre></td></tr></table></figure>
+<p><code>filebeat.inputs</code> 选项用于配置日志的<a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/configuration-filebeat-options.html">输入方式</a>。子选项 <code>type</code> <a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/configuration-filebeat-options.html#filebeat-input-types">支持</a> <code>log</code>、<code>stdin</code>、<code>redis</code>、<code>udp</code>、<code>tcp</code> 等，示例中使用了 <code>log</code>，表明从日志文件输入。</p>
+<p><code>output</code> 选项用于配置日志的<a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/configuring-output.html">输出方式</a>，配置支持 elasticsearch、logstash、kafka、redis、file、console 等，一次只能选择配置其中某一个。示例配置了 <code>output.elasticsearch.hosts</code>，指定日志输出目标 elasticsearch 的主机地址。<code>output.elasticsearch.index</code> 可以用来指定索引 index 名称模式，默认是 <code>filebeat-%&#123;[beat.version]&#125;-%&#123;+yyyy.MM.dd&#125;</code>（比如 <code>filebeat-6.5.4-2019.01.12</code>）[ <a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/elasticsearch-output.html#index-option-es">doc</a> ]。</p>
+<p>完成 <code>filebeat.yml</code> 修改后，重启 filebeat，将可以看到，在 elasticsearch 上新创建的 <code>filebeat-*</code> 索引：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ curl http://192.168.2.109:9200/_cat/indices</span><br><span class="line">yellow open filebeat-6.5.4-2019.01.12 B4JbQDnZQuK5XvsQ77uedA 3 1 11043 0  1.7mb  1.7mb</span><br></pre></td></tr></table></figure>
+<h2 id="输出到-Logstash">输出到 Logstash</h2>
+<p>上文的示例直接把 Filebeat 采集的日志传输到 Elasticsearch，日志数据并没有被解析或者转换。若想解析和转换日志，需要在Filebeat 和 Elasticsearch 中间引入 Logstash。现在看下把日志输出到 Logstash 的示例配置文件，<code>filebeat.yml</code> 示例：</p>
+<figure class="highlight yml"><table><tr><td class="code"><pre><span class="line"><span class="attr">filebeat.inputs:</span></span><br><span class="line"><span class="bullet">-</span> <span class="attr">type:</span> <span class="string">log</span></span><br><span class="line">  <span class="attr">paths:</span></span><br><span class="line">    <span class="bullet">-</span> <span class="string">/home/yulewei/test.log</span></span><br><span class="line"></span><br><span class="line"><span class="attr">output.logstash:</span></span><br><span class="line">  <span class="attr">hosts:</span> [<span class="string">&quot;localhost:5044&quot;</span>]</span><br></pre></td></tr></table></figure>
+<p><code>filebeat.inputs</code> 和上文的示例一样。不同的是，把 <code>output.elasticsearch.hosts</code> 改成了 <code>output.logstash.hosts</code>，指定日志输出目标 <a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/logstash-output.html">Logstash</a> 的主机地址。<code>5044</code> 这个端口是 Logstash 用于监听 Filebeat 的端口。</p>
+<p>现在来看下 Logstash 的管道配置文件，示例 <code>test-beats-stdout.conf</code>：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line">  beats &#123;</span><br><span class="line">    port =&gt; 5044</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  stdout &#123;</span><br><span class="line">    codec =&gt; rubydebug</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>示例中，使用了 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-inputs-beats.html">beats</a> 输入插件，配置的端口就 <code>filebeat.yml</code> 中指定的 <code>5044</code>。输出插件为 <code>stdout</code>，即把 Logstash 采集到日志输出到控制台。</p>
+<p>重启 filebeat 和 logstash：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ <span class="built_in">cat</span> test.log                              <span class="comment"># 查看日志文件内容</span></span><br><span class="line">hello world</span><br><span class="line">$ sudo systemctl restart filebeat.service   <span class="comment"># 重启 filebeat</span></span><br><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-beats-stdout.conf</span><br></pre></td></tr></table></figure>
+<p>控制台输出：</p>
+<figure class="highlight json"><table><tr><td class="code"><pre><span class="line"><span class="punctuation">&#123;</span></span><br><span class="line">          <span class="string">&quot;tags&quot;</span> =&gt; <span class="punctuation">[</span></span><br><span class="line">        <span class="punctuation">[</span><span class="number">0</span><span class="punctuation">]</span> <span class="string">&quot;beats_input_codec_plain_applied&quot;</span></span><br><span class="line">    <span class="punctuation">]</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;source&quot;</span> =&gt; <span class="string">&quot;/home/yulewei/test.log&quot;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;input&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;type&quot;</span> =&gt; <span class="string">&quot;log&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;message&quot;</span> =&gt; <span class="string">&quot;hello world&quot;</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;@timestamp&quot;</span> =&gt; <span class="number">2019</span><span class="number">-01</span><span class="number">-12</span>T13<span class="punctuation">:</span><span class="number">32</span><span class="punctuation">:</span><span class="number">05.131</span>Z<span class="punctuation">,</span></span><br><span class="line">      <span class="string">&quot;@version&quot;</span> =&gt; <span class="string">&quot;1&quot;</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;prospector&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;type&quot;</span> =&gt; <span class="string">&quot;log&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;beat&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;hostname&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;version&quot;</span> =&gt; <span class="string">&quot;6.5.4&quot;</span><span class="punctuation">,</span></span><br><span class="line">            <span class="string">&quot;name&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;offset&quot;</span> =&gt; <span class="number">0</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;host&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">                   <span class="string">&quot;os&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">             <span class="string">&quot;version&quot;</span> =&gt; <span class="string">&quot;16.04.4 LTS (Xenial Xerus)&quot;</span><span class="punctuation">,</span></span><br><span class="line">            <span class="string">&quot;platform&quot;</span> =&gt; <span class="string">&quot;ubuntu&quot;</span><span class="punctuation">,</span></span><br><span class="line">            <span class="string">&quot;codename&quot;</span> =&gt; <span class="string">&quot;xenial&quot;</span><span class="punctuation">,</span></span><br><span class="line">              <span class="string">&quot;family&quot;</span> =&gt; <span class="string">&quot;debian&quot;</span></span><br><span class="line">        <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;architecture&quot;</span> =&gt; <span class="string">&quot;x86_64&quot;</span><span class="punctuation">,</span></span><br><span class="line">                   <span class="string">&quot;id&quot;</span> =&gt; <span class="string">&quot;29b1bf39547d4ca9ae26c3b7656ff9e3&quot;</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;containerized&quot;</span> =&gt; <span class="literal"><span class="keyword">false</span></span><span class="punctuation">,</span></span><br><span class="line">                 <span class="string">&quot;name&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
+<h1 id="集成-Filebeat-Logstash-Elasticsearch-Kibana">集成 Filebeat, Logstash, Elasticsearch, Kibana</h1>
+<p>真实场景下，日志文件可能分布在多台服务器上，同一台服务器上也可能分布着不同来源类型的日志。现在我们来尝试下，使用 Filebeat 把两个日志文件各自采集到两个不同的 Elasticsearch 索引中，并用 Kibana 可视化。有两个日志文件 <code>test-beats1.log</code> 和 <code>test-beats2.log</code>，内容如下：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ <span class="built_in">cat</span> test-beats1.log</span><br><span class="line">hello world1</span><br><span class="line">hello world1</span><br><span class="line">$ <span class="built_in">cat</span> test-beats2.log</span><br><span class="line">hello world2</span><br></pre></td></tr></table></figure>
+<p><code>filebeat.yml</code> 配置示例：</p>
+<figure class="highlight yml"><table><tr><td class="code"><pre><span class="line"><span class="attr">filebeat.inputs:</span></span><br><span class="line"><span class="bullet">-</span> <span class="attr">type:</span> <span class="string">log</span></span><br><span class="line">  <span class="attr">paths:</span></span><br><span class="line">    <span class="bullet">-</span> <span class="string">/home/yulewei/test-beats1.log</span></span><br><span class="line">  <span class="attr">fields:</span></span><br><span class="line">    <span class="attr">log_type:</span> <span class="string">test1</span></span><br><span class="line"><span class="bullet">-</span> <span class="attr">type:</span> <span class="string">log</span> </span><br><span class="line">  <span class="attr">paths:</span></span><br><span class="line">    <span class="bullet">-</span> <span class="string">/home/yulewei/test-beats2.log</span></span><br><span class="line">  <span class="attr">fields:</span></span><br><span class="line">    <span class="attr">log_type:</span> <span class="string">test2</span></span><br><span class="line"></span><br><span class="line"><span class="attr">output.logstash:</span></span><br><span class="line">  <span class="attr">hosts:</span> [<span class="string">&quot;localhost:5044&quot;</span>]</span><br></pre></td></tr></table></figure>
+<p>示例配置文件使用了 <code>filebeat.inputs.fields</code> 选项，<a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/filebeat-input-log.html#filebeat-input-log-fields">fields</a> 选项用于在日志事件输出中添加字段。添加的字段名可以任意指定，示例中名为 <code>log_type</code>。因为现在在 filebeat 配置中同时导入两个日志文件，输出到同一个 logstash 中。使用这个额外字段是为了区分日志是来自 <code>test-beats1.log</code> 还是 <code>test-beats2.log</code>。示例中，第 1 个日志事件输出的 <code>log_type</code> 字段值配置为 <code>test1</code>， 第 2 个日志配置为 <code>test2</code>。</p>
+<p>管道配置文件示例，<code>test-beats-elasticsearch.conf</code>：</p>
+<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line">  beats &#123;</span><br><span class="line">    port =&gt; 5044</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  elasticsearch &#123;</span><br><span class="line">    hosts =&gt; [&quot;http://192.168.2.109:9200&quot;]</span><br><span class="line">    index =&gt; &quot;filebeat-%&#123;[fields][log_type]&#125;-%&#123;+YYYY.MM.dd&#125;&quot;</span><br><span class="line">  &#125;</span><br><span class="line">  stdout &#123;</span><br><span class="line">    codec =&gt; rubydebug</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>输出插件同时使用了 <code>elasticsearch</code> 和 <code>stdout</code>。配置文件中的 <code>elasticsearch</code> 输出插件的 <code>index</code> 指令被设置为 <code>filebeat-%&#123;[fields][log_type]&#125;-%&#123;+YYYY.MM.dd&#125;</code>。<code>[fields][log_type]</code> 引用的是在 <code>filebeat.yml</code> 的 <code>filebeat.inputs.fields</code> 选项添加的 <code>log_type</code> 字段（关于在配置文件引用字段的语法，可以参考<a href="https://www.elastic.co/guide/en/logstash/6.5/event-dependent-configuration.html#logstash-config-field-references">官方文档</a>）。根据 <code>log_type</code> 字段不同，把日志将输出到不同的索引中。因为 <code>filebeat.yml</code> 配置文件中设置的 <code>log_type</code> 字段是 <code>test1</code> 或者 <code>test2</code>，所以最终生成的索引名是 <code>filebeat-test1-*</code> 或者 <code>filebeat-test1-*</code>。<code>filebeat-test1-*</code> 索引中全部日志数据来自 <code>test-beats1.log</code> 日志文件，<code>filebeat-test2-*</code> 索引数据来自 <code>test-beats2.log</code>。</p>
+<p>启动 filebeat 和 logstash：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo systemctl restart filebeat.service</span><br><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-beats-elasticsearch.conf</span><br></pre></td></tr></table></figure>
+<p>控制台输出：</p>
+<figure class="highlight json"><table><tr><td class="code"><pre><span class="line">...</span><br><span class="line"><span class="punctuation">&#123;</span></span><br><span class="line">      <span class="string">&quot;@version&quot;</span> =&gt; <span class="string">&quot;1&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;host&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;name&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;message&quot;</span> =&gt; <span class="string">&quot;hello world2&quot;</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;prospector&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;type&quot;</span> =&gt; <span class="string">&quot;log&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;fields&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;log_type&quot;</span> =&gt; <span class="string">&quot;test2&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;offset&quot;</span> =&gt; <span class="number">0</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;tags&quot;</span> =&gt; <span class="punctuation">[</span></span><br><span class="line">        <span class="punctuation">[</span><span class="number">0</span><span class="punctuation">]</span> <span class="string">&quot;beats_input_codec_plain_applied&quot;</span></span><br><span class="line">    <span class="punctuation">]</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;beat&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">            <span class="string">&quot;name&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;version&quot;</span> =&gt; <span class="string">&quot;6.5.4&quot;</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;hostname&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;@timestamp&quot;</span> =&gt; <span class="number">2019</span><span class="number">-01</span><span class="number">-13</span>T09<span class="punctuation">:</span><span class="number">32</span><span class="punctuation">:</span><span class="number">11.845</span>Z<span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;source&quot;</span> =&gt; <span class="string">&quot;/home/yulewei/test-beats2.log&quot;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;input&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;type&quot;</span> =&gt; <span class="string">&quot;log&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br><span class="line">...</span><br></pre></td></tr></table></figure>
+<p>查看在 elasticsearch 上新创建的 <code>filebeat-test1-*</code> 和 <code>filebeat-test1-*</code> 索引：</p>
+<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ curl http://192.168.2.109:9200/_cat/indices/filebeat-*</span><br><span class="line">yellow open filebeat-test1-2019.01.13 NLVfFJl5TQ-7I1r9KoVLaQ 5 1 5 0 31.8kb 31.8kb</span><br><span class="line">yellow open filebeat-test2-2019.01.13 NnsBp3P9Q3-mLc8chE-Tiw 5 1 3 0 24.1kb 24.1kb</span><br></pre></td></tr></table></figure>
+<p>在 kibana 上查看收集的日志：</p>
+<img width="800" alt="Kibana" title="Kibana" src="https://static.nullwy.me/filebeat-kibana.png">
+<p>整体架构上，如下图所示 [ <a href="https://www.elastic.co/guide/en/logstash/6.8/deploying-and-scaling.html">doc</a> ]：</p>
+<img width="800" alt="Deploying Logstash" title="Deploying Logstash" src="https://static.nullwy.me/logstash-deploy2.png">
+<hr>
+<p><strong>附注</strong>：本文中提到的配置文件，可以在 github 上访问得到，<a href="https://github.com/yulewei/elastic-stack-conf">elastic-stack-conf</a>。</p>
+<h1 id="参考资料">参考资料</h1>
+<ul>
+<li>发展历程| Elastic <a href="https://www.elastic.co/cn/about/history-of-elasticsearch">https://www.elastic.co/cn/about/history-of-elasticsearch</a></li>
+<li>2013-01 Welcome Drew &amp; Rashid (Kibana) <a href="https://www.elastic.co/blog/welcome-drew-rashid">https://www.elastic.co/blog/welcome-drew-rashid</a></li>
+<li>2013-08 Welcome Jordan &amp; Logstash <a href="https://www.elastic.co/blog/welcome-jordan-logstash">https://www.elastic.co/blog/welcome-jordan-logstash</a></li>
+<li>2015-05 Welcome Packetbeat, Tudor &amp; Monica <a href="https://www.elastic.co/blog/welcome-packetbeat-tudor-monica">https://www.elastic.co/blog/welcome-packetbeat-tudor-monica</a></li>
+<li>2015-11 The Beats 1.0.0 <a href="https://www.elastic.co/blog/beats-1-0-0">https://www.elastic.co/blog/beats-1-0-0</a></li>
+<li>2016-02 Heya, Elastic Stack and X-Pack <a href="https://www.elastic.co/blog/heya-elastic-stack-and-x-pack">https://www.elastic.co/blog/heya-elastic-stack-and-x-pack</a></li>
+<li>2016-10 Elastic Stack 5.0 正式发布 <a href="https://www.elastic.co/cn/blog/elastic-stack-5-0-0-released">https://www.elastic.co/cn/blog/elastic-stack-5-0-0-released</a></li>
+<li>2018-05 官方：Logstash 实用介绍 <a href="https://www.elastic.co/cn/blog/a-practical-introduction-to-logstash">https://www.elastic.co/cn/blog/a-practical-introduction-to-logstash</a></li>
+<li>Filebeat vs. Logstash — The Evolution of a Log Shipper <a href="https://logz.io/blog/filebeat-vs-logstash/">https://logz.io/blog/filebeat-vs-logstash/</a></li>
+<li>精通Elastic Stack，Gupta，2017 <a href="https://book.douban.com/subject/30326542/">https://book.douban.com/subject/30326542/</a></li>
+<li>logstash - open source log management <a href="https://web.archive.org/web/20150512135526/http://logstash.net/">https://web.archive.org/web/20150512135526/http://logstash.net/</a></li>
+<li>Logstash Config Language <a href="https://web.archive.org/web/20150907161920/http://logstash.net/docs/1.4.2/configuration">https://web.archive.org/web/20150907161920/http://logstash.net/docs/1.4.2/configuration</a></li>
+<li>Accessing Event Data and Fields in the Configuration <a href="https://www.elastic.co/guide/en/logstash/6.5/event-dependent-configuration.html">https://www.elastic.co/guide/en/logstash/6.5/event-dependent-configuration.html</a></li>
+<li>Logstash Configuration Examples <a href="https://www.elastic.co/guide/en/logstash/6.5/config-examples.html">https://www.elastic.co/guide/en/logstash/6.5/config-examples.html</a></li>
+<li>Logstash Reference: Deploying and Scaling Logstash <a href="https://www.elastic.co/guide/en/logstash/6.8/deploying-and-scaling.html">https://www.elastic.co/guide/en/logstash/6.8/deploying-and-scaling.html</a></li>
+</ul>
+]]></content>
+      <categories>
+        <category>架构</category>
+      </categories>
+      <tags>
+        <tag>架构</tag>
+        <tag>ELK</tag>
+        <tag>Elastic</tag>
+        <tag>日志</tag>
+      </tags>
+  </entry>
   <entry>
     <title>InnoDB 的并发控制：锁与 MVCC</title>
     <url>/2023/07/innodb-locking/</url>
@@ -937,201 +1135,30 @@ This WRITE COMMITTED implementation of REPEATABLE READ is not typical of any oth
       </tags>
   </entry>
   <entry>
-    <title>Elastic Stack 日志分析平台搭建笔记</title>
-    <url>/2019/01/elastic-stack/</url>
-    <content><![CDATA[<p>Elastic Stack（旧称 ELK Stack）是最受欢迎的开源日志平台 [ <a href="https://www.elastic.co/cn/solutions/logging">ref</a> ]。Elastic Stack 由 Elasticsearch、Logstash、Kibana 和 Beats 四个组件组成：</p>
-<ul>
-<li><a href="https://www.elastic.co/cn/products/beats">Beats</a>，是轻量型采集器的平台，从边缘机器向 Logstash 和 Elasticsearch 发送数据。</li>
-<li><a href="https://www.elastic.co/cn/products/logstash">Logstash</a>，集中、转换和存储数据，是动态数据收集管道，拥有可扩展的插件生态系统，能够与 Elasticsearch 产生强大的协同作用。</li>
-<li><a href="https://www.elastic.co/cn/products/elasticsearch">Elasticsearch</a>，搜索、分析和存储您的数据，是基于 JSON 的分布式搜索和分析引擎，专为实现水平扩展、高可靠性和管理便捷性而设计。</li>
-<li><a href="https://www.elastic.co/cn/products/kibana">Kibana</a>，实现数据可视化，导览 Elastic Stack。能够以图表的形式呈现数据，并且具有可扩展的用户界面，供您全方位配置和管理 Elastic Stack。</li>
-</ul>
+    <title>iText处理pdf书签和标注代码乱记</title>
+    <url>/2016/12/itext-pdf/</url>
+    <content><![CDATA[<p>将文档1中的书签转存到文档2​：</p>
 <span id="more"></span>
-<p>Elastic Stack 是逐步发展而来的，一开始只有 Elasticsearch，专注做搜索引擎，2013 年 1 月 Kibana 及其作者 Rashid Khan <a href="https://www.elastic.co/blog/welcome-drew-rashid">加入</a> Elasticsearch 公司，同年 8 月 Logstash 及作者 Jordan Sissel 也<a href="https://www.elastic.co/blog/welcome-jordan-logstash">加入</a>，原本的非官方的 ELK Stack，正式成为官方用语。2015 年 3 月，旧金山举行的第 1 届 Elastic{ON} 大会上，Elasticsearch 公司改名为 Elastic。两个月后，Packetbeat 项目也<a href="https://www.elastic.co/blog/welcome-packetbeat-tudor-monica">加入</a> Elastic，Packetbeat 和 Filebeat（之前叫做 <a href="https://github.com/elastic/logstash-forwarder">Logstash-forwarder</a>，由 Logstash 作者 Jordan Sissel 开发）项目被整合改造为 Beats。加上 Beats 以后，官方不知道如何将 “B” 和 E-L-K 组合在一起（用过 ELKB 或 BELK），ELK Stack 于是改名为 Elastic Stack，并在 2016 年 10 月正式发布 Elastic Stack 5.0 [ <a href="https://www.elastic.co/cn/about/history-of-elasticsearch">ref1</a>, <a href="https://www.elastic.co/elk-stack">ref2</a>, <a href="https://www.elastic.co/cn/blog/elastic-stack-5-0-0-released">ref3</a> ]。</p>
-<h1 id="使用-Logstash">使用 Logstash</h1>
-<p>Logstash（<a href="https://www.elastic.co/cn/products/logstash">home</a>, <a href="https://github.com/elastic/logstash">github</a>）最初是来自 Dreamhost 运维工程师 Jordan Sissel 的开源项目，是管理事件和日志的工具，能够用于采集数据，转换数据，然后将数据发送到您最喜欢的“存储库”中（比如 Elasticsearch）。Logstash 使用 JRuby 开发，2011 年 5 月发布 1.0 版本。2013 年 8 月 Jordan Sissel 带着 Logstash 加入 Elasticsearch 公司，Logstash 成为 Elastic Stack 一员。</p>
-<p>在 Ubuntu 下<a href="https://www.elastic.co/guide/en/logstash/6.5/installing-logstash.html">安装</a>、<a href="https://www.elastic.co/guide/en/logstash/6.5/running-logstash.html">启动</a> Logstash 可以使用下面命令：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo apt-get install logstash                <span class="comment"># 安装 logstash</span></span><br><span class="line">$ sudo systemctl start logstash.service        <span class="comment"># 系统服务方式启动 logstash</span></span><br><span class="line">$ /usr/share/logstash/bin/logstash --version   <span class="comment"># 查看 logstash 版本</span></span><br><span class="line">logstash 6.5.4</span><br><span class="line">$ sudo vim /etc/logstash/logstash.yml          <span class="comment"># 查看默认 logstash.yml</span></span><br><span class="line">$ sudo vim /etc/logstash/logstash-sample.conf  <span class="comment"># 查看示例 logstash-sample.conf</span></span><br></pre></td></tr></table></figure>
-<p>安装完成后，二进制文件在 <code>/usr/share/logstash/bin</code> 目录下，配置文件位于 <code>/etc/logstash</code> 目录，日志输出位于 <code>/var/log/logstash</code> 目录，其他详细的目录位置的分布情况，可以阅读<a href="https://www.elastic.co/guide/en/logstash/6.5/dir-layout.html">官方文档</a>。</p>
-<h2 id="最简单的示例">最简单的示例</h2>
-<p>Logstash 管道（pipeline）由 <code>input</code>、<code>filter</code> 和 <code>output</code> 三个元素组成，其中 <code>input</code> 和 <code>output</code> 必须设置，而 <code>filter</code> 可选。<code>input</code> 插件从数据源中消费数据，<code>filter</code> 插件按指定方式修改数据，<code>output</code> 插件将数据写入特定目标中 [ <a href="https://www.elastic.co/guide/en/logstash/6.5/first-event.html">doc</a> ]。</p>
-<img width="600" alt="Logstash 管道" title="Logstash 管道" src="https://static.nullwy.me/basic_logstash_pipeline.png">
-<p>现在来试试 Logstash 下 Hello Wolrd 级别的示例，运行下面命令：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -e <span class="string">&#x27;input &#123; stdin &#123; &#125; &#125; output &#123; stdout &#123;&#125; &#125;&#x27;</span></span><br></pre></td></tr></table></figure>
-<p><code>-e</code> 选项能够使 Logstash 直接在<a href="https://www.elastic.co/guide/en/logstash/6.5/running-logstash-command-line.html">命令行</a>中设置管道配置。示例中 <code>input</code> 插件为 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-inputs-stdin.html">stdin</a> （标准输入），<code>output</code> 插件是 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-outputs-stdout.html">stdout</a> （标准输出）。若在控制台输入 <code>hello world</code>，相应的控制台将输出：</p>
-<figure class="highlight json"><table><tr><td class="code"><pre><span class="line"><span class="punctuation">&#123;</span></span><br><span class="line">      <span class="string">&quot;@version&quot;</span> =&gt; <span class="string">&quot;1&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;host&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;@timestamp&quot;</span> =&gt; <span class="number">2019</span><span class="number">-01</span><span class="number">-12</span>T05<span class="punctuation">:</span><span class="number">52</span><span class="punctuation">:</span><span class="number">56.291</span>Z<span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;message&quot;</span> =&gt; <span class="string">&quot;hello world&quot;</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
-<p>值得注意的是，输出内容编码格式默认为 <code>rubydebug</code>，使用 Ruby 的 &quot;<a href="https://github.com/awesome-print/awesome_print">awesome_print</a>&quot; 库打印。另外，响应输出 <code>@timestamp</code> 字段的值为 <code>2019-01-12T05:52:56.291Z</code>，这是 <a href="https://en.wikipedia.org/wiki/ISO_8601">ISO 8601</a> 时间格式，时区是 0（zero），和北京时间相差 8 个小时。</p>
-<p>输出内容编码格式，可以通过 <code>codec</code> 指令指定。除了默认的 <code>rubydebug</code> 外，官方还支持其他 20 多种编码格式，参见 <a href="https://www.elastic.co/guide/en/logstash/6.5/codec-plugins.html">doc</a>。若把编码格式改为 <code>json</code>，即 <code>stdout &#123; codec =&gt; json &#125;</code>，输出结果将变成：</p>
-<figure class="highlight json"><table><tr><td class="code"><pre><span class="line"><span class="punctuation">&#123;</span><span class="attr">&quot;message&quot;</span><span class="punctuation">:</span><span class="string">&quot;hello world&quot;</span><span class="punctuation">,</span><span class="attr">&quot;@version&quot;</span><span class="punctuation">:</span><span class="string">&quot;1&quot;</span><span class="punctuation">,</span><span class="attr">&quot;@timestamp&quot;</span><span class="punctuation">:</span><span class="string">&quot;2019-01-12T05:52:56.291Z&quot;</span><span class="punctuation">,</span><span class="attr">&quot;host&quot;</span><span class="punctuation">:</span><span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
-<p>管道配置也可以保存到文件中，以 <code>*.conf</code> 作为文件后缀，比如保存为 <code>test-stdin-stdout.conf</code>：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line">  stdin &#123; &#125;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  stdout &#123; &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-<p>启动 logstash 时，<code>-f</code> 选项用于指定管道配置文件的路径：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -f ~/test-stdin-stdout.conf</span><br></pre></td></tr></table></figure>
-<p>默认情况下，在启动 logstash 后，若再修改管道配置文件，新的修改需要重启 logstash 才能加载生效。在开发调试时，不太方便。解决这个问题，可以使用 <code>-r</code> 命令行<a href="https://www.elastic.co/guide/en/logstash/6.5/running-logstash-command-line.html">选项</a>。开启这个选项后，只要确定配置文件已经发生变更，便会自动重新加载配置文件。</p>
-<h2 id="file-输入插件">file 输入插件</h2>
-<p>上文日志是控制台输入的，但真实情况日志在日志文件中，要想使用 Logstash 读取日志文件，官方提供了 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-inputs-file.html">file</a> 输入插件。管道配置文件示例 <code>test-file-stdout.conf</code>，如下：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line"> file &#123;</span><br><span class="line">   path =&gt; [&quot;/home/yulewei/test.log&quot;]</span><br><span class="line">   sincedb_path =&gt; &quot;/dev/null&quot;</span><br><span class="line">   start_position =&gt; &quot;beginning&quot;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">filter &#123;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  stdout &#123;</span><br><span class="line">    codec =&gt; rubydebug</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-<p>启动 Logstash：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-file-stdout.conf</span><br></pre></td></tr></table></figure>
-<p>配置文件中的 <code>path</code> 指令用于指定日志文件的路径。<code>start_position</code> 指令设置 Logstash 启动时读取日志文件的位置，可以设置为 <code>beginning</code> 或者 <code>end</code>，默认是 <code>end</code>，即文件末尾。</p>
-<p>为了跟踪每个输入文件中已处理了哪些数据，Logstash 文件输入插件会使用名为 sincedb 的文件来记录现有位置。由于我们的配置用于开发，所以我们希望能够重复读取文件，并进而希望禁用 sincedb 文件。在 Linux 系统上，将 <code>sincedb_path</code> 指令设置为 “/dev/null” 即可禁用。若没有禁用，默认保存的 sincedb 文件将在 <code>/usr/share/logstash/data/plugins/inputs/file/</code> 目录下。</p>
-<h2 id="grok-过滤插件">grok 过滤插件</h2>
-<p>上文的例子，做的核心事情就是把日志行转换到 <code>message</code> 字段，并附加某些元数据，如 <code>@timestamp</code>。如果要想解析自己的日志，把非结构化日志转换结构换日志，有两个过滤器特别常用：<a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-filters-dissect.html">dissect</a> 会根据分界符来解析日志，而 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-filters-grok.html">grok</a> 则会根据正则表达式匹配来运行。</p>
-<p>如果数据结构定义非常完善，dissect 过滤插件的运行效果非常好，而且运行速度非常快捷高效。同时，其也更加容易上手，对于不熟悉正则表达式的用户而言，更是如此。通常而言，grok 的功能更加强大，而且可以处理各种各样的数据。然而，正则表达式匹配会耗费更多资源，而且速度也会慢一些，如果未能正确进行优化的话，尤为如此。</p>
-<p>现在先来看下 grok 过滤插件。grok 模式的基本语法是 <code>%&#123;SYNTAX:SEMANTIC&#125;</code>，<code>SYNTAX</code> 是用于匹配数据的模式（或正则表达式）名称，<code>SEMANTIC</code> 是标识符或字段名称。Logstash 提供了超过 120 种默认的 grok 模式，全部预定义的模式可以在 <a href="https://github.com/logstash-plugins/logstash-patterns-core/tree/master/patterns">github</a> 上找到。典型的预定义模式（非完整列表）[ <a href="https://github.com/logstash-plugins/logstash-patterns-core/blob/v4.1.2/patterns/grok-patterns">github</a> ]：</p>
-<ul>
-<li>WORD - 匹配单个词汇的模式</li>
-<li>NUMBER - 匹配整数或浮点数（正值或负值均可）的模式</li>
-<li>POSINT - 匹配正整数的模式</li>
-<li>EMAILADDRESS - 邮箱地址</li>
-<li>IP - 匹配 IPv4 或 IPv6 IP 地址的模式</li>
-<li>URI - URI 地址</li>
-<li>TIMESTAMP_ISO8601 - <a href="https://en.wikipedia.org/wiki/ISO_8601">ISO8601</a> 格式的时间</li>
-<li>NOTSPACE - 匹配非空格的任何内容的格式</li>
-<li>SPACE - 匹配任何数量的连续空格的模式</li>
-<li>DATA - 匹配任何数据类型的限定数量的模式</li>
-<li>GREEDYDATA - 匹配剩余所有数据的格式</li>
-</ul>
-<p>比如，<code>3.44</code> 可以使用 <code>NUMBER</code> 模式进行匹配，<code>192.168.2.104</code> 可以使用 <code>IP</code> 模式。<code>%&#123;NUMBER:num&#125; %&#123;IP:client&#125;</code> 模式，将会用 <code>NUMBER</code> 模式把 <code>3.44</code> 识别为 <code>num</code> 字段，用 <code>IP</code> 模式把 <code>192.168.2.104</code> 识别为 <code>client</code> 字段。默认情况识别获得的字段值是字符串类型，grok 插件支持把类型转换为 <code>int</code> 或 <code>float</code>。要想把 <code>3.44</code> 转换为浮点数，可以使用 <code>%&#123;NUMBER:num:float&#125;</code>。</p>
-<p>假设有如下日志内容：</p>
-<figure class="highlight txt"><table><tr><td class="code"><pre><span class="line">Will, yulewei@gmail.com, 42, 1024, 3.14</span><br></pre></td></tr></table></figure>
-<p>grok 匹配表达式可以写成这样：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">%&#123;WORD:name&#125;, %&#123;EMAILADDRESS:email&#125;, %&#123;NUMBER:num1&#125;, %&#123;NUMBER:num2:int&#125;, %&#123;NUMBER:pi:float&#125;</span><br></pre></td></tr></table></figure>
-<p>即，在这一行日志中依次提取出，<code>name</code>、<code>email</code>、<code>num1</code>、<code>num2</code> 和 <code>pi</code> 字段。完整的 <code>filter</code> 过滤器配置的写法：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">filter &#123;</span><br><span class="line">  grok &#123;</span><br><span class="line">    match =&gt; &#123; &quot;message&quot; =&gt; &quot;%&#123;WORD:name&#125;, %&#123;EMAILADDRESS:email&#125;, %&#123;NUMBER:num1&#125;, %&#123;NUMBER:num2:int&#125;, %&#123;NUMBER:pi:float&#125;&quot; &#125;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-<p>启动 logstash：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-file-grok-stdout.conf</span><br></pre></td></tr></table></figure>
-<p>控制台将输出：</p>
-<figure class="highlight json"><table><tr><td class="code"><pre><span class="line"><span class="punctuation">&#123;</span></span><br><span class="line">      <span class="string">&quot;@version&quot;</span> =&gt; <span class="string">&quot;1&quot;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;message&quot;</span> =&gt; <span class="string">&quot;Will, yulewei@gmail.com, 42, 1024, 3.14&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;num1&quot;</span> =&gt; <span class="string">&quot;42&quot;</span><span class="punctuation">,</span></span><br><span class="line">            <span class="string">&quot;pi&quot;</span> =&gt; <span class="number">3.14</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;@timestamp&quot;</span> =&gt; <span class="number">2019</span><span class="number">-01</span><span class="number">-12</span>T08<span class="punctuation">:</span><span class="number">12</span><span class="punctuation">:</span><span class="number">49.581</span>Z<span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;path&quot;</span> =&gt; <span class="string">&quot;/home/yulewei/test-grok.log&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;host&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;email&quot;</span> =&gt; <span class="string">&quot;yulewei@gmail.com&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;name&quot;</span> =&gt; <span class="string">&quot;Will&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;num2&quot;</span> =&gt; <span class="number">1024</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
-<p>Logstash 提供了超过 120 种默认的 grok 模式，基本上满足大多数使用场景。若没有符合要求的预定义的模式，可以使用 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-filters-grok.html#_regular_expressions">Oniguruma</a> 语法指定正则表达式：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">(?&lt;field_name&gt;the pattern here)</span><br></pre></td></tr></table></figure>
-<p>上文中的 <code>%&#123;WORD:name&#125;</code> 和 <code>%&#123;EMAILADDRESS:email&#125;</code>，等价的正则表达式的写法如下 [ <a href="https://github.com/logstash-plugins/logstash-patterns-core/blob/v4.1.2/patterns/grok-patterns">ref1</a>, <a href="https://stackoverflow.com/a/8829363">ref2</a> ]：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">(?&lt;name&gt;\w+)</span><br><span class="line">(?&lt;email&gt;[a-zA-Z][a-zA-Z0-9_.+-=:]+@[0-9A-Za-z][0-9A-Za-z-]&#123;0,62&#125;\.[0-9A-Za-z][0-9A-Za-z-]&#123;0,62&#125;)</span><br></pre></td></tr></table></figure>
-<p>调试 grok 匹配表达式容易出错，官方提供可视化的 <a href="https://www.elastic.co/guide/en/kibana/6.5/grokdebugger-getting-started.html">Grok Debugger</a> 工具，提高调试效率。</p>
-<img width="800" alt="Grok Debugger" title="Grok Debugger" src="https://static.nullwy.me/kibana-grokdebugger.png">
-<h3 id="解析-http-服务器日志">解析 http 服务器日志</h3>
-<p>现在来看下，真实的日志解析案例，使用 grok 过滤插件解析 http 服务器日志。通用日志格式（<a href="https://en.wikipedia.org/wiki/Common_Log_Format">Common Log Format</a>），是 http 服务器的标准的日志格式。对通用日志格式扩展，加上额外的 referer 和 user-agent 字段，称为组合日志格式（Combined Log Format）。两种日志格式包含的字段如下：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line"># 通用日志格式</span><br><span class="line">%remote-host %ident %authuser %timestamp &quot;%request&quot; %status %bytes</span><br><span class="line"># 组合日志格式</span><br><span class="line">%remote-host %ident %authuser %timestamp &quot;%request&quot; %status %bytes &quot;%referer&quot; &quot;%user-agent&quot;</span><br></pre></td></tr></table></figure>
-<p><a href="https://httpd.apache.org/docs/2.4/logs.html#accesslog">Apache</a> 和 <a href="https://nginx.org/en/docs/http/ngx_http_log_module.html#log_format">Nginx</a> 服务器默认的日志格式，采用的就是通用日志格式或者组合日志格式。解析这两种日志格式，Logstash 提供预定义模式 <a href="https://github.com/logstash-plugins/logstash-patterns-core/blob/v4.1.2/patterns/httpd#L14">COMMONAPACHELOG</a> 和 <a href="https://github.com/logstash-plugins/logstash-patterns-core/blob/v4.1.2/patterns/httpd#L15">COMBINEDAPACHELOG</a>。</p>
-<p>典型的 nginx 日志例子：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">192.168.2.104 - - [13/Jan/2019:02:01:15 +0800] &quot;GET /images/avatar.png HTTP/1.1&quot; 200 266975 &quot;-&quot; &quot;Mozilla/5.0 (Macintosh; Intel Mac OS X 10.13; rv:64.0) Gecko/20100101 Firefox/64.0&quot;</span><br></pre></td></tr></table></figure>
-<p>管道配置文件示例 <code>test-file-grokhttp-stdout.conf</code>，如下：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line">  file &#123;</span><br><span class="line">    path =&gt; [&quot;/var/log/nginx/access.log&quot;]</span><br><span class="line">    sincedb_path =&gt; &quot;/dev/null&quot;</span><br><span class="line">    start_position =&gt; &quot;beginning&quot;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">filter &#123;</span><br><span class="line">  grok &#123;</span><br><span class="line">    match =&gt; &#123; &quot;message&quot; =&gt; &quot;%&#123;COMBINEDAPACHELOG&#125;&quot; &#125;</span><br><span class="line">    remove_field =&gt; [&quot;message&quot;]</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  stdout &#123; &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-<p>示例中使用了 grok 的预定义模式 <a href="https://github.com/logstash-plugins/logstash-patterns-core/blob/v4.1.2/patterns/httpd#L15">COMBINEDAPACHELOG</a>。另外，<code>remove_field</code> <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-filters-grok.html#plugins-filters-grok-remove_field">指令</a>用于把输出事件中某字段删除，示例中是 <code>message</code> 字段。</p>
-<p>启动 logstash：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-file-grokhttp-stdout.conf</span><br></pre></td></tr></table></figure>
-<p>解析获得的结构化数据，如下：</p>
-<figure class="highlight json"><table><tr><td class="code"><pre><span class="line"><span class="punctuation">&#123;</span></span><br><span class="line">           <span class="string">&quot;auth&quot;</span> =&gt; <span class="string">&quot;-&quot;</span><span class="punctuation">,</span></span><br><span class="line">           <span class="string">&quot;host&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">,</span></span><br><span class="line">           <span class="string">&quot;verb&quot;</span> =&gt; <span class="string">&quot;GET&quot;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;clientip&quot;</span> =&gt; <span class="string">&quot;192.168.2.104&quot;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;@version&quot;</span> =&gt; <span class="string">&quot;1&quot;</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;httpversion&quot;</span> =&gt; <span class="string">&quot;1.1&quot;</span><span class="punctuation">,</span></span><br><span class="line">     <span class="string">&quot;@timestamp&quot;</span> =&gt; <span class="number">2019</span><span class="number">-01</span><span class="number">-13</span>T13<span class="punctuation">:</span><span class="number">35</span><span class="punctuation">:</span><span class="number">52.983</span>Z<span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;bytes&quot;</span> =&gt; <span class="string">&quot;266975&quot;</span><span class="punctuation">,</span></span><br><span class="line">      <span class="string">&quot;timestamp&quot;</span> =&gt; <span class="string">&quot;13/Jan/2019:02:01:15 +0800&quot;</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;request&quot;</span> =&gt; <span class="string">&quot;/images/avatar.png&quot;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;response&quot;</span> =&gt; <span class="string">&quot;200&quot;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;referrer&quot;</span> =&gt; <span class="string">&quot;\&quot;-\&quot;&quot;</span><span class="punctuation">,</span></span><br><span class="line">           <span class="string">&quot;path&quot;</span> =&gt; <span class="string">&quot;/var/log/nginx/access.log&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;agent&quot;</span> =&gt; <span class="string">&quot;\&quot;Mozilla/5.0 (Macintosh; Intel Mac OS X 10.13; rv:64.0) Gecko/20100101 Firefox/64.0\&quot;&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;ident&quot;</span> =&gt; <span class="string">&quot;-&quot;</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
-<h2 id="dissect-过滤插件">dissect 过滤插件</h2>
-<p>和 grok 过滤插件使用正则表达式提取字段不同，dissect 过滤插件使用分界符切割来提取字段。由于没有使用正则表达式，运行速度相对 grok 快很多。使用 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-filters-dissect.html">dissect</a> 过滤插件时，需要指明提取字段的顺序，还要指明这些字段之间的分界符。过滤插件会对数据进行单次传输，并匹配模式中的分界符。同时，过滤插件还会将分界符之间的数据分配至指定字段。过滤插件不会对所提取数据的格式进行验证。</p>
-<p>现在看下示例，<code>test-dissect.log</code> 文件内容如下：</p>
-<figure class="highlight txt"><table><tr><td class="code"><pre><span class="line">Will, yulewei@gmail.com, 42, 1024, 3.14</span><br></pre></td></tr></table></figure>
-<p>dissect 匹配规则可以写成这样：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">%&#123;name&#125;, %&#123;email&#125;, %&#123;num1&#125;, %&#123;num2&#125;, %&#123;num3&#125;</span><br></pre></td></tr></table></figure>
-<p>完整的配置文件，<code>test-file-dissect-stdout.conf</code>：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line"> file &#123;</span><br><span class="line">   path =&gt; [&quot;/home/yulewei/test-dissect.log&quot;]</span><br><span class="line">   sincedb_path =&gt; &quot;/dev/null&quot;</span><br><span class="line">   start_position =&gt; &quot;beginning&quot;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">filter &#123;</span><br><span class="line">  dissect &#123;</span><br><span class="line">    mapping =&gt; &#123;</span><br><span class="line">      &quot;message&quot; =&gt; &quot;%&#123;name&#125;, %&#123;email&#125;, %&#123;num1&#125;, %&#123;num2&#125;, %&#123;num3&#125;&quot;</span><br><span class="line">    &#125;</span><br><span class="line">    convert_datatype =&gt; &#123;</span><br><span class="line">      &quot;num2&quot; =&gt; &quot;int&quot;</span><br><span class="line">      &quot;num3&quot; =&gt; &quot;float&quot;</span><br><span class="line">    &#125;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  stdout &#123; &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-<p>和 grok 插件一样，默认提取的字段是字符串类型。配置文件中的 <code>convert_datatype</code> 指令用于将类型转为 <code>int</code> 或 <code>float</code>。</p>
-<p>启动 logstash：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-file-dissect-stdout.conf</span><br></pre></td></tr></table></figure>
-<p>输出结果：</p>
-<figure class="highlight json"><table><tr><td class="code"><pre><span class="line"><span class="punctuation">&#123;</span></span><br><span class="line">          <span class="string">&quot;host&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;num1&quot;</span> =&gt; <span class="string">&quot;42&quot;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;message&quot;</span> =&gt; <span class="string">&quot;Will, yulewei@gmail.com, 42, 1024, 3.14&quot;</span><span class="punctuation">,</span></span><br><span class="line">      <span class="string">&quot;@version&quot;</span> =&gt; <span class="string">&quot;1&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;name&quot;</span> =&gt; <span class="string">&quot;Will&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;num2&quot;</span> =&gt; <span class="number">1024</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;@timestamp&quot;</span> =&gt; <span class="number">2019</span><span class="number">-01</span><span class="number">-13</span>T13<span class="punctuation">:</span><span class="number">32</span><span class="punctuation">:</span><span class="number">10.900</span>Z<span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;path&quot;</span> =&gt; <span class="string">&quot;/home/yulewei/test-dissect.log&quot;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;email&quot;</span> =&gt; <span class="string">&quot;yulewei@gmail.com&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;num3&quot;</span> =&gt; <span class="number">3.14</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
-<h1 id="输出到-Elasticsearch">输出到 Elasticsearch</h1>
-<p>上文举的例子全部都是，输出控制台，使用 <code>stdout</code> 输出插件，没有实用价值。Elastic Stack 的核心其实是 Elasticsearch，使用Elasticsearch 搜索和分析日志。想要将数据发送到 Elasticsearch，可以使用 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-outputs-elasticsearch.html">elasticsearch</a> 输出插件。</p>
-<h2 id="安装-Elasticsearch">安装 Elasticsearch</h2>
-<p>如果没有安装 Elasticsearch，参考<a href="https://www.elastic.co/guide/en/elasticsearch/reference/6.5/deb.html">官方文档</a>按步骤安装。唯一要注意的是，在执行 <code>apt install</code> 命令前，必须先添加 elastic 的软件源地址，否则无法正常启动。核心命令如下：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo apt-get install elasticsearch           <span class="comment"># 安装 elasticsearch</span></span><br><span class="line">$ sudo systemctl start elasticsearch.service   <span class="comment"># 系统服务方式启动 elasticsearch</span></span><br><span class="line">$ curl http://localhost:9200/                  <span class="comment"># 用 rest 接口查看 elasticsearch</span></span><br><span class="line">&#123;</span><br><span class="line">  <span class="string">&quot;name&quot;</span> : <span class="string">&quot;1t9JXt5&quot;</span>,</span><br><span class="line">  <span class="string">&quot;cluster_name&quot;</span> : <span class="string">&quot;elasticsearch&quot;</span>,</span><br><span class="line">  <span class="string">&quot;cluster_uuid&quot;</span> : <span class="string">&quot;yQgVsvupSqGCGQbwqnanIg&quot;</span>,</span><br><span class="line">  <span class="string">&quot;version&quot;</span> : &#123;</span><br><span class="line">    <span class="string">&quot;number&quot;</span> : <span class="string">&quot;6.5.4&quot;</span>,</span><br><span class="line">    <span class="string">&quot;build_flavor&quot;</span> : <span class="string">&quot;default&quot;</span>,</span><br><span class="line">    <span class="string">&quot;build_type&quot;</span> : <span class="string">&quot;deb&quot;</span>,</span><br><span class="line">    <span class="string">&quot;build_hash&quot;</span> : <span class="string">&quot;d2ef93d&quot;</span>,</span><br><span class="line">    <span class="string">&quot;build_date&quot;</span> : <span class="string">&quot;2018-12-17T21:17:40.758843Z&quot;</span>,</span><br><span class="line">    <span class="string">&quot;build_snapshot&quot;</span> : <span class="literal">false</span>,</span><br><span class="line">    <span class="string">&quot;lucene_version&quot;</span> : <span class="string">&quot;7.5.0&quot;</span>,</span><br><span class="line">    <span class="string">&quot;minimum_wire_compatibility_version&quot;</span> : <span class="string">&quot;5.6.0&quot;</span>,</span><br><span class="line">    <span class="string">&quot;minimum_index_compatibility_version&quot;</span> : <span class="string">&quot;5.0.0&quot;</span></span><br><span class="line">  &#125;,</span><br><span class="line">  <span class="string">&quot;tagline&quot;</span> : <span class="string">&quot;You Know, for Search&quot;</span></span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-<p>默认情况下 elasticsearch 服务器绑定的 ip 地址是回环地址 <code>127.0.0.1</code>，若想绑定特定 ip 地址，可以修改 <code>/etc/elasticsearch/elasticsearch.yml</code> 配置文件中的 <a href="https://www.elastic.co/guide/en/elasticsearch/reference/6.5/network.host.html">network.host</a> 选项：</p>
-<figure class="highlight yml"><table><tr><td class="code"><pre><span class="line"><span class="attr">network.host:</span> <span class="number">192.168</span><span class="number">.2</span><span class="number">.109</span></span><br></pre></td></tr></table></figure>
-<p>修改完成并重启后，elasticsearch 服务器访问地址从 <code>http://localhost:9200/</code> 变成 <code>http://192.168.2.109:9200/</code>。</p>
-<h2 id="输出到-Elasticsearch-v2">输出到 Elasticsearch</h2>
-<p>现在来看下 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-outputs-elasticsearch.html">elasticsearch</a> 输出插件。示例，<code>test-file-elasticsearch.conf</code>：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line"> file &#123;</span><br><span class="line">   path =&gt; [&quot;/home/yulewei/test.log&quot;]</span><br><span class="line">   sincedb_path =&gt; &quot;/dev/null&quot;</span><br><span class="line">   start_position =&gt; &quot;beginning&quot;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  elasticsearch &#123;</span><br><span class="line">    hosts =&gt; [&quot;http://192.168.2.109:9200&quot;]</span><br><span class="line">    index =&gt; &quot;logstash-%&#123;+YYYY.MM.dd&#125;&quot;</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-<p>示例的 <code>elasticsearch</code> 输出插件使用了 <code>hosts</code> 和 <code>index</code> 指令。<code>hosts</code> 指令，用于指定 elasticsearch 服务器的地址。而 <code>index</code> 指令，用于指定 elasticsearch 索引的名称模式，该指令默认值为 <code>logstash-%&#123;+YYYY.MM.dd&#125;</code>。在字符串内部的 <code>%&#123;...&#125;</code>，是 Logstash 字符串插值语法，官方称之为 <code>sprintf format</code> [ <a href="https://www.elastic.co/guide/en/logstash/6.5/event-dependent-configuration.html">doc</a> ]。<code>+YYYY.MM.dd</code>，用于指定 <code>@timestamp</code> 的格式化的格式。<code>logstash-%&#123;+YYYY.MM.dd&#125;</code>，格式化后最终生成的值可能将是 <code>logstash-2019.01.13</code>。</p>
-<p>启动 logstash：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-file-elasticsearch.conf</span><br></pre></td></tr></table></figure>
-<p>查看在 elasticsearch 上新创建的 <code>logstash-*</code> 索引以及从 logstash 同步过来的日志数据：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ curl http://192.168.2.109:9200/_cat/indices</span><br><span class="line">yellow open logstash-2019.01.13       tFjc5xL_QYeNw4oqe4odeg 5 1     3 0 15.5kb 15.5kb</span><br><span class="line">$ curl <span class="string">&#x27;http://192.168.2.109:9200/logstash-*/_search?pretty&#x27;</span> -H <span class="string">&#x27;Content-Type: application/json&#x27;</span> -d<span class="string">&#x27;&#123;&quot;size&quot;: 1&#125;&#x27;</span></span><br><span class="line">&#123;</span><br><span class="line">  <span class="string">&quot;took&quot;</span> : 0,</span><br><span class="line">  <span class="string">&quot;timed_out&quot;</span> : <span class="literal">false</span>,</span><br><span class="line">  <span class="string">&quot;_shards&quot;</span> : &#123;</span><br><span class="line">    <span class="string">&quot;total&quot;</span> : 5,</span><br><span class="line">    <span class="string">&quot;successful&quot;</span> : 5,</span><br><span class="line">    <span class="string">&quot;skipped&quot;</span> : 0,</span><br><span class="line">    <span class="string">&quot;failed&quot;</span> : 0</span><br><span class="line">  &#125;,</span><br><span class="line">  <span class="string">&quot;hits&quot;</span> : &#123;</span><br><span class="line">    <span class="string">&quot;total&quot;</span> : 3,</span><br><span class="line">    <span class="string">&quot;max_score&quot;</span> : 1.0,</span><br><span class="line">    <span class="string">&quot;hits&quot;</span> : [</span><br><span class="line">      &#123;</span><br><span class="line">        <span class="string">&quot;_index&quot;</span> : <span class="string">&quot;logstash-2019.01.13&quot;</span>,</span><br><span class="line">        <span class="string">&quot;_type&quot;</span> : <span class="string">&quot;doc&quot;</span>,</span><br><span class="line">        <span class="string">&quot;_id&quot;</span> : <span class="string">&quot;RUHNRWgBLIBntI4FV8Rf&quot;</span>,</span><br><span class="line">        <span class="string">&quot;_score&quot;</span> : 1.0,</span><br><span class="line">        <span class="string">&quot;_source&quot;</span> : &#123;</span><br><span class="line">          <span class="string">&quot;path&quot;</span> : <span class="string">&quot;/home/yulewei/test.log&quot;</span>,</span><br><span class="line">          <span class="string">&quot;@timestamp&quot;</span> : <span class="string">&quot;2019-01-13T06:01:51.303Z&quot;</span>,</span><br><span class="line">          <span class="string">&quot;@version&quot;</span> : <span class="string">&quot;1&quot;</span>,</span><br><span class="line">          <span class="string">&quot;host&quot;</span> : <span class="string">&quot;ubuntu109&quot;</span>,</span><br><span class="line">          <span class="string">&quot;message&quot;</span> : <span class="string">&quot;hello world&quot;</span></span><br><span class="line">        &#125;</span><br><span class="line">      &#125;</span><br><span class="line">    ]</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-<p>可以看到，新的索引名为 <code>logstash-2019.01.13</code>。同步过来的日志记录全部有 5 条，第 1 条日志的 <code>message</code> 内容是 <code>hello world</code>。</p>
-<h2 id="使用-Kibana">使用 Kibana</h2>
-<p>Kibana，能够对 Elasticsearch 中的数据进行可视化，是 Elastic Stack 的窗口。在 Ubuntu 下<a href="https://www.elastic.co/guide/en/kibana/6.5/deb.html">安装</a> Kibana 可以使用下面命令：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo apt-get install kibana          <span class="comment"># 安装 kibana，当前最新版为 6.5.4</span></span><br><span class="line">$ sudo systemctl start kibana.service  <span class="comment"># 系统服务方式启动 kibana</span></span><br></pre></td></tr></table></figure>
-<p>默认配置下，kibana 服务访问地址是 <code>http://localhost:5601/</code>，连接的 elasticsearch 地址是 <code>http://localhost:9200</code>，这两个配置分别由 <code>server.host</code> 和 <code>elasticsearch.url</code> 控制 [ <a href="https://www.elastic.co/guide/en/kibana/6.5/settings.html">doc</a> ]。上文尝试过把 elasticsearch 服务 ip 地址绑定到 <code>192.168.2.109</code>。现在来试下绑定 ip 地址到 kibana，编辑配置文件 <code>/etc/kibana/kibana.yml</code>，修改为：</p>
-<figure class="highlight yml"><table><tr><td class="code"><pre><span class="line"><span class="attr">server.host:</span> <span class="string">&quot;192.168.2.109&quot;</span></span><br><span class="line"><span class="attr">elasticsearch.url:</span> <span class="string">&quot;http://192.168.2.109:9200&quot;</span></span><br></pre></td></tr></table></figure>
-<p>使用 <code>sudo systemctl restart kibana.service</code> 重启后，kibana 服务访问地址变成 <code>http://192.168.2.109:5601/</code>。</p>
-<p>elasticsearch 服务器上存在索引 <code>logstash-2019.01.13</code>，要想把这个索引导入到 kibana，参考官方<a href="https://www.elastic.co/guide/en/kibana/6.5/tutorial-define-index.html">教程</a>即可。点击 <code>Management</code> 菜单，然后创建索引模式（index pattern）。索引模式可以直接为 <code>logstash-2019.01.13</code>，这样匹配单个索引。若要匹配多个时间的 logstash 索引，可以使用通配符 <code>*</code>，比如 <code>logstash-*</code>。如果要匹配全部 2019 年 01 月的索引，可以写成 <code>logstash-2019.01*</code>。完成索引模式定义后，便可以在 <code>Discover</code> 菜单下查看索引，如图：</p>
-<img width="800" alt="Kibana" title="Kibana" src="https://static.nullwy.me/logstash-kibana.png">
-<h1 id="使用-Filebeat">使用 Filebeat</h1>
-<p>Filebeat，轻量型日志采集器 [ <a href="https://www.elastic.co/cn/products/beats/filebeat">home</a> ]。其前身是由 Logstash 作者 Jordan Sissel 开发的 <a href="https://github.com/elastic/logstash-forwarder">Logstash Forwarder</a>。Logstash Forwarder 项目因为和收购过来的 Packetbeat 项目功能相近，并且都是 Go 语言开发，就一起被整合改造为 Beats [ <a href="https://www.elastic.co/blog/beats-1-0-0">ref</a> ]。</p>
-<p>我们知道，Logstash 使用 JRuby 开发，运行依赖 JVM，会消耗较多的系统资源。为了减少系统资源（CPU、内存和网络）的使用，Logstash Forwarder 改用 Go 语言开发。另外，在功能上也做了精简，只做单一的数据传输，不像 Logstash 有数据过滤能力。Logstash 类似于功能多样的“瑞士军刀”，能提供从多个数据源加载数据的功能，使用各种强大的插件来处理日志，并提供将多个来源的输出数据进行存储的功能。简而言之，Logstash 提供数据 ETL（数据的提取、变换和加载）的功能；而 Beats 是轻量级的数据传输工具，能将数据传输到 Logstash 或 Elasticsearch 中，其间没有对数据进行任何转换 [ <a href="https://book.douban.com/subject/30326542/">Gupta2017</a> ]。Filebeat 和 Logstash 的关系如下图所示 [ <a href="https://logz.io/blog/filebeat-vs-logstash/">logz.io</a> ]：</p>
-<img width="600" alt="Filebeat 和 Logstash 的关系" title="Filebeat 和 Logstash 的关系" src="https://static.nullwy.me/filebeat-and-logstash.png">
-<p>安装 filebeat 很简单，参考<a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/setup-repositories.html">官方文档</a>即可，核心命令如下：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo apt-get install filebeat           <span class="comment"># 安装 filebeat</span></span><br><span class="line">$ filebeat version                        <span class="comment"># 查看 filebeat 版本</span></span><br><span class="line">filebeat version 6.5.4 (amd64), libbeat 6.5.4 [bd8922f1c7e93d12b07e0b3f7d349e17107f7826 built 2018-12-17 20:22:29 +0000 UTC]</span><br><span class="line">$ sudo systemctl start filebeat.service   <span class="comment"># 系统服务方式启动 filebeat</span></span><br></pre></td></tr></table></figure>
-<h2 id="输出到-Elasticsearch-v3">输出到 Elasticsearch</h2>
-<p>修改 filebeat 配置文件 /etc/filebeat/<a href="https://github.com/elastic/beats/blob/6.5/filebeat/filebeat.yml">filebeat.yml</a>，示例如下：</p>
-<figure class="highlight yml"><table><tr><td class="code"><pre><span class="line"><span class="attr">filebeat.inputs:</span></span><br><span class="line"><span class="bullet">-</span> <span class="attr">type:</span> <span class="string">log</span></span><br><span class="line">  <span class="attr">paths:</span></span><br><span class="line">    <span class="bullet">-</span> <span class="string">/home/yulewei/test.log</span></span><br><span class="line"></span><br><span class="line"><span class="attr">output.elasticsearch:</span></span><br><span class="line">  <span class="attr">hosts:</span> [<span class="string">&quot;192.168.2.109:9200&quot;</span>]</span><br></pre></td></tr></table></figure>
-<p><code>filebeat.inputs</code> 选项用于配置日志的<a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/configuration-filebeat-options.html">输入方式</a>。子选项 <code>type</code> <a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/configuration-filebeat-options.html#filebeat-input-types">支持</a> <code>log</code>、<code>stdin</code>、<code>redis</code>、<code>udp</code>、<code>tcp</code> 等，示例中使用了 <code>log</code>，表明从日志文件输入。</p>
-<p><code>output</code> 选项用于配置日志的<a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/configuring-output.html">输出方式</a>，配置支持 elasticsearch、logstash、kafka、redis、file、console 等，一次只能选择配置其中某一个。示例配置了 <code>output.elasticsearch.hosts</code>，指定日志输出目标 elasticsearch 的主机地址。<code>output.elasticsearch.index</code> 可以用来指定索引 index 名称模式，默认是 <code>filebeat-%&#123;[beat.version]&#125;-%&#123;+yyyy.MM.dd&#125;</code>（比如 <code>filebeat-6.5.4-2019.01.12</code>）[ <a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/elasticsearch-output.html#index-option-es">doc</a> ]。</p>
-<p>完成 <code>filebeat.yml</code> 修改后，重启 filebeat，将可以看到，在 elasticsearch 上新创建的 <code>filebeat-*</code> 索引：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ curl http://192.168.2.109:9200/_cat/indices</span><br><span class="line">yellow open filebeat-6.5.4-2019.01.12 B4JbQDnZQuK5XvsQ77uedA 3 1 11043 0  1.7mb  1.7mb</span><br></pre></td></tr></table></figure>
-<h2 id="输出到-Logstash">输出到 Logstash</h2>
-<p>上文的示例直接把 Filebeat 采集的日志传输到 Elasticsearch，日志数据并没有被解析或者转换。若想解析和转换日志，需要在Filebeat 和 Elasticsearch 中间引入 Logstash。现在看下把日志输出到 Logstash 的示例配置文件，<code>filebeat.yml</code> 示例：</p>
-<figure class="highlight yml"><table><tr><td class="code"><pre><span class="line"><span class="attr">filebeat.inputs:</span></span><br><span class="line"><span class="bullet">-</span> <span class="attr">type:</span> <span class="string">log</span></span><br><span class="line">  <span class="attr">paths:</span></span><br><span class="line">    <span class="bullet">-</span> <span class="string">/home/yulewei/test.log</span></span><br><span class="line"></span><br><span class="line"><span class="attr">output.logstash:</span></span><br><span class="line">  <span class="attr">hosts:</span> [<span class="string">&quot;localhost:5044&quot;</span>]</span><br></pre></td></tr></table></figure>
-<p><code>filebeat.inputs</code> 和上文的示例一样。不同的是，把 <code>output.elasticsearch.hosts</code> 改成了 <code>output.logstash.hosts</code>，指定日志输出目标 <a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/logstash-output.html">Logstash</a> 的主机地址。<code>5044</code> 这个端口是 Logstash 用于监听 Filebeat 的端口。</p>
-<p>现在来看下 Logstash 的管道配置文件，示例 <code>test-beats-stdout.conf</code>：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line">  beats &#123;</span><br><span class="line">    port =&gt; 5044</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  stdout &#123;</span><br><span class="line">    codec =&gt; rubydebug</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-<p>示例中，使用了 <a href="https://www.elastic.co/guide/en/logstash/6.5/plugins-inputs-beats.html">beats</a> 输入插件，配置的端口就 <code>filebeat.yml</code> 中指定的 <code>5044</code>。输出插件为 <code>stdout</code>，即把 Logstash 采集到日志输出到控制台。</p>
-<p>重启 filebeat 和 logstash：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ <span class="built_in">cat</span> test.log                              <span class="comment"># 查看日志文件内容</span></span><br><span class="line">hello world</span><br><span class="line">$ sudo systemctl restart filebeat.service   <span class="comment"># 重启 filebeat</span></span><br><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-beats-stdout.conf</span><br></pre></td></tr></table></figure>
-<p>控制台输出：</p>
-<figure class="highlight json"><table><tr><td class="code"><pre><span class="line"><span class="punctuation">&#123;</span></span><br><span class="line">          <span class="string">&quot;tags&quot;</span> =&gt; <span class="punctuation">[</span></span><br><span class="line">        <span class="punctuation">[</span><span class="number">0</span><span class="punctuation">]</span> <span class="string">&quot;beats_input_codec_plain_applied&quot;</span></span><br><span class="line">    <span class="punctuation">]</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;source&quot;</span> =&gt; <span class="string">&quot;/home/yulewei/test.log&quot;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;input&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;type&quot;</span> =&gt; <span class="string">&quot;log&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;message&quot;</span> =&gt; <span class="string">&quot;hello world&quot;</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;@timestamp&quot;</span> =&gt; <span class="number">2019</span><span class="number">-01</span><span class="number">-12</span>T13<span class="punctuation">:</span><span class="number">32</span><span class="punctuation">:</span><span class="number">05.131</span>Z<span class="punctuation">,</span></span><br><span class="line">      <span class="string">&quot;@version&quot;</span> =&gt; <span class="string">&quot;1&quot;</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;prospector&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;type&quot;</span> =&gt; <span class="string">&quot;log&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;beat&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;hostname&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;version&quot;</span> =&gt; <span class="string">&quot;6.5.4&quot;</span><span class="punctuation">,</span></span><br><span class="line">            <span class="string">&quot;name&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;offset&quot;</span> =&gt; <span class="number">0</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;host&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">                   <span class="string">&quot;os&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">             <span class="string">&quot;version&quot;</span> =&gt; <span class="string">&quot;16.04.4 LTS (Xenial Xerus)&quot;</span><span class="punctuation">,</span></span><br><span class="line">            <span class="string">&quot;platform&quot;</span> =&gt; <span class="string">&quot;ubuntu&quot;</span><span class="punctuation">,</span></span><br><span class="line">            <span class="string">&quot;codename&quot;</span> =&gt; <span class="string">&quot;xenial&quot;</span><span class="punctuation">,</span></span><br><span class="line">              <span class="string">&quot;family&quot;</span> =&gt; <span class="string">&quot;debian&quot;</span></span><br><span class="line">        <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;architecture&quot;</span> =&gt; <span class="string">&quot;x86_64&quot;</span><span class="punctuation">,</span></span><br><span class="line">                   <span class="string">&quot;id&quot;</span> =&gt; <span class="string">&quot;29b1bf39547d4ca9ae26c3b7656ff9e3&quot;</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;containerized&quot;</span> =&gt; <span class="literal"><span class="keyword">false</span></span><span class="punctuation">,</span></span><br><span class="line">                 <span class="string">&quot;name&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br></pre></td></tr></table></figure>
-<h1 id="集成-Filebeat-Logstash-Elasticsearch-Kibana">集成 Filebeat, Logstash, Elasticsearch, Kibana</h1>
-<p>真实场景下，日志文件可能分布在多台服务器上，同一台服务器上也可能分布着不同来源类型的日志。现在我们来尝试下，使用 Filebeat 把两个日志文件各自采集到两个不同的 Elasticsearch 索引中，并用 Kibana 可视化。有两个日志文件 <code>test-beats1.log</code> 和 <code>test-beats2.log</code>，内容如下：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ <span class="built_in">cat</span> test-beats1.log</span><br><span class="line">hello world1</span><br><span class="line">hello world1</span><br><span class="line">$ <span class="built_in">cat</span> test-beats2.log</span><br><span class="line">hello world2</span><br></pre></td></tr></table></figure>
-<p><code>filebeat.yml</code> 配置示例：</p>
-<figure class="highlight yml"><table><tr><td class="code"><pre><span class="line"><span class="attr">filebeat.inputs:</span></span><br><span class="line"><span class="bullet">-</span> <span class="attr">type:</span> <span class="string">log</span></span><br><span class="line">  <span class="attr">paths:</span></span><br><span class="line">    <span class="bullet">-</span> <span class="string">/home/yulewei/test-beats1.log</span></span><br><span class="line">  <span class="attr">fields:</span></span><br><span class="line">    <span class="attr">log_type:</span> <span class="string">test1</span></span><br><span class="line"><span class="bullet">-</span> <span class="attr">type:</span> <span class="string">log</span> </span><br><span class="line">  <span class="attr">paths:</span></span><br><span class="line">    <span class="bullet">-</span> <span class="string">/home/yulewei/test-beats2.log</span></span><br><span class="line">  <span class="attr">fields:</span></span><br><span class="line">    <span class="attr">log_type:</span> <span class="string">test2</span></span><br><span class="line"></span><br><span class="line"><span class="attr">output.logstash:</span></span><br><span class="line">  <span class="attr">hosts:</span> [<span class="string">&quot;localhost:5044&quot;</span>]</span><br></pre></td></tr></table></figure>
-<p>示例配置文件使用了 <code>filebeat.inputs.fields</code> 选项，<a href="https://www.elastic.co/guide/en/beats/filebeat/6.5/filebeat-input-log.html#filebeat-input-log-fields">fields</a> 选项用于在日志事件输出中添加字段。添加的字段名可以任意指定，示例中名为 <code>log_type</code>。因为现在在 filebeat 配置中同时导入两个日志文件，输出到同一个 logstash 中。使用这个额外字段是为了区分日志是来自 <code>test-beats1.log</code> 还是 <code>test-beats2.log</code>。示例中，第 1 个日志事件输出的 <code>log_type</code> 字段值配置为 <code>test1</code>， 第 2 个日志配置为 <code>test2</code>。</p>
-<p>管道配置文件示例，<code>test-beats-elasticsearch.conf</code>：</p>
-<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">input &#123;</span><br><span class="line">  beats &#123;</span><br><span class="line">    port =&gt; 5044</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br><span class="line">output &#123;</span><br><span class="line">  elasticsearch &#123;</span><br><span class="line">    hosts =&gt; [&quot;http://192.168.2.109:9200&quot;]</span><br><span class="line">    index =&gt; &quot;filebeat-%&#123;[fields][log_type]&#125;-%&#123;+YYYY.MM.dd&#125;&quot;</span><br><span class="line">  &#125;</span><br><span class="line">  stdout &#123;</span><br><span class="line">    codec =&gt; rubydebug</span><br><span class="line">  &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-<p>输出插件同时使用了 <code>elasticsearch</code> 和 <code>stdout</code>。配置文件中的 <code>elasticsearch</code> 输出插件的 <code>index</code> 指令被设置为 <code>filebeat-%&#123;[fields][log_type]&#125;-%&#123;+YYYY.MM.dd&#125;</code>。<code>[fields][log_type]</code> 引用的是在 <code>filebeat.yml</code> 的 <code>filebeat.inputs.fields</code> 选项添加的 <code>log_type</code> 字段（关于在配置文件引用字段的语法，可以参考<a href="https://www.elastic.co/guide/en/logstash/6.5/event-dependent-configuration.html#logstash-config-field-references">官方文档</a>）。根据 <code>log_type</code> 字段不同，把日志将输出到不同的索引中。因为 <code>filebeat.yml</code> 配置文件中设置的 <code>log_type</code> 字段是 <code>test1</code> 或者 <code>test2</code>，所以最终生成的索引名是 <code>filebeat-test1-*</code> 或者 <code>filebeat-test1-*</code>。<code>filebeat-test1-*</code> 索引中全部日志数据来自 <code>test-beats1.log</code> 日志文件，<code>filebeat-test2-*</code> 索引数据来自 <code>test-beats2.log</code>。</p>
-<p>启动 filebeat 和 logstash：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ sudo systemctl restart filebeat.service</span><br><span class="line">$ sudo /usr/share/logstash/bin/logstash -r -f ~/test-beats-elasticsearch.conf</span><br></pre></td></tr></table></figure>
-<p>控制台输出：</p>
-<figure class="highlight json"><table><tr><td class="code"><pre><span class="line">...</span><br><span class="line"><span class="punctuation">&#123;</span></span><br><span class="line">      <span class="string">&quot;@version&quot;</span> =&gt; <span class="string">&quot;1&quot;</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;host&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;name&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">       <span class="string">&quot;message&quot;</span> =&gt; <span class="string">&quot;hello world2&quot;</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;prospector&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;type&quot;</span> =&gt; <span class="string">&quot;log&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;fields&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;log_type&quot;</span> =&gt; <span class="string">&quot;test2&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;offset&quot;</span> =&gt; <span class="number">0</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;tags&quot;</span> =&gt; <span class="punctuation">[</span></span><br><span class="line">        <span class="punctuation">[</span><span class="number">0</span><span class="punctuation">]</span> <span class="string">&quot;beats_input_codec_plain_applied&quot;</span></span><br><span class="line">    <span class="punctuation">]</span><span class="punctuation">,</span></span><br><span class="line">          <span class="string">&quot;beat&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">            <span class="string">&quot;name&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;version&quot;</span> =&gt; <span class="string">&quot;6.5.4&quot;</span><span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;hostname&quot;</span> =&gt; <span class="string">&quot;ubuntu109&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span><span class="punctuation">,</span></span><br><span class="line">    <span class="string">&quot;@timestamp&quot;</span> =&gt; <span class="number">2019</span><span class="number">-01</span><span class="number">-13</span>T09<span class="punctuation">:</span><span class="number">32</span><span class="punctuation">:</span><span class="number">11.845</span>Z<span class="punctuation">,</span></span><br><span class="line">        <span class="string">&quot;source&quot;</span> =&gt; <span class="string">&quot;/home/yulewei/test-beats2.log&quot;</span><span class="punctuation">,</span></span><br><span class="line">         <span class="string">&quot;input&quot;</span> =&gt; <span class="punctuation">&#123;</span></span><br><span class="line">        <span class="string">&quot;type&quot;</span> =&gt; <span class="string">&quot;log&quot;</span></span><br><span class="line">    <span class="punctuation">&#125;</span></span><br><span class="line"><span class="punctuation">&#125;</span></span><br><span class="line">...</span><br></pre></td></tr></table></figure>
-<p>查看在 elasticsearch 上新创建的 <code>filebeat-test1-*</code> 和 <code>filebeat-test1-*</code> 索引：</p>
-<figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">$ curl http://192.168.2.109:9200/_cat/indices/filebeat-*</span><br><span class="line">yellow open filebeat-test1-2019.01.13 NLVfFJl5TQ-7I1r9KoVLaQ 5 1 5 0 31.8kb 31.8kb</span><br><span class="line">yellow open filebeat-test2-2019.01.13 NnsBp3P9Q3-mLc8chE-Tiw 5 1 3 0 24.1kb 24.1kb</span><br></pre></td></tr></table></figure>
-<p>在 kibana 上查看收集的日志：</p>
-<img width="800" alt="Kibana" title="Kibana" src="https://static.nullwy.me/filebeat-kibana.png">
-<p>整体架构上，如下图所示 [ <a href="https://www.elastic.co/guide/en/logstash/6.8/deploying-and-scaling.html">doc</a> ]：</p>
-<img width="800" alt="Deploying Logstash" title="Deploying Logstash" src="https://static.nullwy.me/logstash-deploy2.png">
-<hr>
-<p><strong>附注</strong>：本文中提到的配置文件，可以在 github 上访问得到，<a href="https://github.com/yulewei/elastic-stack-conf">elastic-stack-conf</a>。</p>
-<h1 id="参考资料">参考资料</h1>
-<ul>
-<li>发展历程| Elastic <a href="https://www.elastic.co/cn/about/history-of-elasticsearch">https://www.elastic.co/cn/about/history-of-elasticsearch</a></li>
-<li>2013-01 Welcome Drew &amp; Rashid (Kibana) <a href="https://www.elastic.co/blog/welcome-drew-rashid">https://www.elastic.co/blog/welcome-drew-rashid</a></li>
-<li>2013-08 Welcome Jordan &amp; Logstash <a href="https://www.elastic.co/blog/welcome-jordan-logstash">https://www.elastic.co/blog/welcome-jordan-logstash</a></li>
-<li>2015-05 Welcome Packetbeat, Tudor &amp; Monica <a href="https://www.elastic.co/blog/welcome-packetbeat-tudor-monica">https://www.elastic.co/blog/welcome-packetbeat-tudor-monica</a></li>
-<li>2015-11 The Beats 1.0.0 <a href="https://www.elastic.co/blog/beats-1-0-0">https://www.elastic.co/blog/beats-1-0-0</a></li>
-<li>2016-02 Heya, Elastic Stack and X-Pack <a href="https://www.elastic.co/blog/heya-elastic-stack-and-x-pack">https://www.elastic.co/blog/heya-elastic-stack-and-x-pack</a></li>
-<li>2016-10 Elastic Stack 5.0 正式发布 <a href="https://www.elastic.co/cn/blog/elastic-stack-5-0-0-released">https://www.elastic.co/cn/blog/elastic-stack-5-0-0-released</a></li>
-<li>2018-05 官方：Logstash 实用介绍 <a href="https://www.elastic.co/cn/blog/a-practical-introduction-to-logstash">https://www.elastic.co/cn/blog/a-practical-introduction-to-logstash</a></li>
-<li>Filebeat vs. Logstash — The Evolution of a Log Shipper <a href="https://logz.io/blog/filebeat-vs-logstash/">https://logz.io/blog/filebeat-vs-logstash/</a></li>
-<li>精通Elastic Stack，Gupta，2017 <a href="https://book.douban.com/subject/30326542/">https://book.douban.com/subject/30326542/</a></li>
-<li>logstash - open source log management <a href="https://web.archive.org/web/20150512135526/http://logstash.net/">https://web.archive.org/web/20150512135526/http://logstash.net/</a></li>
-<li>Logstash Config Language <a href="https://web.archive.org/web/20150907161920/http://logstash.net/docs/1.4.2/configuration">https://web.archive.org/web/20150907161920/http://logstash.net/docs/1.4.2/configuration</a></li>
-<li>Accessing Event Data and Fields in the Configuration <a href="https://www.elastic.co/guide/en/logstash/6.5/event-dependent-configuration.html">https://www.elastic.co/guide/en/logstash/6.5/event-dependent-configuration.html</a></li>
-<li>Logstash Configuration Examples <a href="https://www.elastic.co/guide/en/logstash/6.5/config-examples.html">https://www.elastic.co/guide/en/logstash/6.5/config-examples.html</a></li>
-<li>Logstash Reference: Deploying and Scaling Logstash <a href="https://www.elastic.co/guide/en/logstash/6.8/deploying-and-scaling.html">https://www.elastic.co/guide/en/logstash/6.8/deploying-and-scaling.html</a></li>
-</ul>
+<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="type">PdfReader</span> <span class="variable">reader1</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfReader</span>(<span class="string">&quot;in1.pdf&quot;</span>);</span><br><span class="line">List&lt;HashMap&lt;String, Object&gt;&gt; bookmarks = SimpleBookmark.getBookmark(reader1);</span><br><span class="line"> </span><br><span class="line"><span class="type">PdfReader</span> <span class="variable">reader2</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfReader</span>(<span class="string">&quot;in2.pdf&quot;</span>);</span><br><span class="line"><span class="type">PdfStamper</span> <span class="variable">stamper</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfStamper</span>(reader2, <span class="keyword">new</span> <span class="title class_">FileOutputStream</span>(<span class="string">&quot;out.pdf&quot;</span>));</span><br><span class="line">stamper.getWriter().setOutlines(bookmarks);</span><br><span class="line">stamper.close();</span><br></pre></td></tr></table></figure>
+<p>导出书签文件​：</p>
+<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="type">PdfReader</span> <span class="variable">reader</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfReader</span>(<span class="string">&quot;in.pdf&quot;</span>);</span><br><span class="line">List&lt;HashMap&lt;String, Object&gt;&gt; bookmarks = SimpleBookmark.getBookmark(reader);</span><br><span class="line">SimpleBookmark.exportToXML(bookmarks, <span class="keyword">new</span> <span class="title class_">FileWriter</span>(<span class="string">&quot;out.xml&quot;</span>), <span class="string">&quot;utf-8&quot;</span>, <span class="literal">false</span>);</span><br><span class="line"></span><br><span class="line">导入书签到文件​：</span><br><span class="line"><span class="type">PdfReader</span> <span class="variable">reader</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfReader</span>(<span class="string">&quot;in.pdf&quot;</span>);</span><br><span class="line">List&lt;HashMap&lt;String, Object&gt;&gt; bookmarks = SimpleBookmark.importFromXML(<span class="keyword">new</span> <span class="title class_">FileReader</span>(<span class="string">&quot;out.xml&quot;</span>));</span><br><span class="line"><span class="type">PdfStamper</span> <span class="variable">stamper</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfStamper</span>(reader, <span class="keyword">new</span> <span class="title class_">FileOutputStream</span>(<span class="string">&quot;out.pdf&quot;</span>));</span><br><span class="line">stamper.getWriter().setOutlines(bookmarks);</span><br><span class="line">stamper.close();</span><br></pre></td></tr></table></figure>
+<p>将文档1中的标注（包括超链接）转存到文档2​：</p>
+<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="type">PdfReader</span> <span class="variable">reader1</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfReader</span>(<span class="string">&quot;in1.pdf&quot;</span>);</span><br><span class="line"><span class="type">PdfReader</span> <span class="variable">reader2</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfReader</span>(<span class="string">&quot;in2.pdf&quot;</span>);</span><br><span class="line"><span class="type">Document</span> <span class="variable">document</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">Document</span>(reader2.getPageSize(<span class="number">3</span>));</span><br><span class="line"><span class="type">PdfWriter</span> <span class="variable">writer</span> <span class="operator">=</span> PdfWriter.getInstance(document, <span class="keyword">new</span> <span class="title class_">FileOutputStream</span>(<span class="string">&quot;out.pdf&quot;</span>));</span><br><span class="line">document.open();</span><br><span class="line"> </span><br><span class="line">List&lt;HashMap&lt;String, Object&gt;&gt; bookmarks = SimpleBookmark.getBookmark(reader1);</span><br><span class="line">writer.setOutlines(bookmarks);</span><br><span class="line"> </span><br><span class="line"><span class="type">int</span> <span class="variable">num</span> <span class="operator">=</span> reader1.getNumberOfPages();</span><br><span class="line"><span class="keyword">for</span> (<span class="type">int</span> <span class="variable">i</span> <span class="operator">=</span> <span class="number">1</span>; i &lt;= num; i++) &#123;</span><br><span class="line">    <span class="type">PdfImportedPage</span> <span class="variable">page</span> <span class="operator">=</span> writer.getImportedPage(reader2, i);</span><br><span class="line">    <span class="type">PdfContentByte</span> <span class="variable">content</span> <span class="operator">=</span> writer.getDirectContent();</span><br><span class="line">    content.addTemplate(page, <span class="number">0</span>, <span class="number">0</span>);</span><br><span class="line"> </span><br><span class="line">    <span class="type">PdfDictionary</span> <span class="variable">pageDict</span> <span class="operator">=</span> reader1.getPageN(i);</span><br><span class="line">    <span class="type">PdfArray</span> <span class="variable">annotArray</span> <span class="operator">=</span> pageDict.getAsArray(PdfName.ANNOTS);</span><br><span class="line">    <span class="keyword">for</span> (<span class="type">int</span> <span class="variable">j</span> <span class="operator">=</span> <span class="number">0</span>; annotArray != <span class="literal">null</span> &amp;&amp; j &lt; annotArray.size(); ++j) &#123;</span><br><span class="line">        <span class="type">PdfDictionary</span> <span class="variable">curAnnot</span> <span class="operator">=</span> annotArray.getAsDict(j);</span><br><span class="line">        <span class="type">PdfAnnotation</span> <span class="variable">pdfAnnot</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfAnnotation</span>(writer, <span class="literal">null</span>);</span><br><span class="line">        pdfAnnot.putAll(curAnnot);</span><br><span class="line">        writer.addAnnotation(pdfAnnot);</span><br><span class="line">    &#125;</span><br><span class="line">    document.newPage();</span><br><span class="line">&#125;</span><br><span class="line"> </span><br><span class="line">document.close();</span><br><span class="line">reader1.close();</span><br><span class="line">reader2.close();</span><br></pre></td></tr></table></figure>
+<p>如果仅仅读取全部链接，只需将上述代码18行开始的for循环修改为：</p>
+<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="keyword">for</span> (<span class="type">int</span> <span class="variable">j</span> <span class="operator">=</span> <span class="number">0</span>; annotArray != <span class="literal">null</span> &amp;&amp; j &lt; annotArray.size(); ++j) &#123;</span><br><span class="line">    <span class="type">PdfDictionary</span> <span class="variable">curAnnot</span> <span class="operator">=</span> annotArray.getAsDict(j);</span><br><span class="line">    <span class="keyword">if</span> (PdfName.LINK.equals(curAnnot.getAsName(PdfName.SUBTYPE))) &#123;</span><br><span class="line">        <span class="type">PdfAnnotation</span> <span class="variable">pdfAnnot</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfAnnotation</span>(writer, <span class="literal">null</span>);</span><br><span class="line">        pdfAnnot.putAll(curAnnot);</span><br><span class="line">        writer.addAnnotation(pdfAnnot);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p><strong>参考资料：</strong></p>
+<ol>
+<li>iText 5 examples - iText 5 actions and annotations <a href="http://developers.itextpdf.com/content/itext-5-examples">http://developers.itextpdf.com/content/itext-5-examples</a></li>
+<li>iText in Action, 2nd 2010, 7. Making documents interactive <a href="https://www.manning.com/books/itext-in-action-second-edition">https://www.manning.com/books/itext-in-action-second-edition</a></li>
+</ol>
 ]]></content>
       <categories>
-        <category>架构</category>
+        <category>Java</category>
       </categories>
       <tags>
-        <tag>架构</tag>
-        <tag>ELK</tag>
-        <tag>Elastic</tag>
-        <tag>日志</tag>
+        <tag>工具</tag>
+        <tag>代码</tag>
+        <tag>Java</tag>
       </tags>
   </entry>
   <entry>
@@ -1212,47 +1239,20 @@ This WRITE COMMITTED implementation of REPEATABLE READ is not typical of any oth
 <li>minBy</li>
 <li>partitioningBy</li>
 <li>reducing</li>
-<li>summarizing[Double|Int|Long]</li>
-<li>summing[Double|Int|Long]</li>
-<li>toCollection</li>
-<li>toConcurrentMap</li>
-<li>toList</li>
-<li>toMap</li>
-<li>toSet</li>
-</ul>
-]]></content>
-      <categories>
-        <category>Java</category>
-      </categories>
-      <tags>
-        <tag>Java</tag>
-      </tags>
-  </entry>
-  <entry>
-    <title>iText处理pdf书签和标注代码乱记</title>
-    <url>/2016/12/itext-pdf/</url>
-    <content><![CDATA[<p>将文档1中的书签转存到文档2​：</p>
-<span id="more"></span>
-<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="type">PdfReader</span> <span class="variable">reader1</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfReader</span>(<span class="string">&quot;in1.pdf&quot;</span>);</span><br><span class="line">List&lt;HashMap&lt;String, Object&gt;&gt; bookmarks = SimpleBookmark.getBookmark(reader1);</span><br><span class="line"> </span><br><span class="line"><span class="type">PdfReader</span> <span class="variable">reader2</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfReader</span>(<span class="string">&quot;in2.pdf&quot;</span>);</span><br><span class="line"><span class="type">PdfStamper</span> <span class="variable">stamper</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfStamper</span>(reader2, <span class="keyword">new</span> <span class="title class_">FileOutputStream</span>(<span class="string">&quot;out.pdf&quot;</span>));</span><br><span class="line">stamper.getWriter().setOutlines(bookmarks);</span><br><span class="line">stamper.close();</span><br></pre></td></tr></table></figure>
-<p>导出书签文件​：</p>
-<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="type">PdfReader</span> <span class="variable">reader</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfReader</span>(<span class="string">&quot;in.pdf&quot;</span>);</span><br><span class="line">List&lt;HashMap&lt;String, Object&gt;&gt; bookmarks = SimpleBookmark.getBookmark(reader);</span><br><span class="line">SimpleBookmark.exportToXML(bookmarks, <span class="keyword">new</span> <span class="title class_">FileWriter</span>(<span class="string">&quot;out.xml&quot;</span>), <span class="string">&quot;utf-8&quot;</span>, <span class="literal">false</span>);</span><br><span class="line"></span><br><span class="line">导入书签到文件​：</span><br><span class="line"><span class="type">PdfReader</span> <span class="variable">reader</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfReader</span>(<span class="string">&quot;in.pdf&quot;</span>);</span><br><span class="line">List&lt;HashMap&lt;String, Object&gt;&gt; bookmarks = SimpleBookmark.importFromXML(<span class="keyword">new</span> <span class="title class_">FileReader</span>(<span class="string">&quot;out.xml&quot;</span>));</span><br><span class="line"><span class="type">PdfStamper</span> <span class="variable">stamper</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfStamper</span>(reader, <span class="keyword">new</span> <span class="title class_">FileOutputStream</span>(<span class="string">&quot;out.pdf&quot;</span>));</span><br><span class="line">stamper.getWriter().setOutlines(bookmarks);</span><br><span class="line">stamper.close();</span><br></pre></td></tr></table></figure>
-<p>将文档1中的标注（包括超链接）转存到文档2​：</p>
-<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="type">PdfReader</span> <span class="variable">reader1</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfReader</span>(<span class="string">&quot;in1.pdf&quot;</span>);</span><br><span class="line"><span class="type">PdfReader</span> <span class="variable">reader2</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfReader</span>(<span class="string">&quot;in2.pdf&quot;</span>);</span><br><span class="line"><span class="type">Document</span> <span class="variable">document</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">Document</span>(reader2.getPageSize(<span class="number">3</span>));</span><br><span class="line"><span class="type">PdfWriter</span> <span class="variable">writer</span> <span class="operator">=</span> PdfWriter.getInstance(document, <span class="keyword">new</span> <span class="title class_">FileOutputStream</span>(<span class="string">&quot;out.pdf&quot;</span>));</span><br><span class="line">document.open();</span><br><span class="line"> </span><br><span class="line">List&lt;HashMap&lt;String, Object&gt;&gt; bookmarks = SimpleBookmark.getBookmark(reader1);</span><br><span class="line">writer.setOutlines(bookmarks);</span><br><span class="line"> </span><br><span class="line"><span class="type">int</span> <span class="variable">num</span> <span class="operator">=</span> reader1.getNumberOfPages();</span><br><span class="line"><span class="keyword">for</span> (<span class="type">int</span> <span class="variable">i</span> <span class="operator">=</span> <span class="number">1</span>; i &lt;= num; i++) &#123;</span><br><span class="line">    <span class="type">PdfImportedPage</span> <span class="variable">page</span> <span class="operator">=</span> writer.getImportedPage(reader2, i);</span><br><span class="line">    <span class="type">PdfContentByte</span> <span class="variable">content</span> <span class="operator">=</span> writer.getDirectContent();</span><br><span class="line">    content.addTemplate(page, <span class="number">0</span>, <span class="number">0</span>);</span><br><span class="line"> </span><br><span class="line">    <span class="type">PdfDictionary</span> <span class="variable">pageDict</span> <span class="operator">=</span> reader1.getPageN(i);</span><br><span class="line">    <span class="type">PdfArray</span> <span class="variable">annotArray</span> <span class="operator">=</span> pageDict.getAsArray(PdfName.ANNOTS);</span><br><span class="line">    <span class="keyword">for</span> (<span class="type">int</span> <span class="variable">j</span> <span class="operator">=</span> <span class="number">0</span>; annotArray != <span class="literal">null</span> &amp;&amp; j &lt; annotArray.size(); ++j) &#123;</span><br><span class="line">        <span class="type">PdfDictionary</span> <span class="variable">curAnnot</span> <span class="operator">=</span> annotArray.getAsDict(j);</span><br><span class="line">        <span class="type">PdfAnnotation</span> <span class="variable">pdfAnnot</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfAnnotation</span>(writer, <span class="literal">null</span>);</span><br><span class="line">        pdfAnnot.putAll(curAnnot);</span><br><span class="line">        writer.addAnnotation(pdfAnnot);</span><br><span class="line">    &#125;</span><br><span class="line">    document.newPage();</span><br><span class="line">&#125;</span><br><span class="line"> </span><br><span class="line">document.close();</span><br><span class="line">reader1.close();</span><br><span class="line">reader2.close();</span><br></pre></td></tr></table></figure>
-<p>如果仅仅读取全部链接，只需将上述代码18行开始的for循环修改为：</p>
-<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="keyword">for</span> (<span class="type">int</span> <span class="variable">j</span> <span class="operator">=</span> <span class="number">0</span>; annotArray != <span class="literal">null</span> &amp;&amp; j &lt; annotArray.size(); ++j) &#123;</span><br><span class="line">    <span class="type">PdfDictionary</span> <span class="variable">curAnnot</span> <span class="operator">=</span> annotArray.getAsDict(j);</span><br><span class="line">    <span class="keyword">if</span> (PdfName.LINK.equals(curAnnot.getAsName(PdfName.SUBTYPE))) &#123;</span><br><span class="line">        <span class="type">PdfAnnotation</span> <span class="variable">pdfAnnot</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">PdfAnnotation</span>(writer, <span class="literal">null</span>);</span><br><span class="line">        pdfAnnot.putAll(curAnnot);</span><br><span class="line">        writer.addAnnotation(pdfAnnot);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-<p><strong>参考资料：</strong></p>
-<ol>
-<li>iText 5 examples - iText 5 actions and annotations <a href="http://developers.itextpdf.com/content/itext-5-examples">http://developers.itextpdf.com/content/itext-5-examples</a></li>
-<li>iText in Action, 2nd 2010, 7. Making documents interactive <a href="https://www.manning.com/books/itext-in-action-second-edition">https://www.manning.com/books/itext-in-action-second-edition</a></li>
-</ol>
+<li>summarizing[Double|Int|Long]</li>
+<li>summing[Double|Int|Long]</li>
+<li>toCollection</li>
+<li>toConcurrentMap</li>
+<li>toList</li>
+<li>toMap</li>
+<li>toSet</li>
+</ul>
 ]]></content>
       <categories>
         <category>Java</category>
       </categories>
       <tags>
         <tag>Java</tag>
-        <tag>工具</tag>
-        <tag>代码</tag>
       </tags>
   </entry>
   <entry>
@@ -1554,6 +1554,91 @@ An asynchronous I/O operation does not cause the requesting process to be blocke
         <tag>并发</tag>
       </tags>
   </entry>
+  <entry>
+    <title>Java书籍资料整理</title>
+    <url>/2016/11/java-books/</url>
+    <content><![CDATA[<p><a href="https://en.wikipedia.org/wiki/Template:Java_%28software_platform%29">https://en.wikipedia.org/wiki/Template:Java_(software_platform)</a><br>
+<a href="http://c2.com/cgi/wiki?JavaIdioms">http://c2.com/cgi/wiki?JavaIdioms</a><br>
+<a href="http://c2.com/cgi/wiki?JavaDesignFlaws">http://c2.com/cgi/wiki?JavaDesignFlaws</a> Java语言设计缺陷</p>
+<ol>
+<li>2011-06 Java Books Reading Order <a href="http://stackoverflow.com/q/6341593">http://stackoverflow.com/q/6341593</a></li>
+<li>2009-03 Java书籍Top 10 <a href="http://coolshell.cn/articles/14.html">http://coolshell.cn/articles/14.html</a></li>
+<li>2012-03 JVM程序员的阅读清单 <a href="http://blog.jobbole.com/15342/">http://blog.jobbole.com/15342/</a></li>
+</ol>
+<span id="more"></span>
+<hr>
+<h1 id="Java官方文档与书籍">Java官方文档与书籍</h1>
+<p><a href="http://docs.oracle.com/javase/8/">http://docs.oracle.com/javase/8/</a><br>
+<a href="http://docs.oracle.com/javase/tutorial/">http://docs.oracle.com/javase/tutorial/</a></p>
+<p>Java Language and Virtual Machine Specifications <a href="http://docs.oracle.com/javase/specs/">http://docs.oracle.com/javase/specs/</a></p>
+<p>Sun官方Addison-Wesley出版的Java Series，<a href="http://www.informit.com/imprint/series_detail.aspx?ser=334838">link</a></p>
+<ol>
+<li>1996-2014，<a href="http://en.wikipedia.org/wiki/James_Gosling">Gosling</a>, <a href="http://en.wikipedia.org/wiki/Bill_Joy">Joy</a>, <a href="http://en.wikipedia.org/wiki/Guy_L._Steele">Steele</a>, <a href="http://en.wikipedia.org/wiki/Gilad_Bracha">Bracha</a>，《Java语言规范》（The Java Language Specification, <a href="http://amzn.com/0201310082">2nd</a> 2000, <a href="http://amzn.com/0321246780">3rd</a> 2005, <a href="http://amzn.com/013390069X">Java SE 8</a> 2014），Java 7 <a href="http://docs.oracle.com/javase/specs/jls/se7/html/index.html">online</a>，第3版<a href="http://book.douban.com/subject/1837615/">豆瓣</a>，Java 8中文<a href="https://book.douban.com/subject/26740358/">豆瓣</a></li>
+<li>1996-2013，Lindholm, Yellin, <a href="http://en.wikipedia.org/wiki/Gilad_Bracha">Bracha</a>, etc，《<strong>Java虚拟机规范</strong>》（The Java Virtual Machine Specification, <a href="http://amzn.com/020163452X">1st</a> 1996, <a href="http://amzn.com/0201432943">2nd</a> 1999, <a href="http://www.amazon.com/Virtual-Machine-Specification-Edition-Series/dp/0133260445">Java SE 7</a> 2013, <a href="http://amzn.com/013390590X">Java SE 8</a> 2014），Java 7 <a href="http://docs.oracle.com/javase/specs/jvms/se7/html/">online</a>，<a href="http://book.douban.com/subject/25792515/">豆瓣</a></li>
+<li>1996-2005，<a href="http://en.wikipedia.org/wiki/Ken_Arnold">Arnold</a>, <a href="http://en.wikipedia.org/wiki/James_Gosling">Gosling</a>, etc，《Java程序设计语言》（The Java Programming Language, 1st 1996，2nd 1997，<a href="http://amzn.com/0321349806">4th</a> 2005），第4版<a href="http://book.douban.com/subject/1908274/">豆瓣</a>：涵盖J2SE 5.0，内容比《Java编程思想》精简，条理更清晰，覆盖面更广</li>
+<li>1998-2013，《Java教程》（The Java Tutorial: A Short Course on the Basics, <a href="http://amzn.com/0201310074">2nd</a> 1998, <a href="http://amzn.com/0201703939%20">3rd</a> 2001, <a href="http://amzn.com/0321334205">4th</a> 2006, <a href="http://www.amazon.com/The-Java-Tutorial-Course-Edition/dp/0132761696">5th</a> 2013），第4版<a href="http://book.douban.com/subject/2208538/">豆瓣</a>：全书415页，涵盖Java 5.0和6.0，内容比《Java程序设计语言》简单，是官方在线指定文档</li>
+<li>1997，《Java经典问答》（The Java Faq, 1997），<a href="http://book.douban.com/subject/1244713/">豆瓣</a></li>
+<li>1997.06，《Java语言编码规范》（Code Conventions for the Java Programming Language），<a href="http://oracle.com">oracle.com</a> <a href="http://www.oracle.com/technetwork/java/index-135089.html">html</a>, <a href="http://www.oracle.com/technetwork/java/codeconventions-150003.pdf">pdf</a></li>
+</ol>
+<hr>
+<h1 id="Java书籍">Java书籍</h1>
+<ol>
+<li>1998-2006，<a href="http://en.wikipedia.org/wiki/Bruce_Eckel">Bruce Eckel</a>，《Java编程思想》（<a href="http://en.wikipedia.org/wiki/Thinking_in_Java">Thinking in Java</a>, <a href="http://amzn.com/0136597238">1st</a> 1998, <a href="http://www.amazon.com/Thinking-Java-4th-Bruce-Eckel/dp/0131872486">4th</a> 2006），<a href="http://mindview.net/Books/TIJ4">home</a>，<a href="http://book.douban.com/subject/2130190/">豆瓣</a>：内容有深度，但组织混乱，抓不住脉络，杂糅了Java与C++比较、设计模式等内容，2003年Jolt震撼大奖</li>
+<li>1996-2012，Cay S. Horstmann，《Java核心技术，2卷》（Core Java 2, <a href="http://dl.acm.org/citation.cfm?id=230334">1st</a> 1996, <a href="http://www.informit.com/store/core-java-volume-i-fundamentals-9780132354769">8th</a> 2007, <a href="http://www.amazon.com/Core-Java-I--Fundamentals-9th/dp/0137081898">9th</a> 2012），<a href="http://www.horstmann.com/corejava.html">home</a>，第10版卷1<a href="https://book.douban.com/subject/26880667/">豆瓣</a>、卷2<a href="http://book.douban.com/subject/25841326/">豆瓣</a></li>
+<li>2001、2008，<a href="http://en.wikipedia.org/wiki/Joshua_Bloch">Joshua Bloch</a>，《Effective Java》，<a href="http://www.amazon.com/Effective-Java-Edition-Joshua-Bloch/dp/0321356683">2nd</a> 2008，<a href="http://book.douban.com/subject/3360807/">豆瓣</a>：2002年Jolt震撼大奖</li>
+<li>2005，<a href="http://en.wikipedia.org/wiki/Joshua_Bloch">Joshua Bloch</a> &amp; Neal Gafter，《Java解惑》（Java Puzzlers: Traps, Pitfalls, and Corner Cases, <a href="http://www.amazon.com/Java%C2%BF-Puzzlers-Traps-Pitfalls-Corner/dp/032133678X">amazon</a>），<a href="http://www.javapuzzlers.com/">home</a>，<a href="http://www.ituring.com.cn/book/88">图灵</a><a href="http://www.ituring.com.cn/book/88">2010</a>，<a href="http://book.douban.com/subject/5362860/">豆瓣</a></li>
+<li>Java语言精粹 Java: The Good Parts <a href="http://book.douban.com/subject/6516576/">http://book.douban.com/subject/6516576/</a></li>
+<li>2006，Metsker，《Java设计模式》（Design Patterns in Java, <a href="http://amzn.com/0321333020">amazon</a>），<a href="http://book.douban.com/subject/1972333/">豆瓣</a>，修订版<a href="http://book.douban.com/subject/11629400/">豆瓣</a></li>
+<li><a href="http://en.wikipedia.org/wiki/Herbert_Schildt">Herbert Schildt</a>，《Java完全参考手册》（Java: The Complete Reference, <a href="http://amzn.com/0071606300">8th</a> 2011），第8版<a href="http://book.douban.com/subject/19955764/">豆瓣</a>，第9版<a href="http://book.douban.com/subject/26556574/">豆瓣</a>：Oracle Press，全书1105页，参考手册，可读性不高，涵盖Java 7</li>
+<li><a href="http://en.wikipedia.org/wiki/Herbert_Schildt">Herbert Schildt</a>，《Java编程入门教程》（Java: A Beginner's Guide），第6版<a href="http://book.douban.com/subject/26320992/">豆瓣</a></li>
+<li>2012，Sarang，《Java 7编程高级进阶》（Java Programming, <a href="http://amzn.com/007163360X">amazon</a>），<a href="http://book.douban.com/subject/22226750/">豆瓣</a>：Oracle Press，内容条理清晰，但<strong>深度、广度不够</strong>，Java虚拟机技术总监Pampuch作序，客户端软件的首席架构师Coward技术校审</li>
+<li>Jakarta Commons Cookbook中文版 <a href="https://book.douban.com/subject/1936665/">https://book.douban.com/subject/1936665/</a></li>
+</ol>
+<p><a href="https://github.com/iluwatar/java-design-patterns">https://github.com/iluwatar/java-design-patterns</a></p>
+<h1 id="Java并发编程">Java并发编程</h1>
+<ol>
+<li>2006，<a href="https://www.linkedin.com/in/briangoetz">Goetz</a>, Peierls, <a href="http://en.wikipedia.org/wiki/Joshua_Bloch">Joshua Bloch</a>, <a href="http://en.wikipedia.org/wiki/Doug_Lea">Doug Lea</a> &amp; etc，《Java并发编程实战》（Java Concurrency in Practice, <a href="http://www.amazon.com/Java-Concurrency-Practice-Brian-Goetz/dp/0321349601">amazon</a>），<a href="http://book.douban.com/subject/10484692/">豆瓣</a>：top1书籍，Sun官方书籍，相对偏向理论的并发编程书籍见“多处理器编程的艺术，修订版2012”</li>
+<li>2011，Subramaniam，《Java虚拟机并发编程》（Programming Concurrency on the JVM, <a href="http://www.amazon.com/Programming-Concurrency-JVM-Mastering-Synchronization/dp/193435676X">amazon</a>），<a href="http://book.douban.com/subject/24533312/">豆瓣</a>：全书216页，主要讲Scala下的Akka</li>
+<li>1999，<a href="http://en.wikipedia.org/wiki/Doug_Lea">Doug Lea</a>，《Java并发编程：设计原则与模式》（Concurrent Programming in Java, <a href="http://amzn.com/0201310090">2nd</a> 1999），<a href="http://book.douban.com/subject/1244021/">豆瓣</a>：过时</li>
+<li>2012，[西] González，《Java 7并发编程实战手册》（Java 7 Concurrency Cookbook, <a href="http://amzn.com/1849687889%20">amazon</a>），<a href="http://book.douban.com/subject/25844475/">豆瓣</a>：amazon评价不高，可作辅助阅读，难度低于Goetz版</li>
+</ol>
+<p>2012-12 Review : Java 7 Concurrency Cookbook，原文：<a href="http://www.mkyong.com/book-review/review-java-7-concurrency-cookbook/">mkyong.com</a>，译文：<a href="http://www.importnew.com/2346.html">importnew.com</a></p>
+<h1 id="Java高级内容（Java-7-Java-8）">Java高级内容（Java 7 &amp; Java 8）</h1>
+<ol>
+<li>2012，Evans &amp; Verburg，《Java程序员修炼之道》（The Well-Grounded Java Developer, <a href="http://www.amazon.com/The-Well-Grounded-Java-Developer-Programming/dp/1617290068">amazon</a>），<a href="http://www.ituring.com.cn/book/1027">图灵2013</a>，<a href="http://book.douban.com/subject/24841235/">豆瓣</a>：全面解读Groovy、Scala在JVM上的应用</li>
+<li>2014，《Java 8实战》（Java 8 in Action, <a href="http://amzn.com/1617291994">amazon</a>），<a href="https://book.douban.com/subject/26772632/">豆瓣</a></li>
+<li>2014，Horstmann，《写给大忙人看的Java SE 8》（Java SE 8 for the Really Impatient, <a href="https://amzn.com/0321927761">amazon</a>），<a href="http://book.douban.com/subject/26274206/">豆瓣</a>：极好的全面介绍Java 8</li>
+<li>2014，《Java 8函数式编程》（Java 8 Lambdas, <a href="https://amzn.com/1449370772">amazon</a>），<a href="http://book.douban.com/subject/26346017/">豆瓣</a></li>
+<li>2014，Subramaniam，“Functional Programming in Java”, <a href="http://amzn.com/1937785467">amazon</a>，<a href="http://book.douban.com/subject/25830739/">豆瓣</a></li>
+</ol>
+<h1 id="Java虚拟机与底层书籍">Java虚拟机与底层书籍</h1>
+<ol>
+<li>2014，Scott Oaks，《Java性能权威指南》（Java Performance: The Definitive Guide），<a href="https://book.douban.com/subject/26740520/">豆瓣</a></li>
+<li>2011，Charlie Hunt, Binu John，《Java性能优化权威指南》（Java Performance, <a href="http://www.amazon.com/Java-Performance-Charlie-Hunt/dp/0137142528">amazon</a>），<a href="http://book.douban.com/subject/25828043/">豆瓣</a>：第1作者是Oracle JVM性能主管工程师</li>
+<li>2000，Bill Venners，《深入Java虚拟机》（Inside the Java Virtual Machine, <a href="http://www.amazon.com/Inside-Java-2-Virtual-Machine/dp/0071350934">2nd</a> 2000），<a href="http://book.douban.com/subject/1138768/">豆瓣</a></li>
+<li>2011、2013，周志明，《深入理解Java虚拟机：VM高级特性与最佳实践》，<a href="http://book.douban.com/subject/24722612/">豆瓣</a>：相比较陈涛版更偏向概念和理论</li>
+<li>2014，陈涛，《HotSpot实战》，<a href="http://book.douban.com/subject/25847620/">豆瓣</a>：内容有大量的HotSpot源码解析</li>
+<li>2015，高翔龙，《Java虚拟机精讲》，<a href="http://book.douban.com/subject/26353219/">豆瓣</a></li>
+<li>2014，《大规模Java平台虚拟化与调优》</li>
+<li>Scott Oaks, Java Performance: The Definitive Guide，<a href="http://book.douban.com/subject/25872755/">豆瓣</a></li>
+<li>2015，OpenJDK cookbook，<a href="http://amzn.com/1849698406">amazon</a></li>
+</ol>
+<hr>
+<h1 id="偏向Java-EE">偏向Java EE</h1>
+<ol>
+<li>2004，<a href="http://en.wikipedia.org/wiki/Bruce_Tate">Bruce Tate</a>，《轻快的Java》（Better, Faster, Lighter Java, <a href="http://shop.oreilly.com/product/9780596006761.do">O'Reilly</a>, <a href="http://www.amazon.com/Better-Faster-Lighter-Java-Bruce/dp/0596006764">amazon</a>），<a href="http://book.douban.com/subject/1911882/">豆瓣</a>：2005年Jolt震撼大奖</li>
+<li>2005，<a href="http://en.wikipedia.org/wiki/Bruce_Tate">Bruce Tate</a>，《超越Java：探讨程序语言的未来》（Beyond Java, <a href="http://shop.oreilly.com/product/9780596100940.do">O'Reilly</a>, <a href="http://www.amazon.com/Beyond-Java-Bruce-Tate/dp/0596100949">amazon</a>），<a href="http://book.douban.com/subject/2043934/">豆瓣</a></li>
+<li>2010，<a href="http://en.wikipedia.org/wiki/Bruce_Tate">Bruce Tate</a>，《七周七语言：理解多种编程范型》（Seven Languages in Seven Weeks, <a href="http://pragprog.com/book/btlang/seven-languages-in-seven-weeks">Pragmatic</a>, <a href="http://www.amazon.com/Seven-Languages-Weeks-Programming-Programmers/dp/193435659X">amazon</a>），<a href="http://book.douban.com/subject/10555435/">豆瓣</a>：2011年Jolt生产力大奖</li>
+</ol>
+]]></content>
+      <categories>
+        <category>Java</category>
+      </categories>
+      <tags>
+        <tag>书籍</tag>
+        <tag>Java</tag>
+      </tags>
+  </entry>
   <entry>
     <title>Java Agent 学习笔记</title>
     <url>/2018/10/java-agent/</url>
@@ -1656,91 +1741,6 @@ An asynchronous I/O operation does not cause the requesting process to be blocke
         <tag>byte-buddy</tag>
       </tags>
   </entry>
-  <entry>
-    <title>Java书籍资料整理</title>
-    <url>/2016/11/java-books/</url>
-    <content><![CDATA[<p><a href="https://en.wikipedia.org/wiki/Template:Java_%28software_platform%29">https://en.wikipedia.org/wiki/Template:Java_(software_platform)</a><br>
-<a href="http://c2.com/cgi/wiki?JavaIdioms">http://c2.com/cgi/wiki?JavaIdioms</a><br>
-<a href="http://c2.com/cgi/wiki?JavaDesignFlaws">http://c2.com/cgi/wiki?JavaDesignFlaws</a> Java语言设计缺陷</p>
-<ol>
-<li>2011-06 Java Books Reading Order <a href="http://stackoverflow.com/q/6341593">http://stackoverflow.com/q/6341593</a></li>
-<li>2009-03 Java书籍Top 10 <a href="http://coolshell.cn/articles/14.html">http://coolshell.cn/articles/14.html</a></li>
-<li>2012-03 JVM程序员的阅读清单 <a href="http://blog.jobbole.com/15342/">http://blog.jobbole.com/15342/</a></li>
-</ol>
-<span id="more"></span>
-<hr>
-<h1 id="Java官方文档与书籍">Java官方文档与书籍</h1>
-<p><a href="http://docs.oracle.com/javase/8/">http://docs.oracle.com/javase/8/</a><br>
-<a href="http://docs.oracle.com/javase/tutorial/">http://docs.oracle.com/javase/tutorial/</a></p>
-<p>Java Language and Virtual Machine Specifications <a href="http://docs.oracle.com/javase/specs/">http://docs.oracle.com/javase/specs/</a></p>
-<p>Sun官方Addison-Wesley出版的Java Series，<a href="http://www.informit.com/imprint/series_detail.aspx?ser=334838">link</a></p>
-<ol>
-<li>1996-2014，<a href="http://en.wikipedia.org/wiki/James_Gosling">Gosling</a>, <a href="http://en.wikipedia.org/wiki/Bill_Joy">Joy</a>, <a href="http://en.wikipedia.org/wiki/Guy_L._Steele">Steele</a>, <a href="http://en.wikipedia.org/wiki/Gilad_Bracha">Bracha</a>，《Java语言规范》（The Java Language Specification, <a href="http://amzn.com/0201310082">2nd</a> 2000, <a href="http://amzn.com/0321246780">3rd</a> 2005, <a href="http://amzn.com/013390069X">Java SE 8</a> 2014），Java 7 <a href="http://docs.oracle.com/javase/specs/jls/se7/html/index.html">online</a>，第3版<a href="http://book.douban.com/subject/1837615/">豆瓣</a>，Java 8中文<a href="https://book.douban.com/subject/26740358/">豆瓣</a></li>
-<li>1996-2013，Lindholm, Yellin, <a href="http://en.wikipedia.org/wiki/Gilad_Bracha">Bracha</a>, etc，《<strong>Java虚拟机规范</strong>》（The Java Virtual Machine Specification, <a href="http://amzn.com/020163452X">1st</a> 1996, <a href="http://amzn.com/0201432943">2nd</a> 1999, <a href="http://www.amazon.com/Virtual-Machine-Specification-Edition-Series/dp/0133260445">Java SE 7</a> 2013, <a href="http://amzn.com/013390590X">Java SE 8</a> 2014），Java 7 <a href="http://docs.oracle.com/javase/specs/jvms/se7/html/">online</a>，<a href="http://book.douban.com/subject/25792515/">豆瓣</a></li>
-<li>1996-2005，<a href="http://en.wikipedia.org/wiki/Ken_Arnold">Arnold</a>, <a href="http://en.wikipedia.org/wiki/James_Gosling">Gosling</a>, etc，《Java程序设计语言》（The Java Programming Language, 1st 1996，2nd 1997，<a href="http://amzn.com/0321349806">4th</a> 2005），第4版<a href="http://book.douban.com/subject/1908274/">豆瓣</a>：涵盖J2SE 5.0，内容比《Java编程思想》精简，条理更清晰，覆盖面更广</li>
-<li>1998-2013，《Java教程》（The Java Tutorial: A Short Course on the Basics, <a href="http://amzn.com/0201310074">2nd</a> 1998, <a href="http://amzn.com/0201703939%20">3rd</a> 2001, <a href="http://amzn.com/0321334205">4th</a> 2006, <a href="http://www.amazon.com/The-Java-Tutorial-Course-Edition/dp/0132761696">5th</a> 2013），第4版<a href="http://book.douban.com/subject/2208538/">豆瓣</a>：全书415页，涵盖Java 5.0和6.0，内容比《Java程序设计语言》简单，是官方在线指定文档</li>
-<li>1997，《Java经典问答》（The Java Faq, 1997），<a href="http://book.douban.com/subject/1244713/">豆瓣</a></li>
-<li>1997.06，《Java语言编码规范》（Code Conventions for the Java Programming Language），<a href="http://oracle.com">oracle.com</a> <a href="http://www.oracle.com/technetwork/java/index-135089.html">html</a>, <a href="http://www.oracle.com/technetwork/java/codeconventions-150003.pdf">pdf</a></li>
-</ol>
-<hr>
-<h1 id="Java书籍">Java书籍</h1>
-<ol>
-<li>1998-2006，<a href="http://en.wikipedia.org/wiki/Bruce_Eckel">Bruce Eckel</a>，《Java编程思想》（<a href="http://en.wikipedia.org/wiki/Thinking_in_Java">Thinking in Java</a>, <a href="http://amzn.com/0136597238">1st</a> 1998, <a href="http://www.amazon.com/Thinking-Java-4th-Bruce-Eckel/dp/0131872486">4th</a> 2006），<a href="http://mindview.net/Books/TIJ4">home</a>，<a href="http://book.douban.com/subject/2130190/">豆瓣</a>：内容有深度，但组织混乱，抓不住脉络，杂糅了Java与C++比较、设计模式等内容，2003年Jolt震撼大奖</li>
-<li>1996-2012，Cay S. Horstmann，《Java核心技术，2卷》（Core Java 2, <a href="http://dl.acm.org/citation.cfm?id=230334">1st</a> 1996, <a href="http://www.informit.com/store/core-java-volume-i-fundamentals-9780132354769">8th</a> 2007, <a href="http://www.amazon.com/Core-Java-I--Fundamentals-9th/dp/0137081898">9th</a> 2012），<a href="http://www.horstmann.com/corejava.html">home</a>，第10版卷1<a href="https://book.douban.com/subject/26880667/">豆瓣</a>、卷2<a href="http://book.douban.com/subject/25841326/">豆瓣</a></li>
-<li>2001、2008，<a href="http://en.wikipedia.org/wiki/Joshua_Bloch">Joshua Bloch</a>，《Effective Java》，<a href="http://www.amazon.com/Effective-Java-Edition-Joshua-Bloch/dp/0321356683">2nd</a> 2008，<a href="http://book.douban.com/subject/3360807/">豆瓣</a>：2002年Jolt震撼大奖</li>
-<li>2005，<a href="http://en.wikipedia.org/wiki/Joshua_Bloch">Joshua Bloch</a> &amp; Neal Gafter，《Java解惑》（Java Puzzlers: Traps, Pitfalls, and Corner Cases, <a href="http://www.amazon.com/Java%C2%BF-Puzzlers-Traps-Pitfalls-Corner/dp/032133678X">amazon</a>），<a href="http://www.javapuzzlers.com/">home</a>，<a href="http://www.ituring.com.cn/book/88">图灵</a><a href="http://www.ituring.com.cn/book/88">2010</a>，<a href="http://book.douban.com/subject/5362860/">豆瓣</a></li>
-<li>Java语言精粹 Java: The Good Parts <a href="http://book.douban.com/subject/6516576/">http://book.douban.com/subject/6516576/</a></li>
-<li>2006，Metsker，《Java设计模式》（Design Patterns in Java, <a href="http://amzn.com/0321333020">amazon</a>），<a href="http://book.douban.com/subject/1972333/">豆瓣</a>，修订版<a href="http://book.douban.com/subject/11629400/">豆瓣</a></li>
-<li><a href="http://en.wikipedia.org/wiki/Herbert_Schildt">Herbert Schildt</a>，《Java完全参考手册》（Java: The Complete Reference, <a href="http://amzn.com/0071606300">8th</a> 2011），第8版<a href="http://book.douban.com/subject/19955764/">豆瓣</a>，第9版<a href="http://book.douban.com/subject/26556574/">豆瓣</a>：Oracle Press，全书1105页，参考手册，可读性不高，涵盖Java 7</li>
-<li><a href="http://en.wikipedia.org/wiki/Herbert_Schildt">Herbert Schildt</a>，《Java编程入门教程》（Java: A Beginner's Guide），第6版<a href="http://book.douban.com/subject/26320992/">豆瓣</a></li>
-<li>2012，Sarang，《Java 7编程高级进阶》（Java Programming, <a href="http://amzn.com/007163360X">amazon</a>），<a href="http://book.douban.com/subject/22226750/">豆瓣</a>：Oracle Press，内容条理清晰，但<strong>深度、广度不够</strong>，Java虚拟机技术总监Pampuch作序，客户端软件的首席架构师Coward技术校审</li>
-<li>Jakarta Commons Cookbook中文版 <a href="https://book.douban.com/subject/1936665/">https://book.douban.com/subject/1936665/</a></li>
-</ol>
-<p><a href="https://github.com/iluwatar/java-design-patterns">https://github.com/iluwatar/java-design-patterns</a></p>
-<h1 id="Java并发编程">Java并发编程</h1>
-<ol>
-<li>2006，<a href="https://www.linkedin.com/in/briangoetz">Goetz</a>, Peierls, <a href="http://en.wikipedia.org/wiki/Joshua_Bloch">Joshua Bloch</a>, <a href="http://en.wikipedia.org/wiki/Doug_Lea">Doug Lea</a> &amp; etc，《Java并发编程实战》（Java Concurrency in Practice, <a href="http://www.amazon.com/Java-Concurrency-Practice-Brian-Goetz/dp/0321349601">amazon</a>），<a href="http://book.douban.com/subject/10484692/">豆瓣</a>：top1书籍，Sun官方书籍，相对偏向理论的并发编程书籍见“多处理器编程的艺术，修订版2012”</li>
-<li>2011，Subramaniam，《Java虚拟机并发编程》（Programming Concurrency on the JVM, <a href="http://www.amazon.com/Programming-Concurrency-JVM-Mastering-Synchronization/dp/193435676X">amazon</a>），<a href="http://book.douban.com/subject/24533312/">豆瓣</a>：全书216页，主要讲Scala下的Akka</li>
-<li>1999，<a href="http://en.wikipedia.org/wiki/Doug_Lea">Doug Lea</a>，《Java并发编程：设计原则与模式》（Concurrent Programming in Java, <a href="http://amzn.com/0201310090">2nd</a> 1999），<a href="http://book.douban.com/subject/1244021/">豆瓣</a>：过时</li>
-<li>2012，[西] González，《Java 7并发编程实战手册》（Java 7 Concurrency Cookbook, <a href="http://amzn.com/1849687889%20">amazon</a>），<a href="http://book.douban.com/subject/25844475/">豆瓣</a>：amazon评价不高，可作辅助阅读，难度低于Goetz版</li>
-</ol>
-<p>2012-12 Review : Java 7 Concurrency Cookbook，原文：<a href="http://www.mkyong.com/book-review/review-java-7-concurrency-cookbook/">mkyong.com</a>，译文：<a href="http://www.importnew.com/2346.html">importnew.com</a></p>
-<h1 id="Java高级内容（Java-7-Java-8）">Java高级内容（Java 7 &amp; Java 8）</h1>
-<ol>
-<li>2012，Evans &amp; Verburg，《Java程序员修炼之道》（The Well-Grounded Java Developer, <a href="http://www.amazon.com/The-Well-Grounded-Java-Developer-Programming/dp/1617290068">amazon</a>），<a href="http://www.ituring.com.cn/book/1027">图灵2013</a>，<a href="http://book.douban.com/subject/24841235/">豆瓣</a>：全面解读Groovy、Scala在JVM上的应用</li>
-<li>2014，《Java 8实战》（Java 8 in Action, <a href="http://amzn.com/1617291994">amazon</a>），<a href="https://book.douban.com/subject/26772632/">豆瓣</a></li>
-<li>2014，Horstmann，《写给大忙人看的Java SE 8》（Java SE 8 for the Really Impatient, <a href="https://amzn.com/0321927761">amazon</a>），<a href="http://book.douban.com/subject/26274206/">豆瓣</a>：极好的全面介绍Java 8</li>
-<li>2014，《Java 8函数式编程》（Java 8 Lambdas, <a href="https://amzn.com/1449370772">amazon</a>），<a href="http://book.douban.com/subject/26346017/">豆瓣</a></li>
-<li>2014，Subramaniam，“Functional Programming in Java”, <a href="http://amzn.com/1937785467">amazon</a>，<a href="http://book.douban.com/subject/25830739/">豆瓣</a></li>
-</ol>
-<h1 id="Java虚拟机与底层书籍">Java虚拟机与底层书籍</h1>
-<ol>
-<li>2014，Scott Oaks，《Java性能权威指南》（Java Performance: The Definitive Guide），<a href="https://book.douban.com/subject/26740520/">豆瓣</a></li>
-<li>2011，Charlie Hunt, Binu John，《Java性能优化权威指南》（Java Performance, <a href="http://www.amazon.com/Java-Performance-Charlie-Hunt/dp/0137142528">amazon</a>），<a href="http://book.douban.com/subject/25828043/">豆瓣</a>：第1作者是Oracle JVM性能主管工程师</li>
-<li>2000，Bill Venners，《深入Java虚拟机》（Inside the Java Virtual Machine, <a href="http://www.amazon.com/Inside-Java-2-Virtual-Machine/dp/0071350934">2nd</a> 2000），<a href="http://book.douban.com/subject/1138768/">豆瓣</a></li>
-<li>2011、2013，周志明，《深入理解Java虚拟机：VM高级特性与最佳实践》，<a href="http://book.douban.com/subject/24722612/">豆瓣</a>：相比较陈涛版更偏向概念和理论</li>
-<li>2014，陈涛，《HotSpot实战》，<a href="http://book.douban.com/subject/25847620/">豆瓣</a>：内容有大量的HotSpot源码解析</li>
-<li>2015，高翔龙，《Java虚拟机精讲》，<a href="http://book.douban.com/subject/26353219/">豆瓣</a></li>
-<li>2014，《大规模Java平台虚拟化与调优》</li>
-<li>Scott Oaks, Java Performance: The Definitive Guide，<a href="http://book.douban.com/subject/25872755/">豆瓣</a></li>
-<li>2015，OpenJDK cookbook，<a href="http://amzn.com/1849698406">amazon</a></li>
-</ol>
-<hr>
-<h1 id="偏向Java-EE">偏向Java EE</h1>
-<ol>
-<li>2004，<a href="http://en.wikipedia.org/wiki/Bruce_Tate">Bruce Tate</a>，《轻快的Java》（Better, Faster, Lighter Java, <a href="http://shop.oreilly.com/product/9780596006761.do">O'Reilly</a>, <a href="http://www.amazon.com/Better-Faster-Lighter-Java-Bruce/dp/0596006764">amazon</a>），<a href="http://book.douban.com/subject/1911882/">豆瓣</a>：2005年Jolt震撼大奖</li>
-<li>2005，<a href="http://en.wikipedia.org/wiki/Bruce_Tate">Bruce Tate</a>，《超越Java：探讨程序语言的未来》（Beyond Java, <a href="http://shop.oreilly.com/product/9780596100940.do">O'Reilly</a>, <a href="http://www.amazon.com/Beyond-Java-Bruce-Tate/dp/0596100949">amazon</a>），<a href="http://book.douban.com/subject/2043934/">豆瓣</a></li>
-<li>2010，<a href="http://en.wikipedia.org/wiki/Bruce_Tate">Bruce Tate</a>，《七周七语言：理解多种编程范型》（Seven Languages in Seven Weeks, <a href="http://pragprog.com/book/btlang/seven-languages-in-seven-weeks">Pragmatic</a>, <a href="http://www.amazon.com/Seven-Languages-Weeks-Programming-Programmers/dp/193435659X">amazon</a>），<a href="http://book.douban.com/subject/10555435/">豆瓣</a>：2011年Jolt生产力大奖</li>
-</ol>
-]]></content>
-      <categories>
-        <category>Java</category>
-      </categories>
-      <tags>
-        <tag>书籍</tag>
-        <tag>Java</tag>
-      </tags>
-  </entry>
   <entry>
     <title>Java Executor 框架笔记</title>
     <url>/2017/03/java-executor/</url>
@@ -2388,43 +2388,6 @@ Generates only some kinds of debugging information, specified by a comma separat
         <tag>语言</tag>
       </tags>
   </entry>
-  <entry>
-    <title>MyBatis 生成器的表注释</title>
-    <url>/2016/12/mybatis-generator/</url>
-    <content><![CDATA[<p><a href="https://en.wikipedia.org/wiki/MyBatis">MyBatis</a>是流行的持久化框架，通过抽象底层的JDBC代码，在类对象和数据库列之间自动映射SQL的参数和结果，以SQL为映射的间接层，实现SQL映射器。<a href="http://www.mybatis.org/generator/">MyBatis Generator</a> (MBG) 是一个Mybatis的代码生成器，内省数据库的表，然后自动生成映射表的实体类，并生成CRUD（插入，查询，更新，删除）操作的样板代码。MyBatis，之前所在的公司在用，生成器也在用。虽然生成器大大提供了开发效率，但生成的代码可读性比较低，尤其是自动生成的实体类，如下：</p>
-<span id="more"></span>
-<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment">* This field was generated by MyBatis Generator. This field corresponds to the database column author.book_id</span></span><br><span class="line"><span class="comment">* <span class="doctag">@mbggenerated</span>  Tue Jan 19 13:37:24 CST 2016</span></span><br><span class="line"><span class="comment">*/</span></span><br><span class="line"><span class="keyword">private</span> Integer bookId;</span><br></pre></td></tr></table></figure>
-<p>这些自动生成注释，没有实质性信息，其实真正有用的是，设计表时，该字段的用途，即表字段的注释。</p>
-<h1 id="addRemarkComments选项">addRemarkComments选项</h1>
-<p>庆幸的是，MyBatis生成器在版本1.3.3中添加了，<code>addRemarkComments</code>选项 [<a href="https://github.com/mybatis/generator/issues/23">github</a>]，可以在生成的实体类中附带表字段的注释。<code>addRemarkComments</code>官方文档的介绍 [<a href="http://www.mybatis.org/generator/configreference/commentGenerator.html">doc</a>]：</p>
-<blockquote>
-<p>This property is used to specify whether MBG will include table and column remarks from db table in the generated comments. The property supports these values:</p>
-<ul>
-<li><strong>false</strong>: <em>This is the default value</em> When the property is false or unspecified, all generated comments will <strong>not</strong> include table and column remarks from db table when the element was generated.</li>
-<li><strong>true</strong>: When the property is true, table and columns remarks from db table will be added to the generated comments.</li>
-</ul>
-<p><strong>Warning:</strong> If suppressAllComments option is true, this option will be ignored.</p>
-</blockquote>
-<p>使用方法很简单，只需将MyBatis生成器的配置文件中的<code>commentGenerator</code>节点修改为：</p>
-<figure class="highlight xml"><table><tr><td class="code"><pre><span class="line"><span class="tag">&lt;<span class="name">commentGenerator</span>&gt;</span></span><br><span class="line">    <span class="tag">&lt;<span class="name">property</span> <span class="attr">name</span>=<span class="string">&quot;addRemarkComments&quot;</span> <span class="attr">value</span>=<span class="string">&quot;true&quot;</span> /&gt;</span></span><br><span class="line"><span class="tag">&lt;/<span class="name">commentGenerator</span>&gt;</span></span><br></pre></td></tr></table></figure>
-<h1 id="自定义注释生成器类">自定义注释生成器类</h1>
-<p>通过<code>addRemarkComments</code>选项生成的实体类的注释不够精简。于是笔者参考MyBatis的默认的注释生成器<code>DefaultCommentGenerator</code>[<a href="https://github.com/mybatis/generator/blob/master/core/mybatis-generator-core/src/main/java/org/mybatis/generator/internal/DefaultCommentGenerator.java">github</a>]，对其进行改造成如下：</p>
-<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="keyword">package</span> com.test.mbg;</span><br><span class="line"> </span><br><span class="line"><span class="keyword">import</span> java.util.Date;</span><br><span class="line"> </span><br><span class="line"><span class="keyword">import</span> org.apache.commons.lang3.time.DateFormatUtils;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.IntrospectedColumn;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.IntrospectedTable;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.dom.java.Field;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.dom.java.JavaElement;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.dom.java.Method;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.dom.java.TopLevelClass;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.config.MergeConstants;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.internal.DefaultCommentGenerator;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.internal.util.StringUtility;</span><br><span class="line"> </span><br><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment"> * 官方类似的功能见，在版本1.3.3中添加的 addRemarkComments &lt;br&gt;</span></span><br><span class="line"><span class="comment"> * http://www.mybatis.org/generator/configreference/commentGenerator.html &lt;br&gt;</span></span><br><span class="line"><span class="comment"> * https://github.com/mybatis/generator/issues/23</span></span><br><span class="line"><span class="comment"> *</span></span><br><span class="line"><span class="comment"> * <span class="doctag">@see</span> DefaultCommentGenerator#addRemarkComments</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="keyword">public</span> <span class="keyword">class</span> <span class="title class_">RemarksCommentGenerator</span> <span class="keyword">extends</span> <span class="title class_">DefaultCommentGenerator</span> &#123;</span><br><span class="line"> </span><br><span class="line">    <span class="meta">@Override</span></span><br><span class="line">    <span class="keyword">public</span> <span class="keyword">void</span> <span class="title function_">addModelClassComment</span><span class="params">(TopLevelClass topLevelClass, IntrospectedTable introspectedTable)</span> &#123;</span><br><span class="line">        topLevelClass.addJavaDocLine(<span class="string">&quot;/**&quot;</span>);</span><br><span class="line"> </span><br><span class="line">        <span class="type">String</span> <span class="variable">remarks</span> <span class="operator">=</span> introspectedTable.getRemarks();</span><br><span class="line">        <span class="keyword">if</span> (StringUtility.stringHasValue(remarks)) &#123;</span><br><span class="line">            String[] remarkLines = remarks.split(System.getProperty(<span class="string">&quot;line.separator&quot;</span>));</span><br><span class="line">            <span class="keyword">for</span> (String remarkLine : remarkLines) &#123;</span><br><span class="line">                topLevelClass.addJavaDocLine(<span class="string">&quot; * &quot;</span> + remarkLine);</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line"> </span><br><span class="line">        topLevelClass.addJavaDocLine(<span class="string">&quot; * &quot;</span>);</span><br><span class="line">        <span class="type">StringBuilder</span> <span class="variable">sb</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">StringBuilder</span>();</span><br><span class="line">        sb.append(<span class="string">&quot; * &quot;</span>);</span><br><span class="line">        sb.append(introspectedTable.getFullyQualifiedTable());</span><br><span class="line">        topLevelClass.addJavaDocLine(sb.toString());</span><br><span class="line">        topLevelClass.addJavaDocLine(<span class="string">&quot; *&quot;</span>);</span><br><span class="line">        addJavadocTag(topLevelClass, <span class="literal">false</span>);</span><br><span class="line">        topLevelClass.addJavaDocLine(<span class="string">&quot; */&quot;</span>);</span><br><span class="line">    &#125;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">public</span> <span class="keyword">void</span> <span class="title function_">addFieldComment</span><span class="params">(Field field, IntrospectedTable introspectedTable, IntrospectedColumn introspectedColumn)</span> &#123;</span><br><span class="line">        field.addJavaDocLine(<span class="string">&quot;/**&quot;</span>);</span><br><span class="line"> </span><br><span class="line">        <span class="type">String</span> <span class="variable">remarks</span> <span class="operator">=</span> introspectedColumn.getRemarks();</span><br><span class="line">        <span class="keyword">if</span> (StringUtility.stringHasValue(remarks)) &#123;</span><br><span class="line">            String[] remarkLines = remarks.split(System.getProperty(<span class="string">&quot;line.separator&quot;</span>)); </span><br><span class="line">            <span class="keyword">for</span> (String remarkLine : remarkLines) &#123;</span><br><span class="line">                field.addJavaDocLine(<span class="string">&quot; * &quot;</span> + remarkLine);</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line"> </span><br><span class="line">        field.addJavaDocLine(<span class="string">&quot; *&quot;</span>);</span><br><span class="line">        <span class="type">StringBuilder</span> <span class="variable">sb</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">StringBuilder</span>();</span><br><span class="line">        sb.append(<span class="string">&quot; * &quot;</span>);</span><br><span class="line">        sb.append(introspectedTable.getFullyQualifiedTable());</span><br><span class="line">        sb.append(<span class="string">&#x27;.&#x27;</span>);</span><br><span class="line">        sb.append(introspectedColumn.getActualColumnName());</span><br><span class="line">        field.addJavaDocLine(sb.toString());</span><br><span class="line">        field.addJavaDocLine(<span class="string">&quot; *&quot;</span>);</span><br><span class="line">        addJavadocTag(field, <span class="literal">false</span>);</span><br><span class="line">        field.addJavaDocLine(<span class="string">&quot; */&quot;</span>);</span><br><span class="line">    &#125;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">public</span> <span class="keyword">void</span> <span class="title function_">addFieldComment</span><span class="params">(Field field, IntrospectedTable introspectedTable)</span> &#123;</span><br><span class="line">        field.addJavaDocLine(<span class="string">&quot;/**&quot;</span>);</span><br><span class="line">        addJavadocTag(field, <span class="literal">false</span>);</span><br><span class="line">        field.addJavaDocLine(<span class="string">&quot; */&quot;</span>);</span><br><span class="line">    &#125;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">public</span> <span class="keyword">void</span> <span class="title function_">addGetterComment</span><span class="params">(Method method, IntrospectedTable introspectedTable, IntrospectedColumn introspectedColumn)</span> &#123;</span><br><span class="line">        method.addJavaDocLine(<span class="string">&quot;/**&quot;</span>);</span><br><span class="line">        addJavadocTag(method, <span class="literal">false</span>);</span><br><span class="line">        method.addJavaDocLine(<span class="string">&quot; */&quot;</span>);</span><br><span class="line">    &#125;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">public</span> <span class="keyword">void</span> <span class="title function_">addSetterComment</span><span class="params">(Method method, IntrospectedTable introspectedTable, IntrospectedColumn introspectedColumn)</span> &#123;</span><br><span class="line">        method.addJavaDocLine(<span class="string">&quot;/**&quot;</span>);</span><br><span class="line">        addJavadocTag(method, <span class="literal">false</span>);</span><br><span class="line">        method.addJavaDocLine(<span class="string">&quot; */&quot;</span>);</span><br><span class="line">    &#125;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">protected</span> <span class="keyword">void</span> <span class="title function_">addJavadocTag</span><span class="params">(JavaElement javaElement, <span class="type">boolean</span> markAsDoNotDelete)</span> &#123;</span><br><span class="line">        <span class="type">StringBuilder</span> <span class="variable">sb</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">StringBuilder</span>();</span><br><span class="line">        sb.append(<span class="string">&quot; * &quot;</span>);</span><br><span class="line">        sb.append(MergeConstants.NEW_ELEMENT_TAG);</span><br><span class="line">        <span class="keyword">if</span> (markAsDoNotDelete) &#123;</span><br><span class="line">            sb.append(<span class="string">&quot; do_not_delete_during_merge&quot;</span>); <span class="comment">//$NON-NLS-1$</span></span><br><span class="line">        &#125;</span><br><span class="line">        <span class="type">String</span> <span class="variable">s</span> <span class="operator">=</span> getDateString();</span><br><span class="line">        <span class="keyword">if</span> (s != <span class="literal">null</span>) &#123;</span><br><span class="line">            sb.append(<span class="string">&#x27; &#x27;</span>);</span><br><span class="line">            sb.append(s);</span><br><span class="line">        &#125;</span><br><span class="line">        javaElement.addJavaDocLine(sb.toString());</span><br><span class="line">    &#125;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">protected</span> String <span class="title function_">getDateString</span><span class="params">()</span> &#123;</span><br><span class="line">        <span class="keyword">return</span> DateFormatUtils.format(<span class="keyword">new</span> <span class="title class_">Date</span>(), <span class="string">&quot;yyyy-MM-dd HH:mm:ss&quot;</span>);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-<p>MyBatis的配置文件修改为：</p>
-<figure class="highlight xml"><table><tr><td class="code"><pre><span class="line"><span class="tag">&lt;<span class="name">commentGenerator</span> <span class="attr">type</span>=<span class="string">&quot;com.test.mbg.RemarksCommentGenerator&quot;</span>&gt;</span></span><br><span class="line"><span class="tag">&lt;/<span class="name">commentGenerator</span>&gt;</span></span><br></pre></td></tr></table></figure>
-<h1 id="运行MyBatis生成器">运行MyBatis生成器</h1>
-<p>改用自定义的<code>RemarksCommentGenerator</code>后，运行MyBatis插件可能会报错。需要使用Java来运行MyBatis生成器，代码如下 [<a href="http://www.mybatis.org/generator/running/runningWithJava.html">doc</a>]：</p>
-<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="keyword">package</span> com.test.mbg;</span><br><span class="line"> </span><br><span class="line"><span class="keyword">import</span> java.io.File;</span><br><span class="line"><span class="keyword">import</span> java.util.ArrayList;</span><br><span class="line"><span class="keyword">import</span> java.util.List;</span><br><span class="line"> </span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.MyBatisGenerator;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.config.Configuration;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.config.xml.ConfigurationParser;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.internal.DefaultShellCallback;</span><br><span class="line"> </span><br><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment"> *  使用Java运行 MyBatis Generator</span></span><br><span class="line"><span class="comment"> * http://www.mybatis.org/generator/running/runningWithJava.html</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="keyword">public</span> <span class="keyword">class</span> <span class="title class_">MyBatisGen</span> &#123;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title function_">main</span><span class="params">(String[] args)</span> <span class="keyword">throws</span> Exception &#123;</span><br><span class="line">        <span class="type">String</span> <span class="variable">fileName</span> <span class="operator">=</span> <span class="string">&quot;F:/code/mybatis-generator.xml&quot;</span>;</span><br><span class="line">        <span class="type">File</span> <span class="variable">configFile</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">File</span>(fileName);</span><br><span class="line">        List&lt;String&gt; warnings = <span class="keyword">new</span> <span class="title class_">ArrayList</span>&lt;String&gt;();</span><br><span class="line">        <span class="type">boolean</span> <span class="variable">overwrite</span> <span class="operator">=</span> <span class="literal">true</span>;</span><br><span class="line">        <span class="type">ConfigurationParser</span> <span class="variable">cp</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">ConfigurationParser</span>(warnings);</span><br><span class="line">        <span class="type">Configuration</span> <span class="variable">config</span> <span class="operator">=</span> cp.parseConfiguration(configFile);</span><br><span class="line">        <span class="type">DefaultShellCallback</span> <span class="variable">callback</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">DefaultShellCallback</span>(overwrite);</span><br><span class="line">        <span class="type">MyBatisGenerator</span> <span class="variable">myBatisGenerator</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">MyBatisGenerator</span>(config, callback, warnings);</span><br><span class="line">        myBatisGenerator.generate(<span class="literal">null</span>);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-]]></content>
-      <categories>
-        <category>Java</category>
-      </categories>
-      <tags>
-        <tag>数据库</tag>
-        <tag>Java</tag>
-        <tag>MyBatis</tag>
-      </tags>
-  </entry>
   <entry>
     <title>Java 编译器 javac 及 Lombok 实现原理解析</title>
     <url>/2017/04/javac-api/</url>
@@ -2677,10 +2640,47 @@ Generates only some kinds of debugging information, specified by a comma separat
       </categories>
       <tags>
         <tag>Java</tag>
-        <tag>JVM</tag>
-        <tag>编译器</tag>
-        <tag>javac</tag>
-        <tag>Lombok</tag>
+        <tag>JVM</tag>
+        <tag>编译器</tag>
+        <tag>javac</tag>
+        <tag>Lombok</tag>
+      </tags>
+  </entry>
+  <entry>
+    <title>MyBatis 生成器的表注释</title>
+    <url>/2016/12/mybatis-generator/</url>
+    <content><![CDATA[<p><a href="https://en.wikipedia.org/wiki/MyBatis">MyBatis</a>是流行的持久化框架，通过抽象底层的JDBC代码，在类对象和数据库列之间自动映射SQL的参数和结果，以SQL为映射的间接层，实现SQL映射器。<a href="http://www.mybatis.org/generator/">MyBatis Generator</a> (MBG) 是一个Mybatis的代码生成器，内省数据库的表，然后自动生成映射表的实体类，并生成CRUD（插入，查询，更新，删除）操作的样板代码。MyBatis，之前所在的公司在用，生成器也在用。虽然生成器大大提供了开发效率，但生成的代码可读性比较低，尤其是自动生成的实体类，如下：</p>
+<span id="more"></span>
+<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment">* This field was generated by MyBatis Generator. This field corresponds to the database column author.book_id</span></span><br><span class="line"><span class="comment">* <span class="doctag">@mbggenerated</span>  Tue Jan 19 13:37:24 CST 2016</span></span><br><span class="line"><span class="comment">*/</span></span><br><span class="line"><span class="keyword">private</span> Integer bookId;</span><br></pre></td></tr></table></figure>
+<p>这些自动生成注释，没有实质性信息，其实真正有用的是，设计表时，该字段的用途，即表字段的注释。</p>
+<h1 id="addRemarkComments选项">addRemarkComments选项</h1>
+<p>庆幸的是，MyBatis生成器在版本1.3.3中添加了，<code>addRemarkComments</code>选项 [<a href="https://github.com/mybatis/generator/issues/23">github</a>]，可以在生成的实体类中附带表字段的注释。<code>addRemarkComments</code>官方文档的介绍 [<a href="http://www.mybatis.org/generator/configreference/commentGenerator.html">doc</a>]：</p>
+<blockquote>
+<p>This property is used to specify whether MBG will include table and column remarks from db table in the generated comments. The property supports these values:</p>
+<ul>
+<li><strong>false</strong>: <em>This is the default value</em> When the property is false or unspecified, all generated comments will <strong>not</strong> include table and column remarks from db table when the element was generated.</li>
+<li><strong>true</strong>: When the property is true, table and columns remarks from db table will be added to the generated comments.</li>
+</ul>
+<p><strong>Warning:</strong> If suppressAllComments option is true, this option will be ignored.</p>
+</blockquote>
+<p>使用方法很简单，只需将MyBatis生成器的配置文件中的<code>commentGenerator</code>节点修改为：</p>
+<figure class="highlight xml"><table><tr><td class="code"><pre><span class="line"><span class="tag">&lt;<span class="name">commentGenerator</span>&gt;</span></span><br><span class="line">    <span class="tag">&lt;<span class="name">property</span> <span class="attr">name</span>=<span class="string">&quot;addRemarkComments&quot;</span> <span class="attr">value</span>=<span class="string">&quot;true&quot;</span> /&gt;</span></span><br><span class="line"><span class="tag">&lt;/<span class="name">commentGenerator</span>&gt;</span></span><br></pre></td></tr></table></figure>
+<h1 id="自定义注释生成器类">自定义注释生成器类</h1>
+<p>通过<code>addRemarkComments</code>选项生成的实体类的注释不够精简。于是笔者参考MyBatis的默认的注释生成器<code>DefaultCommentGenerator</code>[<a href="https://github.com/mybatis/generator/blob/master/core/mybatis-generator-core/src/main/java/org/mybatis/generator/internal/DefaultCommentGenerator.java">github</a>]，对其进行改造成如下：</p>
+<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="keyword">package</span> com.test.mbg;</span><br><span class="line"> </span><br><span class="line"><span class="keyword">import</span> java.util.Date;</span><br><span class="line"> </span><br><span class="line"><span class="keyword">import</span> org.apache.commons.lang3.time.DateFormatUtils;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.IntrospectedColumn;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.IntrospectedTable;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.dom.java.Field;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.dom.java.JavaElement;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.dom.java.Method;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.dom.java.TopLevelClass;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.config.MergeConstants;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.internal.DefaultCommentGenerator;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.internal.util.StringUtility;</span><br><span class="line"> </span><br><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment"> * 官方类似的功能见，在版本1.3.3中添加的 addRemarkComments &lt;br&gt;</span></span><br><span class="line"><span class="comment"> * http://www.mybatis.org/generator/configreference/commentGenerator.html &lt;br&gt;</span></span><br><span class="line"><span class="comment"> * https://github.com/mybatis/generator/issues/23</span></span><br><span class="line"><span class="comment"> *</span></span><br><span class="line"><span class="comment"> * <span class="doctag">@see</span> DefaultCommentGenerator#addRemarkComments</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="keyword">public</span> <span class="keyword">class</span> <span class="title class_">RemarksCommentGenerator</span> <span class="keyword">extends</span> <span class="title class_">DefaultCommentGenerator</span> &#123;</span><br><span class="line"> </span><br><span class="line">    <span class="meta">@Override</span></span><br><span class="line">    <span class="keyword">public</span> <span class="keyword">void</span> <span class="title function_">addModelClassComment</span><span class="params">(TopLevelClass topLevelClass, IntrospectedTable introspectedTable)</span> &#123;</span><br><span class="line">        topLevelClass.addJavaDocLine(<span class="string">&quot;/**&quot;</span>);</span><br><span class="line"> </span><br><span class="line">        <span class="type">String</span> <span class="variable">remarks</span> <span class="operator">=</span> introspectedTable.getRemarks();</span><br><span class="line">        <span class="keyword">if</span> (StringUtility.stringHasValue(remarks)) &#123;</span><br><span class="line">            String[] remarkLines = remarks.split(System.getProperty(<span class="string">&quot;line.separator&quot;</span>));</span><br><span class="line">            <span class="keyword">for</span> (String remarkLine : remarkLines) &#123;</span><br><span class="line">                topLevelClass.addJavaDocLine(<span class="string">&quot; * &quot;</span> + remarkLine);</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line"> </span><br><span class="line">        topLevelClass.addJavaDocLine(<span class="string">&quot; * &quot;</span>);</span><br><span class="line">        <span class="type">StringBuilder</span> <span class="variable">sb</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">StringBuilder</span>();</span><br><span class="line">        sb.append(<span class="string">&quot; * &quot;</span>);</span><br><span class="line">        sb.append(introspectedTable.getFullyQualifiedTable());</span><br><span class="line">        topLevelClass.addJavaDocLine(sb.toString());</span><br><span class="line">        topLevelClass.addJavaDocLine(<span class="string">&quot; *&quot;</span>);</span><br><span class="line">        addJavadocTag(topLevelClass, <span class="literal">false</span>);</span><br><span class="line">        topLevelClass.addJavaDocLine(<span class="string">&quot; */&quot;</span>);</span><br><span class="line">    &#125;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">public</span> <span class="keyword">void</span> <span class="title function_">addFieldComment</span><span class="params">(Field field, IntrospectedTable introspectedTable, IntrospectedColumn introspectedColumn)</span> &#123;</span><br><span class="line">        field.addJavaDocLine(<span class="string">&quot;/**&quot;</span>);</span><br><span class="line"> </span><br><span class="line">        <span class="type">String</span> <span class="variable">remarks</span> <span class="operator">=</span> introspectedColumn.getRemarks();</span><br><span class="line">        <span class="keyword">if</span> (StringUtility.stringHasValue(remarks)) &#123;</span><br><span class="line">            String[] remarkLines = remarks.split(System.getProperty(<span class="string">&quot;line.separator&quot;</span>)); </span><br><span class="line">            <span class="keyword">for</span> (String remarkLine : remarkLines) &#123;</span><br><span class="line">                field.addJavaDocLine(<span class="string">&quot; * &quot;</span> + remarkLine);</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line"> </span><br><span class="line">        field.addJavaDocLine(<span class="string">&quot; *&quot;</span>);</span><br><span class="line">        <span class="type">StringBuilder</span> <span class="variable">sb</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">StringBuilder</span>();</span><br><span class="line">        sb.append(<span class="string">&quot; * &quot;</span>);</span><br><span class="line">        sb.append(introspectedTable.getFullyQualifiedTable());</span><br><span class="line">        sb.append(<span class="string">&#x27;.&#x27;</span>);</span><br><span class="line">        sb.append(introspectedColumn.getActualColumnName());</span><br><span class="line">        field.addJavaDocLine(sb.toString());</span><br><span class="line">        field.addJavaDocLine(<span class="string">&quot; *&quot;</span>);</span><br><span class="line">        addJavadocTag(field, <span class="literal">false</span>);</span><br><span class="line">        field.addJavaDocLine(<span class="string">&quot; */&quot;</span>);</span><br><span class="line">    &#125;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">public</span> <span class="keyword">void</span> <span class="title function_">addFieldComment</span><span class="params">(Field field, IntrospectedTable introspectedTable)</span> &#123;</span><br><span class="line">        field.addJavaDocLine(<span class="string">&quot;/**&quot;</span>);</span><br><span class="line">        addJavadocTag(field, <span class="literal">false</span>);</span><br><span class="line">        field.addJavaDocLine(<span class="string">&quot; */&quot;</span>);</span><br><span class="line">    &#125;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">public</span> <span class="keyword">void</span> <span class="title function_">addGetterComment</span><span class="params">(Method method, IntrospectedTable introspectedTable, IntrospectedColumn introspectedColumn)</span> &#123;</span><br><span class="line">        method.addJavaDocLine(<span class="string">&quot;/**&quot;</span>);</span><br><span class="line">        addJavadocTag(method, <span class="literal">false</span>);</span><br><span class="line">        method.addJavaDocLine(<span class="string">&quot; */&quot;</span>);</span><br><span class="line">    &#125;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">public</span> <span class="keyword">void</span> <span class="title function_">addSetterComment</span><span class="params">(Method method, IntrospectedTable introspectedTable, IntrospectedColumn introspectedColumn)</span> &#123;</span><br><span class="line">        method.addJavaDocLine(<span class="string">&quot;/**&quot;</span>);</span><br><span class="line">        addJavadocTag(method, <span class="literal">false</span>);</span><br><span class="line">        method.addJavaDocLine(<span class="string">&quot; */&quot;</span>);</span><br><span class="line">    &#125;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">protected</span> <span class="keyword">void</span> <span class="title function_">addJavadocTag</span><span class="params">(JavaElement javaElement, <span class="type">boolean</span> markAsDoNotDelete)</span> &#123;</span><br><span class="line">        <span class="type">StringBuilder</span> <span class="variable">sb</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">StringBuilder</span>();</span><br><span class="line">        sb.append(<span class="string">&quot; * &quot;</span>);</span><br><span class="line">        sb.append(MergeConstants.NEW_ELEMENT_TAG);</span><br><span class="line">        <span class="keyword">if</span> (markAsDoNotDelete) &#123;</span><br><span class="line">            sb.append(<span class="string">&quot; do_not_delete_during_merge&quot;</span>); <span class="comment">//$NON-NLS-1$</span></span><br><span class="line">        &#125;</span><br><span class="line">        <span class="type">String</span> <span class="variable">s</span> <span class="operator">=</span> getDateString();</span><br><span class="line">        <span class="keyword">if</span> (s != <span class="literal">null</span>) &#123;</span><br><span class="line">            sb.append(<span class="string">&#x27; &#x27;</span>);</span><br><span class="line">            sb.append(s);</span><br><span class="line">        &#125;</span><br><span class="line">        javaElement.addJavaDocLine(sb.toString());</span><br><span class="line">    &#125;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">protected</span> String <span class="title function_">getDateString</span><span class="params">()</span> &#123;</span><br><span class="line">        <span class="keyword">return</span> DateFormatUtils.format(<span class="keyword">new</span> <span class="title class_">Date</span>(), <span class="string">&quot;yyyy-MM-dd HH:mm:ss&quot;</span>);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>MyBatis的配置文件修改为：</p>
+<figure class="highlight xml"><table><tr><td class="code"><pre><span class="line"><span class="tag">&lt;<span class="name">commentGenerator</span> <span class="attr">type</span>=<span class="string">&quot;com.test.mbg.RemarksCommentGenerator&quot;</span>&gt;</span></span><br><span class="line"><span class="tag">&lt;/<span class="name">commentGenerator</span>&gt;</span></span><br></pre></td></tr></table></figure>
+<h1 id="运行MyBatis生成器">运行MyBatis生成器</h1>
+<p>改用自定义的<code>RemarksCommentGenerator</code>后，运行MyBatis插件可能会报错。需要使用Java来运行MyBatis生成器，代码如下 [<a href="http://www.mybatis.org/generator/running/runningWithJava.html">doc</a>]：</p>
+<figure class="highlight java"><table><tr><td class="code"><pre><span class="line"><span class="keyword">package</span> com.test.mbg;</span><br><span class="line"> </span><br><span class="line"><span class="keyword">import</span> java.io.File;</span><br><span class="line"><span class="keyword">import</span> java.util.ArrayList;</span><br><span class="line"><span class="keyword">import</span> java.util.List;</span><br><span class="line"> </span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.api.MyBatisGenerator;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.config.Configuration;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.config.xml.ConfigurationParser;</span><br><span class="line"><span class="keyword">import</span> org.mybatis.generator.internal.DefaultShellCallback;</span><br><span class="line"> </span><br><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment"> *  使用Java运行 MyBatis Generator</span></span><br><span class="line"><span class="comment"> * http://www.mybatis.org/generator/running/runningWithJava.html</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="keyword">public</span> <span class="keyword">class</span> <span class="title class_">MyBatisGen</span> &#123;</span><br><span class="line"> </span><br><span class="line">    <span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title function_">main</span><span class="params">(String[] args)</span> <span class="keyword">throws</span> Exception &#123;</span><br><span class="line">        <span class="type">String</span> <span class="variable">fileName</span> <span class="operator">=</span> <span class="string">&quot;F:/code/mybatis-generator.xml&quot;</span>;</span><br><span class="line">        <span class="type">File</span> <span class="variable">configFile</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">File</span>(fileName);</span><br><span class="line">        List&lt;String&gt; warnings = <span class="keyword">new</span> <span class="title class_">ArrayList</span>&lt;String&gt;();</span><br><span class="line">        <span class="type">boolean</span> <span class="variable">overwrite</span> <span class="operator">=</span> <span class="literal">true</span>;</span><br><span class="line">        <span class="type">ConfigurationParser</span> <span class="variable">cp</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">ConfigurationParser</span>(warnings);</span><br><span class="line">        <span class="type">Configuration</span> <span class="variable">config</span> <span class="operator">=</span> cp.parseConfiguration(configFile);</span><br><span class="line">        <span class="type">DefaultShellCallback</span> <span class="variable">callback</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">DefaultShellCallback</span>(overwrite);</span><br><span class="line">        <span class="type">MyBatisGenerator</span> <span class="variable">myBatisGenerator</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">MyBatisGenerator</span>(config, callback, warnings);</span><br><span class="line">        myBatisGenerator.generate(<span class="literal">null</span>);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+]]></content>
+      <categories>
+        <category>Java</category>
+      </categories>
+      <tags>
+        <tag>数据库</tag>
+        <tag>Java</tag>
+        <tag>MyBatis</tag>
       </tags>
   </entry>
   <entry>
@@ -3824,259 +3824,11 @@ NodeChildrenChanged<br>
         <category>计算机系统</category>
       </categories>
       <tags>
-        <tag>编译器</tag>
-        <tag>OS</tag>
-        <tag>C</tag>
-        <tag>ASM</tag>
-        <tag>ABI</tag>
-      </tags>
-  </entry>
-  <entry>
-    <title>可靠性工程概述</title>
-    <url>/2023/11/reliability-engineering/</url>
-    <content><![CDATA[<p>为了应对负载的增长，目前大型网站普遍都采用分布式架构。相对于采用单体架构的系统，分布式系统中有大量的服务器及设备，各模块之间存在错综复杂的依赖关系，存在更多的不确定性。整个系统的故障率会随设备的增加而呈指数级增加，单一节点问题可能会被无限放大，日常运行过程中一定会伴随故障发生。所以，可靠性开始成为大型网站关注的最重要的质量属性之一，并因此发展出了站点可靠性工程（<a href="https://en.wikipedia.org/wiki/Site_reliability_engineering">Site reliability engineering</a>，SRE）。站点可靠性工程，是从可靠性工程发展而来的，从可靠性工程中借鉴了概念和成果。本文溯本求源，内容主要是总结概括，可靠性工程的历史演进和核心概念，软件可靠性工程的核心概念，以及可靠性设计的方法。</p>
-<span id="more"></span>
-<h1 id="历史演进">历史演进</h1>
-<p>可靠性工程起源于第二次世界大战<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>。“二战”期间，美国 60% 的机载电子设备运到远东后不能使用，50% 的电子设备在存储期间失效。经过分析，发现这些电子设备故障的主要原因是电子管的可靠性太差，为此美国在 1943 年成立电子管研究委员会，在 1952 年美国国防部成立一个由军方、工业部门及学术界组成的小组，名为“电子设备可靠性咨询小组”（AGREE，Advisory Group on the Reliability of Electronic Equipment）。1957 年 6 月，AGREE 小组出版报告《军用电子设备可靠性》（Reliability of Military Electronic Equipment），该报告是公认的可靠性工程的奠基性文件，研究报告提出一整套可靠性设计、试验和管理方法，确立了可靠性工程发展方向，标志着可靠性工程学科诞生。此后，它不断向工业和民用产品领域渗透，20 世纪 60 年代推广到核工业, 70 年代在化学工业普及，并陆续扩散到其他工程领域。</p>
-<p>随着可靠性工程学科的发展演进，围绕故障展开，逐渐衍生出对产品的维修性（maintainability）、可用性（availability）、保障性（supportability）、测试性（testability）、安全性（safety）等质量特性的工程学研究。“维修性工程”和“安全性工程”是从“可靠性工程”中分离出来的，而“保障性工程”和“测试性工程”又是从“维修性工程”中独立出来的。新的 XX 性陆续分出，因为这些特性紧密相关，已经分出的 XX 性围绕可靠性又重新集成起来，在 20 世纪 80 年代呈现综合化发展趋势。可靠性的含义不断扩展，从狭义可靠性演变为广义可靠性，从狭义可靠性工程演变为广义可靠性工程。</p>
-<p>1980 年代初期，为了避免因为扩展可靠性固有的含义引发的可靠性定性含义和可靠性的定量含义之间的理解混乱，Jean-Claude Laprie 选择“可信性”（dependability）作为术语，根据国际电工委员会标准，可信性的定义是，用以描述可用性及其影响因素（可靠性、维修性和维修保障性）的集合性术语，可信性仅用于非定量术语的一般描述。某些情况下，可信性还包含耐久性（durability）、安全性（safety）、安全保密性（security）等其他特性。<strong>可信性可以理解为广义可靠性</strong>。</p>
-<p>当今在国际上有两个比较完整的可靠性标准化体系，一个是美国军用标准（MIL-STD），另一个是国际电工委员会（IEC）标准。美国军用标准多年来一直扮演着研究开发可靠性相关标准文件的带头角色，也是最早制定可靠性标准的。最早的可靠性定义是由美国 AGREE 在 1957 年的报告中提出的，1966 年美国的 MIL-STD-721B 又给出了传统的或经典的可靠性定义，即产品在规定的条件下和规定的时间内完成规定功能的能力。最主要的可靠性国际标准组织是国际电工委员会的 TC56 技术委员会，TC56 的发展时间线<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup>：</p>
-<ul>
-<li>1965，国际电工委员会 IEC 成立名为“电子元件和设备可靠性”（Reliability of Electronic Components and Equipment）的技术委员会，即 TC56。</li>
-<li>1973，TC56 更名为“可靠性与维修性”（Reliability and Maintainability）技术委员会。</li>
-<li>1985，TC56 技术委员会成立了软件可靠性工作组，开始制定软件可靠性和维修性标准。</li>
-<li>1989，TC56 更名为“可信性”（Dependability）技术委员会，此名称一直沿用至今。</li>
-<li>1990，TC56 在与国际标准化组织（ISO）协商后，工作范围应不再局限于电工技术领域，而是解决所有学科的通用可靠性问题，从而使 IEC/TC56 成为所谓的横向委员会。</li>
-</ul>
-<p>我国与 IEC/TC56 对口的专业技术标准化组织是，TC24 全国电工电子产品可靠性与维修性标准化技术委员会（简称“可标委”），成立于 1982 年，挂靠在工业和信息化部电子第五研究所（又名中国电子产品可靠性与环境试验研究所）。</p>
-<h1 id="可信性与质量六性">可信性与质量六性</h1>
-<p>除了上文的“可信性”集合性术语外，有些资料将广义可靠性解释为，“可用性 + 可靠性 + 维修性”，这三个质量特性也被缩写为 RAM。RAM 有时候会再加上安全性（Safety），被缩写为 <a href="https://en.wikipedia.org/wiki/RAMS">RAMS</a>。使用 RAMS 缩写的典型例子是国际电工委员会的 <a href="https://webstore.iec.ch/publication/6747">IEC 62278:2002</a> 标准（等同的国家标准 <a href="https://std.samr.gov.cn/gb/search/gbDetailed?id=71F772D76DCCD3A7E05397BE0A0AB82A">GB/T 21562-2008</a>）。</p>
-<p>另外，常见的可靠性相关的缩写是 RMS 和 RMTSS。RMS 代表可靠性、维修性、保障性，或称“三性”。RMTSS 代表可靠性、维修性、测试性、保障性、安全性，或称“五性”。质量“三性”或“五性”，也是我国军用武器装备的军用标准要求的通用质量特性。我国武器装备的军用标准学习和借鉴的是美国军用标准，军用装备的质量特性分为专用质量特性和通用质量特性。专用质量特性，反映的是不同系统或者装备自身的特点和个性特征，主要指的是功能和性能，如某型飞机的最大（最小）飞行速度、巡航速度、飞行高度等指标。通用质量特性，则表征不同装备的共性特征。通用质量特性是逐渐演变的，从一开始的“二性”演变为“六性”<sup class="footnote-ref"><a href="#fn3" id="fnref3">[3]</a></sup><sup class="footnote-ref"><a href="#fn4" id="fnref4">[4]</a></sup>，通用质量特性包含的特性如下：</p>
-<ul>
-<li>二性：可靠性、维修性（也缩写为 R&amp;M）</li>
-<li>三性：可靠性、维修性、保障性（也缩写为 RMS）</li>
-<li>五性：可靠性、维修性、测试性、保障性、安全性（也缩写为 RMTSS）</li>
-<li>六性：可靠性、维修性、保障性、测试性、安全性、环境适应性</li>
-</ul>
-<p><strong>通用质量特性与可信性的含义大体上相同</strong>。质量特性、可信性、可靠性的关系，如下图所示：</p>
-<img width="700" alt="质量特性、可信性、可靠性的关系" title="质量特性、可信性、可靠性的关系" src="https://static.nullwy.me/quality-characteristics-classification.png">
-<p>根据国际电工委员会 IEC 60050 (191):1990（等同的国家标准 GB/T 3187-1994 《可靠性、维修性术语》）、IEC 60050-192:2015（等同于 GB/T 2900.99-2016 《电工术语 可信性》）以及国家军用标准 GJB 451A-2005 《可靠性维修性保障性术语》（与美国军用标准 <a href="http://everyspec.com/MIL-STD/MIL-STD-0700-0799/MIL-STD-721C_1040/">MIL-STD-721C</a> 相似）等标准文档，相关特性的定义和度量指标如下：</p>
-<ul>
-<li><strong>可信性（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-01-22">dependability</a>）</strong>：用以描述可用性及其影响因索（可靠性、维修性和维修保障性）的集合性术语。可信性仅用于非定量术语的一般描述。</li>
-<li><strong>可靠性（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-01-24">reliability</a>）</strong>：在给定的条件，给定的时间区间，能无故障地执行要求的能力。可靠性一般用可靠度（reliability）、平均故障间隔时间（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-13">MTBF</a>）、使用寿命（useful life）等参数来度量。</li>
-<li><strong>可用性（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-01-23">availability</a>）</strong>：在所要求的外部资源得到提供的情况下，产品在给定的条件下，在给定的时刻或时间区间内处于能完成要求的功能的状态的能力。此能力是产品的可靠性、维修性和维修保障性的综合反映。可用性的度量指标称为可用度（availability），表示为平均可用时间同平均可用时间与平均不可用时间的和之比。</li>
-<li><strong>维修性（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-01-27">maintainability</a>）</strong>：在给定的条件下，使用所述的程序和资源实施维修时，产品在给定的使用条件下保持或恢复能完成要求的功能的状态的能力。维修性反映产品修理的难易程度，主要使用平均修复时间（MTTR）来度量。</li>
-<li><strong>保障性（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-01-31">supportability</a>）</strong>：在规定的运行剖面和给定的后勤与维修资源下，保防能维待要求的可用性的能力。维修保障（maintenance support），是维修产品的资源的供给，资源包括人力资源、保障设备、材料和备件、维修设施、文档和信息以及维修信息系统。保障性一般用平均保障延误时间、资源满足率、资源利用率等参数来度量。</li>
-<li><strong>测试性（testability）</strong>：是指产品能及时并准确地确定其状态（可工作、不可工作或性能下降），并隔离其内部故障的能力。测试性反映产品是否易于测试、出现故障时是否易于检测和隔离，一般用检测时间、技术准备时间、故障检测率、故障隔离率等参数来度量。</li>
-<li><strong>安全性（safety）</strong>：是指产品所具有的不导致人员伤亡、系统毁坏、重大财产损失或不危及人员健康和环境的能力。安全性可理解为产品在任何情况下对人员、系统、财产和环境都不构成安全威胁。它可定义为产品在规定的条件下和规定的时间内，以可接受的风险执行规定功能的能力。安全性一般用事故概率、损失率、安全可靠度等参数来度量。</li>
-<li><strong>环境适应性（environmental worthiness）</strong>：是指产品在其寿命期内预计可能遇到的各种环境作用下能实现其所有预定功能、性能和（或）不被破坏的能力。它反映了产品对各种环境的适应能力，即在其可能遇到的各种环境下均能正常工作的能力，是可靠性的一种特殊情况。环境适应性鉴定试验通过的判定准则是，在所有试验条件下“零故障”。</li>
-</ul>
-<p><strong>通用质量特性的“六性”之间是紧密联系的</strong><sup class="footnote-ref"><a href="#fn4" id="fnref4:1">[4:1]</a></sup><sup class="footnote-ref"><a href="#fn5" id="fnref5">[5]</a></sup>：</p>
-<ul>
-<li>维修性是对可靠性的补充，如果产品不发生故障就不需要修复性维修。</li>
-<li>可用性是产品的可靠性、维修性和维修保障性的综合反映。</li>
-<li>保障性为产品正常使用与维修提供外部资源的支持，提供使用保障和维修保障，可靠性和维修性依赖于保障性。</li>
-<li>测试性是维修性的基础，维修依赖于测试，产品要修理一定要先发现故障和隔离故障，所以测试性设计得好，维修时间就可大大缩短。</li>
-<li>安全性本是可靠性的一部分，是避免人员伤亡、健康损害、财产或环境损害风险的可靠性。可靠性是安全性的基础，很多安全性问题都是因为产品不可靠造成的，所以提高产品可靠性也能提高安全性，当然并非所有安全性问题都是不可靠引起的。</li>
-<li>环境适应性是可靠性的一种特殊情况，是可靠性研究的前提，研究可靠性首先要确定产品是否有足够的环境适应性。</li>
-</ul>
-<p>通用质量特性的“六性”工作围绕故障（failure）而展开，也被人称为“故障六性”<sup class="footnote-ref"><a href="#fn6" id="fnref6">[6]</a></sup><sup class="footnote-ref"><a href="#fn4" id="fnref4:2">[4:2]</a></sup>。可靠性的目标是减少故障；维修性的目标是修复故障；测试性的目标是检测故障；保障性保证出现故障时可以快速供应维修资源；安全性旨在出现故障以后降低风险；环境适应性鉴定试验通过的判定准则是，在所有试验条件下“零故障”<sup class="footnote-ref"><a href="#fn5" id="fnref5:1">[5:1]</a></sup>。</p>
-<img width="450" alt="故障六性" title="故障六性" src="https://static.nullwy.me/quality-6-characteristics.png">
-<p>可靠性是产品质量特性之一，是一种面向时间的质量特性（time oriented quality characteristic）<sup class="footnote-ref"><a href="#fn7" id="fnref7">[7]</a></sup>。Lloyd Condra 在<a href="https://www.amazon.com/dp/B00SC8DKDG">书中</a>对可靠性和质量的关系的解释是，“可靠性是质量随着时间的变化（reliability is quality over time）”，“为了衡量产品的质量水平，我们对现在的产品进行评判，而为了度量产品的可靠性水平，则要对产品未来会是什么样子进行评判”。这里的讨论的质量其实指的是符合性质量，质量管理一开始是从符合性质量开始的，质量管理的主要工作是质量检验（Quality Inspection），检测产品是否符合规格，质量检验的结果即合格品率。质量管理的关注焦点是产品的合格品率，而可靠性关注焦点是产品在用户使用过程中合格水平随着时间的保持能力，如下图所示 <sup class="footnote-ref"><a href="#fn5" id="fnref5:2">[5:2]</a></sup>：</p>
-<img width="600" alt="质量与可靠性关系示意图" title="质量与可靠性关系示意图" src="https://static.nullwy.me/quality-vs-reliability.png">
-<h1 id="故障与失效的区别">故障与失效的区别</h1>
-<p>可靠性工程中有两个基本而重要的术语“fault”和“failure”。在我国的可靠性标准文档中，把“fault”翻译为“故障”，把“failure”翻译为“失效”或“故障”，也就是说，“失效”对应的英文只有“failure”；而“故障”对应的英文是“fault”或“failure”<sup class="footnote-ref"><a href="#fn8" id="fnref8">[8]</a></sup><sup class="footnote-ref"><a href="#fn9" id="fnref9">[9]</a></sup>。</p>
-<p>我国第一个定义可靠性相关的常用术语的国家标准是 GB 3187-1982 《可靠性基本名词术语及定义》，该标准对英文术语“failure”的中文翻译是“失效”或“故障”，并把“mean time between failures”翻译是“平均无故障时间”：<sup class="footnote-ref"><a href="#fn8" id="fnref8:1">[8:1]</a></sup></p>
-<blockquote>
-<p>2.2.1 失效（故障） failure：产品丧失规定的功能。对可修复产品通常也称故障。<br>
-2.5.5 平均寿命（平均无故障时间） mean life (mean time between failures)：寿命（无故障时间）的平均值。</p>
-</blockquote>
-<p>替代 GB 3187-1982 的新国家标准是 <a href="https://std.samr.gov.cn/gb/search/gbDetailed?id=71F772D7962ED3A7E05397BE0A0AB82A">GB/T 3187-1994</a> 《可靠性、维修性术语》（等同于 IEC 60050-191:1991），该标准把“failure”仅翻译为“失效”，不再又称“故障”。完整的术语定义如下：</p>
-<blockquote>
-<p>4.1.1 失效 failure<br>
-产品终止完成规定功能的能力这样的事件。<br>
-4.2.1 故障 fault<br>
-产品不能执行规定功能的状态。预防性维修或共他计划性活动或缺乏外部资源的情况除外。故障通常是产品本身失效后的状态，但也可能在失效前就存在。</p>
-</blockquote>
-<p>基于上述的定义，对于性能随时间逐渐退化的产品，故障（fault）与失效（failure）的区别，如下图所示<sup class="footnote-ref"><a href="#fn10" id="fnref10">[10]</a></sup>：</p>
-<img width="600" alt="故障（fault）与失效（failure）的区别" title="故障（fault）与失效（failure）的区别" src="https://static.nullwy.me/reliability-fault-vs-failure.png">
-<p>国外历来都是将“fault”和“failure”的定义加以区分的，我国新的标准文档也区分翻译为“故障”和“失效”，但是实际上在我国的电工行业中的惯用情况是把“fault”和“failure”都翻译为“故障”，很多书籍资料也不严格区分。比如，中国质量协会的《可靠性工程师手册》（第 2 版 2017<sup class="footnote-ref"><a href="#fn5" id="fnref5:3">[5:3]</a></sup>)，不严格区分“故障”与“失效”术语，统一都使用“故障”，书中的解释如下：</p>
-<blockquote>
-<p>在我国的可靠性工程应用中，一般不对故障与失效进行严格的区分，如失效树分析也称为故障树分析，故障模式、影响分析也称为失效模式、影响分析。因此本书也不做严格区分，多数情况下故障一词也可用失效代替。</p>
-</blockquote>
-<p>一般而言，故障是产品本身失效后的状态，此时产品处于故障状态，这时故障和失效是不需要严格加以区分。对无故障容忍能力的产品而言，故障即失效。然而，对有故障容忍能力的产品，产品可以出故障，但不会失效，这时我们就必须区分失效和故障的概念<sup class="footnote-ref"><a href="#fn9" id="fnref9:1">[9:1]</a></sup>。故障容忍（容错，<a href="https://en.wikipedia.org/wiki/Fault_tolerance">fault tolerance</a>），是在某些故障出现时继续运行的能力，只有当所有冗余的硬件同时有故障时，产品才失效。</p>
-<h1 id="可靠性的度量">可靠性的度量</h1>
-<p>可靠性的度量指标是<strong>可靠度</strong>（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-05">reliability</a>），根据国际电工委员会的标准文档，可靠度的定义是：在给定的条件下在时间区间 (t1, t2) 内按要求执行的概率。当 t1=0 和 t2=t，则 R(0,t) 可简化为 R(t)，并称为产品的<strong>可靠度函数</strong>（reliability function）。</p>
-<p>若在 t=0 时产品的总数为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>N</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">N_0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，在 0 ~ t 的时间内累计的故障数为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>N</mi><mi>f</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">N_f(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span>，正常的产品数为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">N_s(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span>，则有：</p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>N</mi><mn>0</mn></msub><mo>=</mo><msub><mi>N</mi><mi>f</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">N_0 = N_f(t) + N_s(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span></p>
-<p>产品在 t 时刻的可靠度的估计值为：</p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>^</mo></mover><mo>=</mo><mfrac><mrow><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><msub><mi>N</mi><mn>0</mn></msub></mfrac></mrow><annotation encoding="application/x-tex">\hat{R(t)}=\frac{N_s(t)}{N_0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2634em;vertical-align:-0.25em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0134em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span><span style="top:-3.319em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.4551em;vertical-align:-0.4451em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
-<p>显然，当 t=0 时，R(0) = 1，当 t=∞ 时，R(∞) = 0。</p>
-<p>可靠度的反面是<strong>不可靠度</strong>（unreliability），含义是：在规定的条件下，在规定的时间内，不能完成规定功能的概率。<strong>不可靠度函数</strong>通常记为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span>，不可靠度的估计值的计算公式为：</p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>^</mo></mover><mo>=</mo><mfrac><mrow><msub><mi>N</mi><mi>f</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><msub><mi>N</mi><mn>0</mn></msub></mfrac><mo>=</mo><mfrac><mrow><msub><mi>N</mi><mn>0</mn></msub><mo>−</mo><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><msub><mi>N</mi><mn>0</mn></msub></mfrac><mo>=</mo><mn>1</mn><mo>−</mo><mover accent="true"><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">\hat{F(t)} = \frac{N_f(t)}{N_0} = \frac{N_0 - N_s(t)}{N_0} = 1 - \hat{R(t)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2634em;vertical-align:-0.25em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0134em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span><span style="top:-3.319em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.4832em;vertical-align:-0.4451em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0381em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5131em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3488em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2901em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.4551em;vertical-align:-0.4451em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.2634em;vertical-align:-0.25em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0134em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span><span style="top:-3.319em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25em;"><span></span></span></span></span></span></span></span></span></p>
-<p><strong>示例</strong>：假设在 t=0，投入工作的 10000 只灯泡，以天作为度量时间的单位，在 t= 365 天时，发现有 300 只灯泡坏了，这时的可靠度和不可靠度的计算如下：</p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>R</mi><mo stretchy="false">(</mo><mn>365</mn><mo stretchy="false">)</mo></mrow><mo>^</mo></mover><mo>=</mo><mfrac><mrow><mn>1000</mn><mo>−</mo><mn>300</mn></mrow><mn>1000</mn></mfrac><mo>=</mo><mn>0.97</mn></mrow><annotation encoding="application/x-tex">\hat{R(365)} = \frac{1000 - 300}{1000} = 0.97</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2634em;vertical-align:-0.25em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0134em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord">365</span><span class="mclose">)</span></span></span><span style="top:-3.319em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1000</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1000</span><span class="mbin mtight">−</span><span class="mord mtight">300</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0.97</span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>F</mi><mo stretchy="false">(</mo><mn>365</mn><mo stretchy="false">)</mo></mrow><mo>^</mo></mover><mo>=</mo><mfrac><mn>300</mn><mn>1000</mn></mfrac><mo>=</mo><mn>0.03</mn></mrow><annotation encoding="application/x-tex">\hat{F(365)} = \frac{300}{1000} = 0.03</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2634em;vertical-align:-0.25em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0134em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord">365</span><span class="mclose">)</span></span></span><span style="top:-3.319em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1000</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">300</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0.03</span></span></span></span></p>
-<p>对不可靠度函数求导，其导数称为<strong>故障概率密度函数</strong>，通常记为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">f(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span>：</p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>lim</mi><mo>⁡</mo></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi><mo>→</mo><mn>0</mn></mrow></msub><mfrac><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">f(t) = \lim_{\Delta t \to 0} \frac{F(t + \Delta t) - F(t)} {\Delta t}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.355em;vertical-align:-0.345em;"></span><span class="mop"><span class="mop">lim</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mrel mtight">→</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">F</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.13889em;">F</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
-<p>某时刻尚未发生故障的产品，在该时刻后单位时间内发生故障的概率，称为产品的<strong>故障率</strong>（<a href="https://en.wikipedia.org/wiki/Failure_rate">failure rate</a>），记为记为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">λ(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">λ</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span>。故障率的计算公式如下：</p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>λ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>^</mo></mover><mo>=</mo><mfrac><mrow><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mtext>间隔时间内的故障数</mtext><mrow><mtext>间隔起点的存活数</mtext><mo>×</mo><mtext>时间间隔</mtext></mrow></mfrac></mrow><annotation encoding="application/x-tex">\hat{λ(t)} = \frac{N_s(t) - N_s(t + \Delta t)} {N_s(t) \Delta t} = \frac{间隔时间内的故障数}{间隔起点的存活数 × 时间间隔}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2634em;vertical-align:-0.25em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0134em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">λ</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span><span style="top:-3.319em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.53em;vertical-align:-0.52em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2757em;vertical-align:-0.4033em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord cjk_fallback mtight">间隔起点的存活数</span><span class="mbin mtight">×</span><span class="mord cjk_fallback mtight">时间间隔</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord cjk_fallback mtight">间隔时间内的故障数</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4033em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>lim</mi><mo>⁡</mo></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi><mo>→</mo><mn>0</mn></mrow></msub><mfrac><mrow><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mrow><mi>lim</mi><mo>⁡</mo></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi><mo>→</mo><mn>0</mn></mrow></msub><mfrac><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">λ(t) = \lim_{\Delta t \to 0} \frac{N_s(t) - N_s(t + \Delta t)} {N_s(t) \Delta t} = \lim_{\Delta t \to 0} \frac{F(t + \Delta t) - F(t)}{R(t)\Delta t} = \frac{f(t)}{R(t)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">λ</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.53em;vertical-align:-0.52em;"></span><span class="mop"><span class="mop">lim</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mrel mtight">→</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.53em;vertical-align:-0.52em;"></span><span class="mop"><span class="mop">lim</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mrel mtight">→</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.00773em;">R</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">F</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.13889em;">F</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.53em;vertical-align:-0.52em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.00773em;">R</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
-<p>在长期的可靠性实践中，人们发现许多产品的故障率随时间的变化曲线形似浴盆，所以习惯性的将故障率曲线称为“浴盆曲线”（<a href="https://en.wikipedia.org/wiki/Bathtub_curve">bathtub curve</a>），如下图所示<sup class="footnote-ref"><a href="#fn5" id="fnref5:4">[5:4]</a></sup>。大多数电子产品的故障率曲线的形状就是浴盆曲线。</p>
-<img width="600" alt="产品典型的故障率曲线" title="产品典型的故障率曲线" src="https://static.nullwy.me/reliability-bathtub-curve.png">
-<p>故障率随时间的变化大致可以分为以下三个阶段：早期故障期（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-02-28">early failure period</a>）、偶然故障期（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-02-30">random failure period</a>）、耗损故障期（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-02-31">wear-out failure period</a>）。三个阶段有时也被称为：早夭期（infant mortality period）、使用寿命期（useful life period）和耗损期（wear-out period）。故障率曲线与人类的死亡率曲线相似，曲线的三个阶段分别对应人类生命周期的婴幼儿时期、壮年期以及老年期。在偶然故障期，产品的故障率可降到一个较低的水平，且基本处于平稳状态，可以近似认为故障率为常数。</p>
-<p>如果产品的故障率为常数，那么其故障的概率分布可以用指数分布（<a href="https://zh.wikipedia.org/wiki/%E6%8C%87%E6%95%B0%E5%88%86%E5%B8%83">exponential distribution</a>）描述，指数分布是唯一具有恒定故障率的连续概率分布。恒定故障率的特性也被称为“无记忆性”（<a href="https://en.wikipedia.org/wiki/Memorylessness">memorylessness</a>），该特性说明故障率在任何时刻都与系统已工作过的时间长短没有关系。服从指数分布的概率密度函数为：</p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>λ</mi><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><mi>t</mi></mrow></msup></mrow><annotation encoding="application/x-tex">f(t) = {\lambda} e^{-\lambda t}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8491em;"></span><span class="mord"><span class="mord mathnormal">λ</span></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">λ</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span></span></span></p>
-<p>服从指数分布的可靠度函数、不可靠度函数和故障率函数依次为：</p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><mi>t</mi></mrow></msup></mrow><annotation encoding="application/x-tex">R(t) = e^{-\lambda t}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8491em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">λ</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo>−</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><mi>t</mi></mrow></msup></mrow><annotation encoding="application/x-tex">F(t) = 1 - e^{-\lambda t}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8491em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">λ</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda(t) = \lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">λ</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">λ</span></span></span></span></p>
-<p>公式中的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">λ</span></span></span></span>为常数。</p>
-<p>上面提到的这些指标是概率相关的度量指标。另外，还有一些是时间相关的度量指标：</p>
-<ul>
-<li><strong>平均故障间隔时间</strong>（MTBF，mean time between failures）：相邻两次故障间的持续时间的平均值。失效间隔时间（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-03">time between failures</a>）包括可用时间和不可用时间。MTBF 只能用于可修复产品。</li>
-<li><strong>平均故障间隔工作时间</strong>（MTBF /<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-13">MOTBF</a>，mean operating time between failures）：相邻两次故障间的累计工作时间的平均值。MOTBF 只能用于可修复产品，该值也被成为可修复产品的平均寿命（mean life）。</li>
-<li><strong>平均故障前工作时间</strong>（<a href="">MTTF</a>，mean operating time to failure）：故障前工作时间的平均值。等同于，平均失效前时间（MTTF，mean time to failure）。MTTF 可以用于不可修复产品和可修复产品。MTTF 值也被成为不可修复产品的平均寿命（mean life）。</li>
-<li><strong>平均恢复时间</strong>（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-07-23">MTTR</a>，mean time to restoration）：恢复时间的平均值。最新的国际电工委员会 IEV 标准文档，废弃了平均恢复时间（mean time to recovery）和平均修理时间（mean time to repair）。平均恢复时间是维修性的主要度量指标。</li>
-<li><strong>可用性</strong>（<a href="https://en.wikipedia.org/wiki/Availability">availability</a>）：或者翻译为“可用度”，可以表示为平均可用时间除以平均可用时间与平均不可用时间之和。可用性是反映可靠性和维修的综合性指标。</li>
-</ul>
-<p>根据国际电工委员会标准文档 IEC 60050-192:2015（等同的国家标准文档是 <a href="https://std.samr.gov.cn/gb/search/gbDetailed?id=71F772D81729D3A7E05397BE0A0AB82A">GB/T 2900.99-2016</a>《电工术语 可信性》），MTBF 和 <a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-13">MOTBF</a> 缩写代表的都是<strong>平均故障间隔工作时间</strong>（mean operating time between failures），统计的值是<strong>故障间隔工作时间</strong>（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-04">operating time between failures</a>），即相邻两次故障间的累计工作时间；而<strong>故障间隔时间</strong>（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-03">time between failures</a>），包括可用时间和不可用时间。所以，<strong>平均故障间隔时间</strong>和<strong>平均故障间隔工作时间</strong>的含义是不同的，前者同时统计包括工作时间（operating time）和非工作时间（non-operating time），而后者只统计工作时间（operating time）。但是在很多其他文档中，比如维基百科的词条“平均故障间隔时间”（<a href="https://en.wikipedia.org/wiki/Mean_time_between_failures">Mean time between failures</a>）词条，“平均失效间隔时间”的缩写也是 MTBF。<strong>也就说， MTBF 即是“平均故障间隔时间”的缩写，也是“平均故障间隔工作时间”的缩写，但两者含义却不同，需要读者自行辨别</strong>。本文使用 MTBF，统一都表示“平均故障间隔时间”。</p>
-<p><strong>MTBF 只能用于可修复产品，MTTF 用于不可修复产品和可修复产品</strong>。对于不可修复产品，MTTF 等同于 MTBF，对于可修复产品，MTTF 等同于 MOTBF。MTBF 是 MTTR 和 MTTF 的总和，即<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>T</mi><mi>B</mi><mi>F</mi><mo>=</mo><mi>M</mi><mi>T</mi><mi>T</mi><mi>R</mi><mo>+</mo><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi></mrow><annotation encoding="application/x-tex">MTBF = MTTR + MTTF</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MTBF</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">MTTR</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MTTF</span></span></span></span>。</p>
-<p>产品的<strong>平均寿命</strong>（mean life）的理论值为故障概率密度函数的<a href="https://zh.wikipedia.org/wiki/%E6%9C%9F%E6%9C%9B%E5%80%BC">期望值</a>，记为 θ。该期望值也是可修复产品的 MOTBF 的理论值，是不可修复产品的 MTTF 的理论值。平均寿命或 MTTF 的计算公式如下：</p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi><mo>=</mo><mi>θ</mi><mo>=</mo><mi>E</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∫</mo><mn>0</mn><mi mathvariant="normal">∞</mi></msubsup><mi>t</mi><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">d</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">MTTF = θ = E(T) = \int_{0}^\infty t f(t)\,\mathrm{d}x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MTTF</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2151em;vertical-align:-0.3558em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8593em;"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span><span style="top:-3.2579em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">∞</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3558em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathrm">d</span><span class="mord mathnormal">x</span></span></span></span></p>
-<p>如果概率密度函数服从指数分布，那么平均寿命或 MTTF 值为：</p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi><mo>=</mo><mi>θ</mi><mo>=</mo><mn>1</mn><mi mathvariant="normal">/</mi><mi>λ</mi></mrow><annotation encoding="application/x-tex">MTTF = θ = 1/\lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MTTF</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1/</span><span class="mord mathnormal">λ</span></span></span></span></p>
-<p>对于服从指数分布的产品，当产品工作时间到达平均寿命时，可靠度的值 36.8%：</p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>e</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><mn>36.8</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">R(θ) = e^{-1} = 36.8\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">36.8%</span></span></span></span></p>
-<p>假设某可修复产品的正常工作时间为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><msub><mrow><mi>T</mi><mi>F</mi><mi>F</mi></mrow><mn>1</mn></msub><mo separator="true">,</mo><msub><mrow><mi>T</mi><mi>F</mi><mi>F</mi></mrow><mn>2</mn></msub><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><msub><mrow><mi>T</mi><mi>F</mi><mi>F</mi></mrow><mi>n</mi></msub><mo fence="true">}</mo></mrow><annotation encoding="application/x-tex">\left\{ {TFF}_1, {TFF}_2 ...,  {TFF}_n \right\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">{</span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">TFF</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">TFF</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">...</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">TFF</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">}</span></span></span></span></span>，故障时间为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><msub><mrow><mi>T</mi><mi>T</mi><mi>R</mi></mrow><mn>1</mn></msub><mo separator="true">,</mo><msub><mrow><mi>T</mi><mi>T</mi><mi>R</mi></mrow><mn>2</mn></msub><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><msub><mrow><mi>T</mi><mi>T</mi><mi>R</mi></mrow><mi>n</mi></msub><mo fence="true">}</mo></mrow><annotation encoding="application/x-tex">\left\{ {TTR}_1, {TTR}_2 ..., {TTR}_n \right\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">{</span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">TTR</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">TTR</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">...</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">TTR</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">}</span></span></span></span></span>，如下图所示：</p>
-<img width="600" alt="MTBF、MTTF 和 MTTR 示意图" title="MTBF、MTTF 和 MTTR 示意图" src="https://static.nullwy.me/reliability-mtbf-mttf-mttr.png">
-<p>MTBF、MTTF、MTTR 和可用性（availability）的估计值的计算公式如下：</p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>T</mi><mi>B</mi><mi>F</mi><mo>=</mo><mfrac><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mrow><mi>T</mi><mi>B</mi><mi>F</mi></mrow><mi>i</mi></msub></mrow><mi>n</mi></mfrac><mo>=</mo><mfrac><mtext>total uptime + total downtime</mtext><mtext>total number of failures</mtext></mfrac></mrow><annotation encoding="application/x-tex">MTBF = \frac{\sum_{i=1}^n {TBF}_i}{n} = \frac{\text{total uptime + total downtime}}{\text{total number of failures}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MTBF</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.405em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.06em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.535em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mop op-symbol small-op mtight" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7385em;"><span style="top:-2.1786em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3214em;"><span></span></span></span></span></span></span><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">TBF</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3281em;"><span style="top:-2.357em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2772em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9322em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total number of failures</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4461em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total uptime + total downtime</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi><mo>=</mo><mfrac><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mrow><mi>T</mi><mi>T</mi><mi>F</mi></mrow><mi>i</mi></msub></mrow><mi>n</mi></mfrac><mo>=</mo><mfrac><mtext>total uptime</mtext><mtext>total number of failures</mtext></mfrac></mrow><annotation encoding="application/x-tex">MTTF = \frac{\sum_{i=1}^n {TTF}_i}{n} = \frac{\text{total uptime}}{\text{total number of failures}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MTTF</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.405em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.06em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.535em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mop op-symbol small-op mtight" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7385em;"><span style="top:-2.1786em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3214em;"><span></span></span></span></span></span></span><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">TTF</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3281em;"><span style="top:-2.357em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2772em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9322em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total number of failures</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4461em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total uptime</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>R</mi><mo>=</mo><mfrac><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mrow><mi>T</mi><mi>T</mi><mi>R</mi></mrow><mi>i</mi></msub></mrow><mi>n</mi></mfrac><mo>=</mo><mfrac><mtext>total downtime</mtext><mtext>total number of failures</mtext></mfrac></mrow><annotation encoding="application/x-tex">MTTR = \frac{\sum_{i=1}^n {TTR}_i}{n} = \frac{\text{total downtime}}{\text{total number of failures}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">MTTR</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.405em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.06em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.535em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mop op-symbol small-op mtight" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7385em;"><span style="top:-2.1786em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3214em;"><span></span></span></span></span></span></span><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.00773em;">TTR</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3281em;"><span style="top:-2.357em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2251em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total number of failures</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total downtime</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
-<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>可用性</mtext><mo>=</mo><mfrac><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi></mrow><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi><mo>+</mo><mi>M</mi><mi>T</mi><mi>T</mi><mi>R</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi></mrow><mrow><mi>M</mi><mi>T</mi><mi>B</mi><mi>F</mi></mrow></mfrac><mo>=</mo><mfrac><mtext>total uptime</mtext><mrow><mtext>total uptime</mtext><mo>+</mo><mtext>total downtime</mtext></mrow></mfrac></mrow><annotation encoding="application/x-tex">可用性 = \frac {MTTF} {MTTF + MTTR} = \frac {MTTF} {MTBF} = \frac{\text{total uptime}}{\text{total uptime} + \text{total downtime}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord cjk_fallback">可用性</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2757em;vertical-align:-0.4033em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">MTTF</span><span class="mbin mtight">+</span><span class="mord mathnormal mtight" style="margin-right:0.00773em;">MTTR</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">MTTF</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4033em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">MTBF</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">MTTF</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.4133em;vertical-align:-0.4811em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9322em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total uptime</span></span><span class="mbin mtight">+</span><span class="mord text mtight"><span class="mord mtight">total downtime</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4461em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total uptime</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4811em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
-<p>对于电子设备，MTBF 近似常量，比如，典型的企业级固态硬盘 SSD 的 MTBF 值可能是 200 万小时<sup class="footnote-ref"><a href="#fn11" id="fnref11">[11]</a></sup>，也就是 228 年，年故障率 AFR（<a href="https://en.wikipedia.org/wiki/Annualized_failure_rate">Annualized Failure Rate</a>） 为 0.44%（1/228）。</p>
-<p>可以利用数学和统计方法对可靠性进行预计和度量，并分析可靠性数据。但是可靠性的量化涉及大量不确定性，由于可靠性经常关系到制造和使用产品的人，人的行为和表现不像植物对肥料的反应、气象模型对海洋温度的反应那样服从于数学分析和预测，而且产品可能在大范围变化的环境中工作，因此还会有其他不确定性因素被引入。数学和统计方法虽然在适当的场合是非常有价值的，但是由于涉及大量不确定性，在实际的可靠性工程中的作用有限，在实际的工程实践中优先需要确定的是故障的原因和解决方案<sup class="footnote-ref"><a href="#fn12" id="fnref12">[12]</a></sup>。</p>
-<h1 id="软件可靠性工程">软件可靠性工程</h1>
-<p>软件可靠性工程是从硬件可靠性工程发展而来的<sup class="footnote-ref"><a href="#fn13" id="fnref13">[13]</a></sup>。在软件工程学建立初期，一些软件工程专家利用和改造硬件可靠性工程学的成果，使之移植到软件领域，从而开创了软件可靠性学科。</p>
-<p>类似的，起源于 Google 的“站点可靠性工程”（SRE, <a href="https://en.wikipedia.org/wiki/Site_reliability_engineering">Site reliability engineering</a>）也源自可靠性工程，区别是站点可靠性工程关注的是大型网站和网络服务这样的软件系统 <sup class="footnote-ref"><a href="#fn14" id="fnref14">[14]</a></sup><sup class="footnote-ref"><a href="#fn15" id="fnref15">[15]</a></sup>。</p>
-<h2 id="术语与概念">术语与概念</h2>
-<p>国家标准 <a href="https://std.samr.gov.cn/gb/search/gbDetailed?id=71F772D7805FD3A7E05397BE0A0AB82A">GB/T 11457-2006</a> 《信息技术 软件工程术语》，对软件可靠性的定义如下：</p>
-<blockquote>
-<p>2.1662 系统可靠性 system reliability<br>
-包括全部硬件和软件子系统在内的某个系统，在规定的环境及时间里正确执行所要求的任务或使命的概率。<br>
-2.1528 软件可靠性 software reliability<br>
-a) 在规定条件下，在规定的时间内，软件不引起系统失效的概率。该概率是系统输人和系统使用的函数，也是软件中存在的缺陷的函数。系统输人将确定是否会遇到已存在的缺陷（如果有缺陷存在的话）。<br>
-b) 在规定的时间周期内所述条件下程序执行所需要的功能的能力。</p>
-</blockquote>
-<p>GB/T 11457-2006 吸收了 <a href="https://standards.ieee.org/ieee/610.12/855/">IEEE Std 610.12-1990</a> 全部术语，包括术语“软件可靠性”，国标的术语定义只是对 IEEE 术语定义的中文翻译。IEEE 最早在标准文档中定义“软件可靠性”是在 <a href="https://standards.ieee.org/ieee/729/967/">IEEE Std 729-1983</a>，这个标准之后被 IEEE Std 610.12-1990 替代。</p>
-<p>IEEE 对“软件可靠性”术语给出两个定义，定义 a) 是定量的定义，也就是“可靠度”，定义 b) 是定性的定义。对比后容易发现，硬件可靠性和软件可靠性的定义是相同的。这种相容性，使这种可靠性定义能够用于既包括软件又包括硬件的系统。</p>
-<p>故障相关的术语，国家标准 GB/T 11457-2006 《信息技术 软件工程术语》的定义是：</p>
-<blockquote>
-<p><strong>2.163 隐错 bug</strong><br>
-见：出错 error(2.561) 和故障 fault(2.609)。<br>
-<strong>2.421 缺陷 defect</strong><br>
-见：故障 fault(2.609)。<br>
-<strong>2.561 出错, 误差, 差错 error</strong><br>
-a) 计算的、观察的或测量的值或条件与实际的、规定的或理论上正确的值或条件的差别。例如，在计算的结果和正确的结果之间差30m；<br>
-b) 不正确的步骤、过程或数据定义。例如，在计算机程序中的不正确的指定；<br>
-c) 不正确的结果。例如，当正确的结果是10，而计算的结果是12；<br>
-d) 产生不正确结果的人为动作。例如，在编程或操作的一部分上的不正确动作。<br>
-注：当上述所有四种定义是公共使用时，一种区分赋给定义 a) 为字差错（error），定义 b) 为字过错（fault），定义 c) 为字失效（failure）和定义 d) 为字错误（mistake）。<br>
-<strong>2.601 失效 failure</strong><br>
-系统或部件不能按规定的性能要求执行它所要求的功能。注：故障容忍在人们的动作（弄错-mistake）、它的显示（硬件或软件故障 fault）、故障的结果（失效 failure）和不正确（差错－error）结果的总数之间进行区分<br>
-<strong>2.609 故障, 缺陷 fault</strong><br>
-a) 硬件设备或部件中的缺陷。例如，短路或断线。<br>
-b) 在计算机程序中不正确的步骤、过程或数据定义。注：此定义最初由容错（fault tolerance）系统使用。在通常用法中，术语“差错（error）”和“隐错（bug）”表示同样含义。</p>
-</blockquote>
-<p>基于 IEEE 的定义，容易发现术语“fault、“<a href="https://en.wikipedia.org/wiki/Software_bug">bug</a>”和“defect”是同义词，术语“error”同时具有“mistake”、“fault”和“failure”的含义。这些术语之间的因果关系是，开发者在软件开发过程中产生人为失误（mistake），导致在软件中存在缺陷（fault, bug, defect），在软件运行时如果用户遭遇缺陷（fault, bug, defect），会引发失效（failure），如下图所示：</p>
-<img width="600" alt="软件故障的因果关系" title="软件故障的因果关系" src="https://static.nullwy.me/reliability-software-failure-cause.png">
-<p>失效（failure）是指系统或部件在特定约束下不能完成所要求的功能，用户在测试或实际使用中会观察到失效（failure）。<strong>失效（failure）是系统运行行为对用户要求的偏离，是一种面向用户的概念。故障（fault）是在系统运行时引起或可能潜在地引起失效（failure）的缺陷（defect），是一种面向开发者的概念。</strong></p>
-<h2 id="可靠性的度量-v2">可靠性的度量</h2>
-<p>早期的软件可靠性度量工作试图将硬件可靠性理论中的数学公式外推来进行软件可靠性的预测。大多数与硬件相关的可靠性模型依据的是由于“磨损”而导致的故障，而不是由于设计缺陷而导致的故障。在硬件中，由于物理磨损（如温度、腐蚀、振动的影响）导致的故障远比与设计缺陷有关的故障多。不幸的是，软件恰好相反。实际上，所有软件故障都可以追溯到设计或实现问题，磨损根本没有影响<sup class="footnote-ref"><a href="#fn16" id="fnref16">[16]</a></sup>。</p>
-<p>软件系统的故障主要是人为差错造成，涉及大量不确定性，利用数学和统计方法对可靠性进行预计和度量，在实际的工程实践中的作用有限。少数常用的与可靠性相关的度量指标是：MTBF、MTTR 和可用性。</p>
-<p>MTBF 指标衡量的是系统无故障运行的能力，也就是可靠性。MTTR 指标衡量的是系统快速从故障中恢复的能力，这种能力在硬件产品下被称为“维修性”（maintainability），但在软件系统下通常为称“韧性”（resilience）。术语“maintainability”，在硬件上下文中通常被翻译为“维修性”，而在软件上下文中通常被翻译为“维护性”或“可维护性”，软件可维护性指的是软件可被修改的能力，修改可能包括修复缺陷、增加或完善功能等。</p>
-<p>MTBF 反映的是硬件产品的寿命，是硬件产品质量的最重要的指标之一。与硬件不同，软件的 MTBF 不可控，而故障恢复的工作流程清晰，可干预程度高，研发团队可以对各环节展开精细化管理，轻松、高效地达成 MTTR 优化目标，所以软件系统的 <strong>MTTR 相对 MTBF 更加重要</strong><sup class="footnote-ref"><a href="#fn17" id="fnref17">[17]</a></sup><sup class="footnote-ref"><a href="#fn18" id="fnref18">[18]</a></sup>。</p>
-<p>可用性是衡量可靠性和韧性的综合性指标。想要提高系统的可用性，需要做的是延长无故障时间（MTTF）和缩短故障恢复时间（MTTR）。</p>
-<h1 id="可靠性设计">可靠性设计</h1>
-<p>Laprie 等人把提高系统可靠性的方法总结为<a href="https://en.wikipedia.org/wiki/Dependability#Means">四种</a>：</p>
-<ul>
-<li><strong>故障避免（fault avoidonce，简称“避错”）</strong>：在系统的设计和实现过程中使用一些开发方法来减少故障发生，并在系统投入使用之前发现系统中的故障。</li>
-<li><strong>故障排除（fault removal，简称“排错”）</strong>：故障排除可以细分为两个子类别：开发期间的排除和使用期间的排除。在系统使用之前通过<a href="https://zh.wikipedia.org/wiki/%E9%A9%97%E8%AD%89%E5%8F%8A%E7%A2%BA%E8%AA%8D">验证和确认</a>（V&amp;V）来发现和去除系统中的故障；如果系统已经投入使用，通过维护周期将其消除。</li>
-<li><strong>故障容忍（<a href="https://en.wikipedia.org/wiki/Fault_tolerance">fault tolerance</a>，简称“容错”）</strong>：容错是使系统在其某些组件中出现一个或多个故障时能够继续提供服务的能力，尽管该服务可能处于降级级别。容错技术主要是采用<strong>冗余</strong>（<a href="https://en.wikipedia.org/wiki/Redundancy_(engineering)">redundancy</a>）方法来消除故障的影响，冗余的含意是指当系统无故障时取消冗余资源不会影响系统正常运行。</li>
-<li><strong>故障预报（fault forecasting）</strong>：通过收集故障数据，建立可靠性建模，预测可能的故障。</li>
-</ul>
-<p>针对软件可靠性设计，软件故障避免技术，包括采用优秀的软件设计方法、使用强类型的程序设计语言、全面的编译器检查等；软件故障排除技术，主要是代码评审和软件测试；故障预报，能提高硬件可靠性，但是很少应用于软件可靠性。</p>
-<p>系统的资源包括硬件资源、软件资源、信息资源、时间资源，所以冗余区分 4 种方式：</p>
-<ul>
-<li><strong>硬件冗余</strong>（hardware redundancy）：通过配置额外的硬件组件实现冗余</li>
-<li><strong>软件冗余</strong>（software redundancy）：通过配置额外的软件版本实现冗余，例如 N 版本编程（<a href="https://en.wikipedia.org/wiki/N-version_programming">NVP</a>）</li>
-<li><strong>信息冗余</strong>（information redundancy）：通过对信息中外加一部分信息码或将信息存放在多个内存单元或将信息进行备份等实现冗余，例如循环冗余校验码、数据库备份等。</li>
-<li><strong>时间冗余</strong>（time redundancy）：多次执行相同的操作（重试）实现冗余，例如多次执行程序或传输数据的多个副本。</li>
-</ul>
-<p>硬件冗余和软件冗余被合称为结构冗余（structural redundancy）。相对与时间冗余，硬件冗余、软件冗余、信息冗余被合称为空间冗余（space redundancy）。</p>
-<p>在工程领域，利用冗余提高可靠性的例子很多，比如汽车的备胎、大货车的多个轮子、飞机的四台发动机或双台发动机、火箭的多台引擎和多台计算机等。《像火箭科学家一样思考》书中的“为什么冗余不是多余的”小节<sup class="footnote-ref"><a href="#fn19" id="fnref19">[19]</a></sup>中有这样一段阐述：</p>
-<blockquote>
-<p>航天器上的计算机也使用冗余装置。在地球上，电脑往往免不了崩溃或死机，而在有压力的太空环境中，计算机发生故障的概率有增无减，因为计算机在太空中要经历无数振动、冲击、变化的电流和波动的温度。正因为如此，航天飞机的计算机是4倍冗余的，即飞机上有4台计算机在运行着同样的软件。这4台计算机会通过一个多数投票系统就下一步动作进行单独投票。如果其中一台计算机发生故障，开始乱输出数据，其他3台计算机就会投票将其排除在外（没错，伙计们，火箭科学比你想象的更民主）。<br>
-冗余装置要正常工作，就必须独立运行。一架航天飞机配备4台计算机，这听起来非常棒，但由于它们运行着相同的软件，所以只要一个软件出现错误，4台计算机就会同时瘫痪。因此，航天飞机还配备了第5个备用飞行系统。该系统安装有一款不同的软件，而这款软件由不同于其他4款软件的分包商提供。如果某个一般性的软件错误使4台相同的主计算机瘫痪，则备用系统将启动，并会将航天飞机送回地球。</p>
-</blockquote>
-<p>在航天飞机上配备 4 台计算机属于硬件冗余，第 5 个备用飞行系统属于软件冗余。</p>
-<p>IDC 数据中心等级划分（<a href="https://en.wikipedia.org/wiki/Data_centre_tiers">data centre tiers</a>）主要是根据线路、电源、冷却等核心组件的冗余程度而划分的，不同的等级代表不同的可靠性和可用性。按 Uptime Institute 和 TIA-942 标准的建议，数据中心由低到高划分为 T1、T2、T3、T4 共 4 个等级，T1 级为基本型、T2 级为冗余型、T3 级为可并行维护冗余型、T4 级为容错型。4 个等级的冗余程度分别是，T1 级无冗余，T2 级部分 N+1 冗余，T3 级全部 N+1 冗余，T4 级 2N 或 2N+1 冗余。按我国国家标准《GB 50174-2017 数据中心设计规范》，数据中心由高到低划分为 A、B、C 三级，A 级为容错型，B 级为冗余型，C 级为基本型。不同的数据中心等级的对比，如下表所示（表格参考自 <sup class="footnote-ref"><a href="#fn20" id="fnref20">[20]</a></sup>）：</p>
-<img width="700" alt="数据中心等级划分" title="数据中心等级划分" src="https://static.nullwy.me/data-centre-tiers.png">
-<p>大多数商业数据中心都介于 T3 级和 T4 级之间，平衡了建设成本和可靠性。金融等行业的数据中心，如银行的数据中心，通常会同时遵循最高等级的国家标准 A 级和 Uptime Institute 的 Tier 4 级标准来建设。</p>
-<p>在生物学中，冗余是生物体的一种重要特征。生物体中的冗余结构和功能可以提高生物体的适应性和生存能力。例如，人体的很多器官是冗余的，比如耳朵、眼睛、肾、肺。冗余的器官如果出现“故障”，虽然不会让人完全失去该器官的机能，但会导致机能降级。其中一个眼睛如果完全失去视力，不会让人失明，不过视觉上无法识别远近。其中一个耳朵如果完全没有听力，不会让人失聪，但无法透过耳朵识别声音的位置。</p>
-<p>尽管冗余是一种很好的提高可靠性的措施，但额外的冗余增加到某种程度之后，就会无谓地增加设备的复杂性和成本，遵循边际效益递减规律。典型的例子是客机，随着发动机本身可靠性的提高，出于安全性和成本之间的权衡，之前的四发动机的客机越来越少见，逐渐被更省油、更低维护成本的双发动机的客机取代。</p>
-<h1 id="参考资料">参考资料</h1>
-<hr class="footnotes-sep">
-<section class="footnotes">
-<ol class="footnotes-list">
-<li id="fn1" class="footnote-item"><p>秦咏红，吕乃基：工程系统可靠性的演进，东北大学学报，2011年第4期295-299，<a href="https://qikan.cqvip.com/Qikan/Article/Detail?id=38777595">cqvip</a> <a href="#fnref1" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn2" class="footnote-item"><p>可靠性概论，工信部电子第五研究所潘勇，2015，<a href="https://book.douban.com/subject/26870237/">豆瓣</a>：第11章 可靠性标准 <a href="#fnref2" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn3" class="footnote-item"><p>2022-09 【标准解读】用标准语言解读装备“六性” <a href="https://mp.weixin.qq.com/s/FqfLL_ovGIZ-GO998HB4uw">https://mp.weixin.qq.com/s/FqfLL_ovGIZ-GO998HB4uw</a> <a href="#fnref3" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn4" class="footnote-item"><p>2021-07 张健：装备通用质量特性关系概述 <a href="https://mp.weixin.qq.com/s/nXmrTrz7c5EnEh4C_h4JEg">https://mp.weixin.qq.com/s/nXmrTrz7c5EnEh4C_h4JEg</a> <a href="#fnref4" class="footnote-backref">↩︎</a> <a href="#fnref4:1" class="footnote-backref">↩︎</a> <a href="#fnref4:2" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn5" class="footnote-item"><p>可靠性工程师手册，中国质量协会，第2版 2017，<a href="https://book.douban.com/subject/10607952/">豆瓣</a> <a href="#fnref5" class="footnote-backref">↩︎</a> <a href="#fnref5:1" class="footnote-backref">↩︎</a> <a href="#fnref5:2" class="footnote-backref">↩︎</a> <a href="#fnref5:3" class="footnote-backref">↩︎</a> <a href="#fnref5:4" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn6" class="footnote-item"><p>2018-01 北航康锐：可靠性的历史与今世 | 可靠性系统工程三部曲（上） <a href="https://mp.weixin.qq.com/s/275pk9Z-V4T3lntI-ZzYCA">https://mp.weixin.qq.com/s/275pk9Z-V4T3lntI-ZzYCA</a> <a href="#fnref6" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn7" class="footnote-item"><p>可靠性工程（Reliability Engineering），Kapur &amp; Pecht，2014，<a href="https://book.douban.com/subject/30619305/">豆瓣</a>：第1章 21世纪的可靠性工程 <a href="#fnref7" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn8" class="footnote-item"><p>2002-03 褚善元：failure和fault的定名问题 <a href="http://www.term.org.cn/CN/abstract/abstract10076.shtml">http://www.term.org.cn/CN/abstract/abstract10076.shtml</a> <a href="#fnref8" class="footnote-backref">↩︎</a> <a href="#fnref8:1" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn9" class="footnote-item"><p>2002-03 朱美娴：关于failure和fault定义的研讨 <a href="http://www.term.org.cn/CN/abstract/abstract10081.shtml">http://www.term.org.cn/CN/abstract/abstract10081.shtml</a> <a href="#fnref9" class="footnote-backref">↩︎</a> <a href="#fnref9:1" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn10" class="footnote-item"><p>System Reliability Theory, Rausand, etc., 3rd 2020，<a href="https://book.douban.com/subject/35473900/">豆瓣</a>：3 Failures and Faults, Figure 3.3 Illustration of the difference between failure and fault for a degrading item. <a href="#fnref10" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn11" class="footnote-item"><p>2021-09 揭秘：SSD 的“可靠性”到底可不可靠 <a href="https://memblaze.com/innovate/technical-articles/169.html">https://memblaze.com/innovate/technical-articles/169.html</a> <a href="#fnref11" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn12" class="footnote-item"><p>实用可靠性工程（Practical Reliability Engineering），O'Connor, etc.，第5版2012，<a href="https://book.douban.com/subject/35263950/">豆瓣</a> <a href="#fnref12" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn13" class="footnote-item"><p>陈光宇，黄锡滋：软件可靠性学科发展现状及展望，电子科技大学学报社科版，2002年第3期99-102，<a href="https://qikan.cqvip.com/Qikan/Article/Detail?id=6859748">cqvip</a> <a href="#fnref13" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn14" class="footnote-item"><p>SRE：Google运维解密，Beyer, etc. 2016，<a href="https://book.douban.com/subject/26875239/">豆瓣</a>：序言 <a href="#fnref14" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn15" class="footnote-item"><p>SRE原理与实践：构建高可靠性互联网应用，张观石，2022，<a href="https://book.douban.com/subject/36202918/">豆瓣</a>：第1章 互联网软件可靠性概论 <a href="#fnref15" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn16" class="footnote-item"><p>软件工程：实践者的研究方法，Pressman，第8版2014，<a href="https://book.douban.com/subject/26918148/">豆瓣</a>：第21章 软件质量保证，21.7 软件可靠性 <a href="#fnref16" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn17" class="footnote-item"><p>2010-07 John Allspaw: Thoughts on systems safety, software operations, and sociotechnical systems <a href="https://www.kitchensoap.com/2010/11/07/mttr-mtbf-for-most-types-of-f/">https://www.kitchensoap.com/2010/11/07/mttr-mtbf-for-most-types-of-f/</a> <a href="#fnref17" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn18" class="footnote-item"><p>2023-07 LigaAI：研发质量指标大 PK：MTTR vs MTBF，谁是靠谱王？ <a href="https://segmentfault.com/a/1190000043971564">https://segmentfault.com/a/1190000043971564</a> <a href="#fnref18" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn19" class="footnote-item"><p>像火箭科学家一样思考，Ozan Varol，2020，<a href="https://book.douban.com/subject/35228079/">豆瓣</a>：第1章 与不确定性共舞，为什么冗余不是多余的 <a href="#fnref19" class="footnote-backref">↩︎</a></p>
-</li>
-<li id="fn20" class="footnote-item"><p>2020-12 艾瑞咨询：2020年中国数据中心行业研究报告 <a href="https://report.iresearch.cn/report/202012/3699.shtml">https://report.iresearch.cn/report/202012/3699.shtml</a> <a href="#fnref20" class="footnote-backref">↩︎</a></p>
-</li>
-</ol>
-</section>
-]]></content>
-      <categories>
-        <category>架构</category>
-      </categories>
-      <tags>
-        <tag>架构</tag>
-        <tag>可靠性</tag>
-        <tag>SRE</tag>
+        <tag>编译器</tag>
+        <tag>OS</tag>
+        <tag>C</tag>
+        <tag>ASM</tag>
+        <tag>ABI</tag>
       </tags>
   </entry>
   <entry>
@@ -4824,4 +4576,252 @@ b) 在计算机程序中不正确的步骤、过程或数据定义。注：此
         <tag>Java</tag>
       </tags>
   </entry>
+  <entry>
+    <title>可靠性工程概述</title>
+    <url>/2023/11/reliability-engineering/</url>
+    <content><![CDATA[<p>为了应对负载的增长，目前大型网站普遍都采用分布式架构。相对于采用单体架构的系统，分布式系统中有大量的服务器及设备，各模块之间存在错综复杂的依赖关系，存在更多的不确定性。整个系统的故障率会随设备的增加而呈指数级增加，单一节点问题可能会被无限放大，日常运行过程中一定会伴随故障发生。所以，可靠性开始成为大型网站关注的最重要的质量属性之一，并因此发展出了站点可靠性工程（<a href="https://en.wikipedia.org/wiki/Site_reliability_engineering">Site reliability engineering</a>，SRE）。站点可靠性工程，是从可靠性工程发展而来的，从可靠性工程中借鉴了概念和成果。本文溯本求源，内容主要是总结概括，可靠性工程的历史演进和核心概念，软件可靠性工程的核心概念，以及可靠性设计的方法。</p>
+<span id="more"></span>
+<h1 id="历史演进">历史演进</h1>
+<p>可靠性工程起源于第二次世界大战<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>。“二战”期间，美国 60% 的机载电子设备运到远东后不能使用，50% 的电子设备在存储期间失效。经过分析，发现这些电子设备故障的主要原因是电子管的可靠性太差，为此美国在 1943 年成立电子管研究委员会，在 1952 年美国国防部成立一个由军方、工业部门及学术界组成的小组，名为“电子设备可靠性咨询小组”（AGREE，Advisory Group on the Reliability of Electronic Equipment）。1957 年 6 月，AGREE 小组出版报告《军用电子设备可靠性》（Reliability of Military Electronic Equipment），该报告是公认的可靠性工程的奠基性文件，研究报告提出一整套可靠性设计、试验和管理方法，确立了可靠性工程发展方向，标志着可靠性工程学科诞生。此后，它不断向工业和民用产品领域渗透，20 世纪 60 年代推广到核工业, 70 年代在化学工业普及，并陆续扩散到其他工程领域。</p>
+<p>随着可靠性工程学科的发展演进，围绕故障展开，逐渐衍生出对产品的维修性（maintainability）、可用性（availability）、保障性（supportability）、测试性（testability）、安全性（safety）等质量特性的工程学研究。“维修性工程”和“安全性工程”是从“可靠性工程”中分离出来的，而“保障性工程”和“测试性工程”又是从“维修性工程”中独立出来的。新的 XX 性陆续分出，因为这些特性紧密相关，已经分出的 XX 性围绕可靠性又重新集成起来，在 20 世纪 80 年代呈现综合化发展趋势。可靠性的含义不断扩展，从狭义可靠性演变为广义可靠性，从狭义可靠性工程演变为广义可靠性工程。</p>
+<p>1980 年代初期，为了避免因为扩展可靠性固有的含义引发的可靠性定性含义和可靠性的定量含义之间的理解混乱，Jean-Claude Laprie 选择“可信性”（dependability）作为术语，根据国际电工委员会标准，可信性的定义是，用以描述可用性及其影响因素（可靠性、维修性和维修保障性）的集合性术语，可信性仅用于非定量术语的一般描述。某些情况下，可信性还包含耐久性（durability）、安全性（safety）、安全保密性（security）等其他特性。<strong>可信性可以理解为广义可靠性</strong>。</p>
+<p>当今在国际上有两个比较完整的可靠性标准化体系，一个是美国军用标准（MIL-STD），另一个是国际电工委员会（IEC）标准。美国军用标准多年来一直扮演着研究开发可靠性相关标准文件的带头角色，也是最早制定可靠性标准的。最早的可靠性定义是由美国 AGREE 在 1957 年的报告中提出的，1966 年美国的 MIL-STD-721B 又给出了传统的或经典的可靠性定义，即产品在规定的条件下和规定的时间内完成规定功能的能力。最主要的可靠性国际标准组织是国际电工委员会的 TC56 技术委员会，TC56 的发展时间线<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup>：</p>
+<ul>
+<li>1965，国际电工委员会 IEC 成立名为“电子元件和设备可靠性”（Reliability of Electronic Components and Equipment）的技术委员会，即 TC56。</li>
+<li>1973，TC56 更名为“可靠性与维修性”（Reliability and Maintainability）技术委员会。</li>
+<li>1985，TC56 技术委员会成立了软件可靠性工作组，开始制定软件可靠性和维修性标准。</li>
+<li>1989，TC56 更名为“可信性”（Dependability）技术委员会，此名称一直沿用至今。</li>
+<li>1990，TC56 在与国际标准化组织（ISO）协商后，工作范围应不再局限于电工技术领域，而是解决所有学科的通用可靠性问题，从而使 IEC/TC56 成为所谓的横向委员会。</li>
+</ul>
+<p>我国与 IEC/TC56 对口的专业技术标准化组织是，TC24 全国电工电子产品可靠性与维修性标准化技术委员会（简称“可标委”），成立于 1982 年，挂靠在工业和信息化部电子第五研究所（又名中国电子产品可靠性与环境试验研究所）。</p>
+<h1 id="可信性与质量六性">可信性与质量六性</h1>
+<p>除了上文的“可信性”集合性术语外，有些资料将广义可靠性解释为，“可用性 + 可靠性 + 维修性”，这三个质量特性也被缩写为 RAM。RAM 有时候会再加上安全性（Safety），被缩写为 <a href="https://en.wikipedia.org/wiki/RAMS">RAMS</a>。使用 RAMS 缩写的典型例子是国际电工委员会的 <a href="https://webstore.iec.ch/publication/6747">IEC 62278:2002</a> 标准（等同的国家标准 <a href="https://std.samr.gov.cn/gb/search/gbDetailed?id=71F772D76DCCD3A7E05397BE0A0AB82A">GB/T 21562-2008</a>）。</p>
+<p>另外，常见的可靠性相关的缩写是 RMS 和 RMTSS。RMS 代表可靠性、维修性、保障性，或称“三性”。RMTSS 代表可靠性、维修性、测试性、保障性、安全性，或称“五性”。质量“三性”或“五性”，也是我国军用武器装备的军用标准要求的通用质量特性。我国武器装备的军用标准学习和借鉴的是美国军用标准，军用装备的质量特性分为专用质量特性和通用质量特性。专用质量特性，反映的是不同系统或者装备自身的特点和个性特征，主要指的是功能和性能，如某型飞机的最大（最小）飞行速度、巡航速度、飞行高度等指标。通用质量特性，则表征不同装备的共性特征。通用质量特性是逐渐演变的，从一开始的“二性”演变为“六性”<sup class="footnote-ref"><a href="#fn3" id="fnref3">[3]</a></sup><sup class="footnote-ref"><a href="#fn4" id="fnref4">[4]</a></sup>，通用质量特性包含的特性如下：</p>
+<ul>
+<li>二性：可靠性、维修性（也缩写为 R&amp;M）</li>
+<li>三性：可靠性、维修性、保障性（也缩写为 RMS）</li>
+<li>五性：可靠性、维修性、测试性、保障性、安全性（也缩写为 RMTSS）</li>
+<li>六性：可靠性、维修性、保障性、测试性、安全性、环境适应性</li>
+</ul>
+<p><strong>通用质量特性与可信性的含义大体上相同</strong>。质量特性、可信性、可靠性的关系，如下图所示：</p>
+<img width="700" alt="质量特性、可信性、可靠性的关系" title="质量特性、可信性、可靠性的关系" src="https://static.nullwy.me/quality-characteristics-classification.png">
+<p>根据国际电工委员会 IEC 60050 (191):1990（等同的国家标准 GB/T 3187-1994 《可靠性、维修性术语》）、IEC 60050-192:2015（等同于 GB/T 2900.99-2016 《电工术语 可信性》）以及国家军用标准 GJB 451A-2005 《可靠性维修性保障性术语》（与美国军用标准 <a href="http://everyspec.com/MIL-STD/MIL-STD-0700-0799/MIL-STD-721C_1040/">MIL-STD-721C</a> 相似）等标准文档，相关特性的定义和度量指标如下：</p>
+<ul>
+<li><strong>可信性（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-01-22">dependability</a>）</strong>：用以描述可用性及其影响因索（可靠性、维修性和维修保障性）的集合性术语。可信性仅用于非定量术语的一般描述。</li>
+<li><strong>可靠性（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-01-24">reliability</a>）</strong>：在给定的条件，给定的时间区间，能无故障地执行要求的能力。可靠性一般用可靠度（reliability）、平均故障间隔时间（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-13">MTBF</a>）、使用寿命（useful life）等参数来度量。</li>
+<li><strong>可用性（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-01-23">availability</a>）</strong>：在所要求的外部资源得到提供的情况下，产品在给定的条件下，在给定的时刻或时间区间内处于能完成要求的功能的状态的能力。此能力是产品的可靠性、维修性和维修保障性的综合反映。可用性的度量指标称为可用度（availability），表示为平均可用时间同平均可用时间与平均不可用时间的和之比。</li>
+<li><strong>维修性（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-01-27">maintainability</a>）</strong>：在给定的条件下，使用所述的程序和资源实施维修时，产品在给定的使用条件下保持或恢复能完成要求的功能的状态的能力。维修性反映产品修理的难易程度，主要使用平均修复时间（MTTR）来度量。</li>
+<li><strong>保障性（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-01-31">supportability</a>）</strong>：在规定的运行剖面和给定的后勤与维修资源下，保防能维待要求的可用性的能力。维修保障（maintenance support），是维修产品的资源的供给，资源包括人力资源、保障设备、材料和备件、维修设施、文档和信息以及维修信息系统。保障性一般用平均保障延误时间、资源满足率、资源利用率等参数来度量。</li>
+<li><strong>测试性（testability）</strong>：是指产品能及时并准确地确定其状态（可工作、不可工作或性能下降），并隔离其内部故障的能力。测试性反映产品是否易于测试、出现故障时是否易于检测和隔离，一般用检测时间、技术准备时间、故障检测率、故障隔离率等参数来度量。</li>
+<li><strong>安全性（safety）</strong>：是指产品所具有的不导致人员伤亡、系统毁坏、重大财产损失或不危及人员健康和环境的能力。安全性可理解为产品在任何情况下对人员、系统、财产和环境都不构成安全威胁。它可定义为产品在规定的条件下和规定的时间内，以可接受的风险执行规定功能的能力。安全性一般用事故概率、损失率、安全可靠度等参数来度量。</li>
+<li><strong>环境适应性（environmental worthiness）</strong>：是指产品在其寿命期内预计可能遇到的各种环境作用下能实现其所有预定功能、性能和（或）不被破坏的能力。它反映了产品对各种环境的适应能力，即在其可能遇到的各种环境下均能正常工作的能力，是可靠性的一种特殊情况。环境适应性鉴定试验通过的判定准则是，在所有试验条件下“零故障”。</li>
+</ul>
+<p><strong>通用质量特性的“六性”之间是紧密联系的</strong><sup class="footnote-ref"><a href="#fn4" id="fnref4:1">[4:1]</a></sup><sup class="footnote-ref"><a href="#fn5" id="fnref5">[5]</a></sup>：</p>
+<ul>
+<li>维修性是对可靠性的补充，如果产品不发生故障就不需要修复性维修。</li>
+<li>可用性是产品的可靠性、维修性和维修保障性的综合反映。</li>
+<li>保障性为产品正常使用与维修提供外部资源的支持，提供使用保障和维修保障，可靠性和维修性依赖于保障性。</li>
+<li>测试性是维修性的基础，维修依赖于测试，产品要修理一定要先发现故障和隔离故障，所以测试性设计得好，维修时间就可大大缩短。</li>
+<li>安全性本是可靠性的一部分，是避免人员伤亡、健康损害、财产或环境损害风险的可靠性。可靠性是安全性的基础，很多安全性问题都是因为产品不可靠造成的，所以提高产品可靠性也能提高安全性，当然并非所有安全性问题都是不可靠引起的。</li>
+<li>环境适应性是可靠性的一种特殊情况，是可靠性研究的前提，研究可靠性首先要确定产品是否有足够的环境适应性。</li>
+</ul>
+<p>通用质量特性的“六性”工作围绕故障（failure）而展开，也被人称为“故障六性”<sup class="footnote-ref"><a href="#fn6" id="fnref6">[6]</a></sup><sup class="footnote-ref"><a href="#fn4" id="fnref4:2">[4:2]</a></sup>。可靠性的目标是减少故障；维修性的目标是修复故障；测试性的目标是检测故障；保障性保证出现故障时可以快速供应维修资源；安全性旨在出现故障以后降低风险；环境适应性鉴定试验通过的判定准则是，在所有试验条件下“零故障”<sup class="footnote-ref"><a href="#fn5" id="fnref5:1">[5:1]</a></sup>。</p>
+<img width="450" alt="故障六性" title="故障六性" src="https://static.nullwy.me/quality-6-characteristics.png">
+<p>可靠性是产品质量特性之一，是一种面向时间的质量特性（time oriented quality characteristic）<sup class="footnote-ref"><a href="#fn7" id="fnref7">[7]</a></sup>。Lloyd Condra 在<a href="https://www.amazon.com/dp/B00SC8DKDG">书中</a>对可靠性和质量的关系的解释是，“可靠性是质量随着时间的变化（reliability is quality over time）”，“为了衡量产品的质量水平，我们对现在的产品进行评判，而为了度量产品的可靠性水平，则要对产品未来会是什么样子进行评判”。这里的讨论的质量其实指的是符合性质量，质量管理一开始是从符合性质量开始的，质量管理的主要工作是质量检验（Quality Inspection），检测产品是否符合规格，质量检验的结果即合格品率。质量管理的关注焦点是产品的合格品率，而可靠性关注焦点是产品在用户使用过程中合格水平随着时间的保持能力，如下图所示 <sup class="footnote-ref"><a href="#fn5" id="fnref5:2">[5:2]</a></sup>：</p>
+<img width="600" alt="质量与可靠性关系示意图" title="质量与可靠性关系示意图" src="https://static.nullwy.me/quality-vs-reliability.png">
+<h1 id="故障与失效的区别">故障与失效的区别</h1>
+<p>可靠性工程中有两个基本而重要的术语“fault”和“failure”。在我国的可靠性标准文档中，把“fault”翻译为“故障”，把“failure”翻译为“失效”或“故障”，也就是说，“失效”对应的英文只有“failure”；而“故障”对应的英文是“fault”或“failure”<sup class="footnote-ref"><a href="#fn8" id="fnref8">[8]</a></sup><sup class="footnote-ref"><a href="#fn9" id="fnref9">[9]</a></sup>。</p>
+<p>我国第一个定义可靠性相关的常用术语的国家标准是 GB 3187-1982 《可靠性基本名词术语及定义》，该标准对英文术语“failure”的中文翻译是“失效”或“故障”，并把“mean time between failures”翻译是“平均无故障时间”：<sup class="footnote-ref"><a href="#fn8" id="fnref8:1">[8:1]</a></sup></p>
+<blockquote>
+<p>2.2.1 失效（故障） failure：产品丧失规定的功能。对可修复产品通常也称故障。<br>
+2.5.5 平均寿命（平均无故障时间） mean life (mean time between failures)：寿命（无故障时间）的平均值。</p>
+</blockquote>
+<p>替代 GB 3187-1982 的新国家标准是 <a href="https://std.samr.gov.cn/gb/search/gbDetailed?id=71F772D7962ED3A7E05397BE0A0AB82A">GB/T 3187-1994</a> 《可靠性、维修性术语》（等同于 IEC 60050-191:1991），该标准把“failure”仅翻译为“失效”，不再又称“故障”。完整的术语定义如下：</p>
+<blockquote>
+<p>4.1.1 失效 failure<br>
+产品终止完成规定功能的能力这样的事件。<br>
+4.2.1 故障 fault<br>
+产品不能执行规定功能的状态。预防性维修或共他计划性活动或缺乏外部资源的情况除外。故障通常是产品本身失效后的状态，但也可能在失效前就存在。</p>
+</blockquote>
+<p>基于上述的定义，对于性能随时间逐渐退化的产品，故障（fault）与失效（failure）的区别，如下图所示<sup class="footnote-ref"><a href="#fn10" id="fnref10">[10]</a></sup>：</p>
+<img width="600" alt="故障（fault）与失效（failure）的区别" title="故障（fault）与失效（failure）的区别" src="https://static.nullwy.me/reliability-fault-vs-failure.png">
+<p>国外历来都是将“fault”和“failure”的定义加以区分的，我国新的标准文档也区分翻译为“故障”和“失效”，但是实际上在我国的电工行业中的惯用情况是把“fault”和“failure”都翻译为“故障”，很多书籍资料也不严格区分。比如，中国质量协会的《可靠性工程师手册》（第 2 版 2017<sup class="footnote-ref"><a href="#fn5" id="fnref5:3">[5:3]</a></sup>)，不严格区分“故障”与“失效”术语，统一都使用“故障”，书中的解释如下：</p>
+<blockquote>
+<p>在我国的可靠性工程应用中，一般不对故障与失效进行严格的区分，如失效树分析也称为故障树分析，故障模式、影响分析也称为失效模式、影响分析。因此本书也不做严格区分，多数情况下故障一词也可用失效代替。</p>
+</blockquote>
+<p>一般而言，故障是产品本身失效后的状态，此时产品处于故障状态，这时故障和失效是不需要严格加以区分。对无故障容忍能力的产品而言，故障即失效。然而，对有故障容忍能力的产品，产品可以出故障，但不会失效，这时我们就必须区分失效和故障的概念<sup class="footnote-ref"><a href="#fn9" id="fnref9:1">[9:1]</a></sup>。故障容忍（容错，<a href="https://en.wikipedia.org/wiki/Fault_tolerance">fault tolerance</a>），是在某些故障出现时继续运行的能力，只有当所有冗余的硬件同时有故障时，产品才失效。</p>
+<h1 id="可靠性的度量">可靠性的度量</h1>
+<p>可靠性的度量指标是<strong>可靠度</strong>（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-05">reliability</a>），根据国际电工委员会的标准文档，可靠度的定义是：在给定的条件下在时间区间 (t1, t2) 内按要求执行的概率。当 t1=0 和 t2=t，则 R(0,t) 可简化为 R(t)，并称为产品的<strong>可靠度函数</strong>（reliability function）。</p>
+<p>若在 t=0 时产品的总数为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>N</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">N_0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，在 0 ~ t 的时间内累计的故障数为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>N</mi><mi>f</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">N_f(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span>，正常的产品数为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">N_s(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span>，则有：</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>N</mi><mn>0</mn></msub><mo>=</mo><msub><mi>N</mi><mi>f</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">N_0 = N_f(t) + N_s(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span></p>
+<p>产品在 t 时刻的可靠度的估计值为：</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>^</mo></mover><mo>=</mo><mfrac><mrow><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><msub><mi>N</mi><mn>0</mn></msub></mfrac></mrow><annotation encoding="application/x-tex">\hat{R(t)}=\frac{N_s(t)}{N_0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2634em;vertical-align:-0.25em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0134em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span><span style="top:-3.319em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.4551em;vertical-align:-0.4451em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
+<p>显然，当 t=0 时，R(0) = 1，当 t=∞ 时，R(∞) = 0。</p>
+<p>可靠度的反面是<strong>不可靠度</strong>（unreliability），含义是：在规定的条件下，在规定的时间内，不能完成规定功能的概率。<strong>不可靠度函数</strong>通常记为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span>，不可靠度的估计值的计算公式为：</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>^</mo></mover><mo>=</mo><mfrac><mrow><msub><mi>N</mi><mi>f</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><msub><mi>N</mi><mn>0</mn></msub></mfrac><mo>=</mo><mfrac><mrow><msub><mi>N</mi><mn>0</mn></msub><mo>−</mo><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><msub><mi>N</mi><mn>0</mn></msub></mfrac><mo>=</mo><mn>1</mn><mo>−</mo><mover accent="true"><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">\hat{F(t)} = \frac{N_f(t)}{N_0} = \frac{N_0 - N_s(t)}{N_0} = 1 - \hat{R(t)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2634em;vertical-align:-0.25em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0134em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span><span style="top:-3.319em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.4832em;vertical-align:-0.4451em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0381em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5131em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3488em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2901em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.4551em;vertical-align:-0.4451em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.2634em;vertical-align:-0.25em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0134em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span><span style="top:-3.319em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25em;"><span></span></span></span></span></span></span></span></span></p>
+<p><strong>示例</strong>：假设在 t=0，投入工作的 10000 只灯泡，以天作为度量时间的单位，在 t= 365 天时，发现有 300 只灯泡坏了，这时的可靠度和不可靠度的计算如下：</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>R</mi><mo stretchy="false">(</mo><mn>365</mn><mo stretchy="false">)</mo></mrow><mo>^</mo></mover><mo>=</mo><mfrac><mrow><mn>1000</mn><mo>−</mo><mn>300</mn></mrow><mn>1000</mn></mfrac><mo>=</mo><mn>0.97</mn></mrow><annotation encoding="application/x-tex">\hat{R(365)} = \frac{1000 - 300}{1000} = 0.97</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2634em;vertical-align:-0.25em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0134em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord">365</span><span class="mclose">)</span></span></span><span style="top:-3.319em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1000</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1000</span><span class="mbin mtight">−</span><span class="mord mtight">300</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0.97</span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>F</mi><mo stretchy="false">(</mo><mn>365</mn><mo stretchy="false">)</mo></mrow><mo>^</mo></mover><mo>=</mo><mfrac><mn>300</mn><mn>1000</mn></mfrac><mo>=</mo><mn>0.03</mn></mrow><annotation encoding="application/x-tex">\hat{F(365)} = \frac{300}{1000} = 0.03</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2634em;vertical-align:-0.25em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0134em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord">365</span><span class="mclose">)</span></span></span><span style="top:-3.319em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1000</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">300</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0.03</span></span></span></span></p>
+<p>对不可靠度函数求导，其导数称为<strong>故障概率密度函数</strong>，通常记为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">f(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span>：</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>lim</mi><mo>⁡</mo></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi><mo>→</mo><mn>0</mn></mrow></msub><mfrac><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">f(t) = \lim_{\Delta t \to 0} \frac{F(t + \Delta t) - F(t)} {\Delta t}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.355em;vertical-align:-0.345em;"></span><span class="mop"><span class="mop">lim</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mrel mtight">→</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">F</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.13889em;">F</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
+<p>某时刻尚未发生故障的产品，在该时刻后单位时间内发生故障的概率，称为产品的<strong>故障率</strong>（<a href="https://en.wikipedia.org/wiki/Failure_rate">failure rate</a>），记为记为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">λ(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">λ</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span>。故障率的计算公式如下：</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>λ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>^</mo></mover><mo>=</mo><mfrac><mrow><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mtext>间隔时间内的故障数</mtext><mrow><mtext>间隔起点的存活数</mtext><mo>×</mo><mtext>时间间隔</mtext></mrow></mfrac></mrow><annotation encoding="application/x-tex">\hat{λ(t)} = \frac{N_s(t) - N_s(t + \Delta t)} {N_s(t) \Delta t} = \frac{间隔时间内的故障数}{间隔起点的存活数 × 时间间隔}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2634em;vertical-align:-0.25em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0134em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">λ</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span><span style="top:-3.319em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.53em;vertical-align:-0.52em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2757em;vertical-align:-0.4033em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord cjk_fallback mtight">间隔起点的存活数</span><span class="mbin mtight">×</span><span class="mord cjk_fallback mtight">时间间隔</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord cjk_fallback mtight">间隔时间内的故障数</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4033em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>lim</mi><mo>⁡</mo></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi><mo>→</mo><mn>0</mn></mrow></msub><mfrac><mrow><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><msub><mi>N</mi><mi>s</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mrow><mi>lim</mi><mo>⁡</mo></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi><mo>→</mo><mn>0</mn></mrow></msub><mfrac><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">λ(t) = \lim_{\Delta t \to 0} \frac{N_s(t) - N_s(t + \Delta t)} {N_s(t) \Delta t} = \lim_{\Delta t \to 0} \frac{F(t + \Delta t) - F(t)}{R(t)\Delta t} = \frac{f(t)}{R(t)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">λ</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.53em;vertical-align:-0.52em;"></span><span class="mop"><span class="mop">lim</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mrel mtight">→</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em;"><span style="top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.53em;vertical-align:-0.52em;"></span><span class="mop"><span class="mop">lim</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mrel mtight">→</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.00773em;">R</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">F</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mbin mtight">+</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.13889em;">F</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.53em;vertical-align:-0.52em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.00773em;">R</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
+<p>在长期的可靠性实践中，人们发现许多产品的故障率随时间的变化曲线形似浴盆，所以习惯性的将故障率曲线称为“浴盆曲线”（<a href="https://en.wikipedia.org/wiki/Bathtub_curve">bathtub curve</a>），如下图所示<sup class="footnote-ref"><a href="#fn5" id="fnref5:4">[5:4]</a></sup>。大多数电子产品的故障率曲线的形状就是浴盆曲线。</p>
+<img width="600" alt="产品典型的故障率曲线" title="产品典型的故障率曲线" src="https://static.nullwy.me/reliability-bathtub-curve.png">
+<p>故障率随时间的变化大致可以分为以下三个阶段：早期故障期（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-02-28">early failure period</a>）、偶然故障期（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-02-30">random failure period</a>）、耗损故障期（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-02-31">wear-out failure period</a>）。三个阶段有时也被称为：早夭期（infant mortality period）、使用寿命期（useful life period）和耗损期（wear-out period）。故障率曲线与人类的死亡率曲线相似，曲线的三个阶段分别对应人类生命周期的婴幼儿时期、壮年期以及老年期。在偶然故障期，产品的故障率可降到一个较低的水平，且基本处于平稳状态，可以近似认为故障率为常数。</p>
+<p>如果产品的故障率为常数，那么其故障的概率分布可以用指数分布（<a href="https://zh.wikipedia.org/wiki/%E6%8C%87%E6%95%B0%E5%88%86%E5%B8%83">exponential distribution</a>）描述，指数分布是唯一具有恒定故障率的连续概率分布。恒定故障率的特性也被称为“无记忆性”（<a href="https://en.wikipedia.org/wiki/Memorylessness">memorylessness</a>），该特性说明故障率在任何时刻都与系统已工作过的时间长短没有关系。服从指数分布的概率密度函数为：</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>λ</mi><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><mi>t</mi></mrow></msup></mrow><annotation encoding="application/x-tex">f(t) = {\lambda} e^{-\lambda t}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8491em;"></span><span class="mord"><span class="mord mathnormal">λ</span></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">λ</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span></span></span></p>
+<p>服从指数分布的可靠度函数、不可靠度函数和故障率函数依次为：</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><mi>t</mi></mrow></msup></mrow><annotation encoding="application/x-tex">R(t) = e^{-\lambda t}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8491em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">λ</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo>−</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><mi>t</mi></mrow></msup></mrow><annotation encoding="application/x-tex">F(t) = 1 - e^{-\lambda t}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8491em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">λ</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda(t) = \lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">λ</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">λ</span></span></span></span></p>
+<p>公式中的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">λ</span></span></span></span>为常数。</p>
+<p>上面提到的这些指标是概率相关的度量指标。另外，还有一些是时间相关的度量指标：</p>
+<ul>
+<li><strong>平均故障间隔时间</strong>（MTBF，mean time between failures）：相邻两次故障间的持续时间的平均值。失效间隔时间（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-03">time between failures</a>）包括可用时间和不可用时间。MTBF 只能用于可修复产品。</li>
+<li><strong>平均故障间隔工作时间</strong>（MTBF /<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-13">MOTBF</a>，mean operating time between failures）：相邻两次故障间的累计工作时间的平均值。MOTBF 只能用于可修复产品，该值也被成为可修复产品的平均寿命（mean life）。</li>
+<li><strong>平均故障前工作时间</strong>（<a href="">MTTF</a>，mean operating time to failure）：故障前工作时间的平均值。等同于，平均失效前时间（MTTF，mean time to failure）。MTTF 可以用于不可修复产品和可修复产品。MTTF 值也被成为不可修复产品的平均寿命（mean life）。</li>
+<li><strong>平均恢复时间</strong>（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-07-23">MTTR</a>，mean time to restoration）：恢复时间的平均值。最新的国际电工委员会 IEV 标准文档，废弃了平均恢复时间（mean time to recovery）和平均修理时间（mean time to repair）。平均恢复时间是维修性的主要度量指标。</li>
+<li><strong>可用性</strong>（<a href="https://en.wikipedia.org/wiki/Availability">availability</a>）：或者翻译为“可用度”，可以表示为平均可用时间除以平均可用时间与平均不可用时间之和。可用性是反映可靠性和维修的综合性指标。</li>
+</ul>
+<p>根据国际电工委员会标准文档 IEC 60050-192:2015（等同的国家标准文档是 <a href="https://std.samr.gov.cn/gb/search/gbDetailed?id=71F772D81729D3A7E05397BE0A0AB82A">GB/T 2900.99-2016</a>《电工术语 可信性》），MTBF 和 <a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-13">MOTBF</a> 缩写代表的都是<strong>平均故障间隔工作时间</strong>（mean operating time between failures），统计的值是<strong>故障间隔工作时间</strong>（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-04">operating time between failures</a>），即相邻两次故障间的累计工作时间；而<strong>故障间隔时间</strong>（<a href="https://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=192-05-03">time between failures</a>），包括可用时间和不可用时间。所以，<strong>平均故障间隔时间</strong>和<strong>平均故障间隔工作时间</strong>的含义是不同的，前者同时统计包括工作时间（operating time）和非工作时间（non-operating time），而后者只统计工作时间（operating time）。但是在很多其他文档中，比如维基百科的词条“平均故障间隔时间”（<a href="https://en.wikipedia.org/wiki/Mean_time_between_failures">Mean time between failures</a>）词条，“平均失效间隔时间”的缩写也是 MTBF。<strong>也就说， MTBF 即是“平均故障间隔时间”的缩写，也是“平均故障间隔工作时间”的缩写，但两者含义却不同，需要读者自行辨别</strong>。本文使用 MTBF，统一都表示“平均故障间隔时间”。</p>
+<p><strong>MTBF 只能用于可修复产品，MTTF 用于不可修复产品和可修复产品</strong>。对于不可修复产品，MTTF 等同于 MTBF，对于可修复产品，MTTF 等同于 MOTBF。MTBF 是 MTTR 和 MTTF 的总和，即<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>T</mi><mi>B</mi><mi>F</mi><mo>=</mo><mi>M</mi><mi>T</mi><mi>T</mi><mi>R</mi><mo>+</mo><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi></mrow><annotation encoding="application/x-tex">MTBF = MTTR + MTTF</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MTBF</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">MTTR</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MTTF</span></span></span></span>。</p>
+<p>产品的<strong>平均寿命</strong>（mean life）的理论值为故障概率密度函数的<a href="https://zh.wikipedia.org/wiki/%E6%9C%9F%E6%9C%9B%E5%80%BC">期望值</a>，记为 θ。该期望值也是可修复产品的 MOTBF 的理论值，是不可修复产品的 MTTF 的理论值。平均寿命或 MTTF 的计算公式如下：</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi><mo>=</mo><mi>θ</mi><mo>=</mo><mi>E</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∫</mo><mn>0</mn><mi mathvariant="normal">∞</mi></msubsup><mi>t</mi><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">d</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">MTTF = θ = E(T) = \int_{0}^\infty t f(t)\,\mathrm{d}x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MTTF</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2151em;vertical-align:-0.3558em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8593em;"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span><span style="top:-3.2579em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">∞</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3558em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathrm">d</span><span class="mord mathnormal">x</span></span></span></span></p>
+<p>如果概率密度函数服从指数分布，那么平均寿命或 MTTF 值为：</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi><mo>=</mo><mi>θ</mi><mo>=</mo><mn>1</mn><mi mathvariant="normal">/</mi><mi>λ</mi></mrow><annotation encoding="application/x-tex">MTTF = θ = 1/\lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MTTF</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1/</span><span class="mord mathnormal">λ</span></span></span></span></p>
+<p>对于服从指数分布的产品，当产品工作时间到达平均寿命时，可靠度的值 36.8%：</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>e</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><mn>36.8</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">R(θ) = e^{-1} = 36.8\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">36.8%</span></span></span></span></p>
+<p>假设某可修复产品的正常工作时间为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><msub><mrow><mi>T</mi><mi>F</mi><mi>F</mi></mrow><mn>1</mn></msub><mo separator="true">,</mo><msub><mrow><mi>T</mi><mi>F</mi><mi>F</mi></mrow><mn>2</mn></msub><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><msub><mrow><mi>T</mi><mi>F</mi><mi>F</mi></mrow><mi>n</mi></msub><mo fence="true">}</mo></mrow><annotation encoding="application/x-tex">\left\{ {TFF}_1, {TFF}_2 ...,  {TFF}_n \right\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">{</span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">TFF</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">TFF</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">...</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">TFF</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">}</span></span></span></span></span>，故障时间为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><msub><mrow><mi>T</mi><mi>T</mi><mi>R</mi></mrow><mn>1</mn></msub><mo separator="true">,</mo><msub><mrow><mi>T</mi><mi>T</mi><mi>R</mi></mrow><mn>2</mn></msub><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><msub><mrow><mi>T</mi><mi>T</mi><mi>R</mi></mrow><mi>n</mi></msub><mo fence="true">}</mo></mrow><annotation encoding="application/x-tex">\left\{ {TTR}_1, {TTR}_2 ..., {TTR}_n \right\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">{</span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">TTR</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">TTR</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">...</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">TTR</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">}</span></span></span></span></span>，如下图所示：</p>
+<img width="600" alt="MTBF、MTTF 和 MTTR 示意图" title="MTBF、MTTF 和 MTTR 示意图" src="https://static.nullwy.me/reliability-mtbf-mttf-mttr.png">
+<p>MTBF、MTTF、MTTR 和可用性（availability）的估计值的计算公式如下：</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>T</mi><mi>B</mi><mi>F</mi><mo>=</mo><mfrac><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mrow><mi>T</mi><mi>B</mi><mi>F</mi></mrow><mi>i</mi></msub></mrow><mi>n</mi></mfrac><mo>=</mo><mfrac><mtext>total uptime + total downtime</mtext><mtext>total number of failures</mtext></mfrac></mrow><annotation encoding="application/x-tex">MTBF = \frac{\sum_{i=1}^n {TBF}_i}{n} = \frac{\text{total uptime + total downtime}}{\text{total number of failures}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MTBF</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.405em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.06em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.535em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mop op-symbol small-op mtight" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7385em;"><span style="top:-2.1786em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3214em;"><span></span></span></span></span></span></span><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">TBF</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3281em;"><span style="top:-2.357em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2772em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9322em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total number of failures</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4461em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total uptime + total downtime</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi><mo>=</mo><mfrac><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mrow><mi>T</mi><mi>T</mi><mi>F</mi></mrow><mi>i</mi></msub></mrow><mi>n</mi></mfrac><mo>=</mo><mfrac><mtext>total uptime</mtext><mtext>total number of failures</mtext></mfrac></mrow><annotation encoding="application/x-tex">MTTF = \frac{\sum_{i=1}^n {TTF}_i}{n} = \frac{\text{total uptime}}{\text{total number of failures}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MTTF</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.405em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.06em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.535em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mop op-symbol small-op mtight" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7385em;"><span style="top:-2.1786em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3214em;"><span></span></span></span></span></span></span><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">TTF</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3281em;"><span style="top:-2.357em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2772em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9322em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total number of failures</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4461em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total uptime</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>R</mi><mo>=</mo><mfrac><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mrow><mi>T</mi><mi>T</mi><mi>R</mi></mrow><mi>i</mi></msub></mrow><mi>n</mi></mfrac><mo>=</mo><mfrac><mtext>total downtime</mtext><mtext>total number of failures</mtext></mfrac></mrow><annotation encoding="application/x-tex">MTTR = \frac{\sum_{i=1}^n {TTR}_i}{n} = \frac{\text{total downtime}}{\text{total number of failures}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">MTTR</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.405em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.06em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.535em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mop op-symbol small-op mtight" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7385em;"><span style="top:-2.1786em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3214em;"><span></span></span></span></span></span></span><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.00773em;">TTR</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3281em;"><span style="top:-2.357em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2251em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total number of failures</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total downtime</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>可用性</mtext><mo>=</mo><mfrac><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi></mrow><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi><mo>+</mo><mi>M</mi><mi>T</mi><mi>T</mi><mi>R</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>M</mi><mi>T</mi><mi>T</mi><mi>F</mi></mrow><mrow><mi>M</mi><mi>T</mi><mi>B</mi><mi>F</mi></mrow></mfrac><mo>=</mo><mfrac><mtext>total uptime</mtext><mrow><mtext>total uptime</mtext><mo>+</mo><mtext>total downtime</mtext></mrow></mfrac></mrow><annotation encoding="application/x-tex">可用性 = \frac {MTTF} {MTTF + MTTR} = \frac {MTTF} {MTBF} = \frac{\text{total uptime}}{\text{total uptime} + \text{total downtime}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord cjk_fallback">可用性</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2757em;vertical-align:-0.4033em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">MTTF</span><span class="mbin mtight">+</span><span class="mord mathnormal mtight" style="margin-right:0.00773em;">MTTR</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">MTTF</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4033em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">MTBF</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">MTTF</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.4133em;vertical-align:-0.4811em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9322em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total uptime</span></span><span class="mbin mtight">+</span><span class="mord text mtight"><span class="mord mtight">total downtime</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4461em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">total uptime</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4811em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
+<p>对于电子设备，MTBF 近似常量，比如，典型的企业级固态硬盘 SSD 的 MTBF 值可能是 200 万小时<sup class="footnote-ref"><a href="#fn11" id="fnref11">[11]</a></sup>，也就是 228 年，年故障率 AFR（<a href="https://en.wikipedia.org/wiki/Annualized_failure_rate">Annualized Failure Rate</a>） 为 0.44%（1/228）。</p>
+<p>可以利用数学和统计方法对可靠性进行预计和度量，并分析可靠性数据。但是可靠性的量化涉及大量不确定性，由于可靠性经常关系到制造和使用产品的人，人的行为和表现不像植物对肥料的反应、气象模型对海洋温度的反应那样服从于数学分析和预测，而且产品可能在大范围变化的环境中工作，因此还会有其他不确定性因素被引入。数学和统计方法虽然在适当的场合是非常有价值的，但是由于涉及大量不确定性，在实际的可靠性工程中的作用有限，在实际的工程实践中优先需要确定的是故障的原因和解决方案<sup class="footnote-ref"><a href="#fn12" id="fnref12">[12]</a></sup>。</p>
+<h1 id="软件可靠性工程">软件可靠性工程</h1>
+<p>软件可靠性工程是从硬件可靠性工程发展而来的<sup class="footnote-ref"><a href="#fn13" id="fnref13">[13]</a></sup>。在软件工程学建立初期，一些软件工程专家利用和改造硬件可靠性工程学的成果，使之移植到软件领域，从而开创了软件可靠性学科。</p>
+<p>类似的，起源于 Google 的“站点可靠性工程”（SRE, <a href="https://en.wikipedia.org/wiki/Site_reliability_engineering">Site reliability engineering</a>）也源自可靠性工程，区别是站点可靠性工程关注的是大型网站和网络服务这样的软件系统 <sup class="footnote-ref"><a href="#fn14" id="fnref14">[14]</a></sup><sup class="footnote-ref"><a href="#fn15" id="fnref15">[15]</a></sup>。</p>
+<h2 id="术语与概念">术语与概念</h2>
+<p>国家标准 <a href="https://std.samr.gov.cn/gb/search/gbDetailed?id=71F772D7805FD3A7E05397BE0A0AB82A">GB/T 11457-2006</a> 《信息技术 软件工程术语》，对软件可靠性的定义如下：</p>
+<blockquote>
+<p>2.1662 系统可靠性 system reliability<br>
+包括全部硬件和软件子系统在内的某个系统，在规定的环境及时间里正确执行所要求的任务或使命的概率。<br>
+2.1528 软件可靠性 software reliability<br>
+a) 在规定条件下，在规定的时间内，软件不引起系统失效的概率。该概率是系统输人和系统使用的函数，也是软件中存在的缺陷的函数。系统输人将确定是否会遇到已存在的缺陷（如果有缺陷存在的话）。<br>
+b) 在规定的时间周期内所述条件下程序执行所需要的功能的能力。</p>
+</blockquote>
+<p>GB/T 11457-2006 吸收了 <a href="https://standards.ieee.org/ieee/610.12/855/">IEEE Std 610.12-1990</a> 全部术语，包括术语“软件可靠性”，国标的术语定义只是对 IEEE 术语定义的中文翻译。IEEE 最早在标准文档中定义“软件可靠性”是在 <a href="https://standards.ieee.org/ieee/729/967/">IEEE Std 729-1983</a>，这个标准之后被 IEEE Std 610.12-1990 替代。</p>
+<p>IEEE 对“软件可靠性”术语给出两个定义，定义 a) 是定量的定义，也就是“可靠度”，定义 b) 是定性的定义。对比后容易发现，硬件可靠性和软件可靠性的定义是相同的。这种相容性，使这种可靠性定义能够用于既包括软件又包括硬件的系统。</p>
+<p>故障相关的术语，国家标准 GB/T 11457-2006 《信息技术 软件工程术语》的定义是：</p>
+<blockquote>
+<p><strong>2.163 隐错 bug</strong><br>
+见：出错 error(2.561) 和故障 fault(2.609)。<br>
+<strong>2.421 缺陷 defect</strong><br>
+见：故障 fault(2.609)。<br>
+<strong>2.561 出错, 误差, 差错 error</strong><br>
+a) 计算的、观察的或测量的值或条件与实际的、规定的或理论上正确的值或条件的差别。例如，在计算的结果和正确的结果之间差30m；<br>
+b) 不正确的步骤、过程或数据定义。例如，在计算机程序中的不正确的指定；<br>
+c) 不正确的结果。例如，当正确的结果是10，而计算的结果是12；<br>
+d) 产生不正确结果的人为动作。例如，在编程或操作的一部分上的不正确动作。<br>
+注：当上述所有四种定义是公共使用时，一种区分赋给定义 a) 为字差错（error），定义 b) 为字过错（fault），定义 c) 为字失效（failure）和定义 d) 为字错误（mistake）。<br>
+<strong>2.601 失效 failure</strong><br>
+系统或部件不能按规定的性能要求执行它所要求的功能。注：故障容忍在人们的动作（弄错-mistake）、它的显示（硬件或软件故障 fault）、故障的结果（失效 failure）和不正确（差错－error）结果的总数之间进行区分<br>
+<strong>2.609 故障, 缺陷 fault</strong><br>
+a) 硬件设备或部件中的缺陷。例如，短路或断线。<br>
+b) 在计算机程序中不正确的步骤、过程或数据定义。注：此定义最初由容错（fault tolerance）系统使用。在通常用法中，术语“差错（error）”和“隐错（bug）”表示同样含义。</p>
+</blockquote>
+<p>基于 IEEE 的定义，容易发现术语“fault、“<a href="https://en.wikipedia.org/wiki/Software_bug">bug</a>”和“defect”是同义词，术语“error”同时具有“mistake”、“fault”和“failure”的含义。这些术语之间的因果关系是，开发者在软件开发过程中产生人为失误（mistake），导致在软件中存在缺陷（fault, bug, defect），在软件运行时如果用户遭遇缺陷（fault, bug, defect），会引发失效（failure），如下图所示：</p>
+<img width="600" alt="软件故障的因果关系" title="软件故障的因果关系" src="https://static.nullwy.me/reliability-software-failure-cause.png">
+<p>失效（failure）是指系统或部件在特定约束下不能完成所要求的功能，用户在测试或实际使用中会观察到失效（failure）。<strong>失效（failure）是系统运行行为对用户要求的偏离，是一种面向用户的概念。故障（fault）是在系统运行时引起或可能潜在地引起失效（failure）的缺陷（defect），是一种面向开发者的概念。</strong></p>
+<h2 id="可靠性的度量-v2">可靠性的度量</h2>
+<p>早期的软件可靠性度量工作试图将硬件可靠性理论中的数学公式外推来进行软件可靠性的预测。大多数与硬件相关的可靠性模型依据的是由于“磨损”而导致的故障，而不是由于设计缺陷而导致的故障。在硬件中，由于物理磨损（如温度、腐蚀、振动的影响）导致的故障远比与设计缺陷有关的故障多。不幸的是，软件恰好相反。实际上，所有软件故障都可以追溯到设计或实现问题，磨损根本没有影响<sup class="footnote-ref"><a href="#fn16" id="fnref16">[16]</a></sup>。</p>
+<p>软件系统的故障主要是人为差错造成，涉及大量不确定性，利用数学和统计方法对可靠性进行预计和度量，在实际的工程实践中的作用有限。少数常用的与可靠性相关的度量指标是：MTBF、MTTR 和可用性。</p>
+<p>MTBF 指标衡量的是系统无故障运行的能力，也就是可靠性。MTTR 指标衡量的是系统快速从故障中恢复的能力，这种能力在硬件产品下被称为“维修性”（maintainability），但在软件系统下通常为称“韧性”（resilience）。术语“maintainability”，在硬件上下文中通常被翻译为“维修性”，而在软件上下文中通常被翻译为“维护性”或“可维护性”，软件可维护性指的是软件可被修改的能力，修改可能包括修复缺陷、增加或完善功能等。</p>
+<p>MTBF 反映的是硬件产品的寿命，是硬件产品质量的最重要的指标之一。与硬件不同，软件的 MTBF 不可控，而故障恢复的工作流程清晰，可干预程度高，研发团队可以对各环节展开精细化管理，轻松、高效地达成 MTTR 优化目标，所以软件系统的 <strong>MTTR 相对 MTBF 更加重要</strong><sup class="footnote-ref"><a href="#fn17" id="fnref17">[17]</a></sup><sup class="footnote-ref"><a href="#fn18" id="fnref18">[18]</a></sup>。</p>
+<p>可用性是衡量可靠性和韧性的综合性指标。想要提高系统的可用性，需要做的是延长无故障时间（MTTF）和缩短故障恢复时间（MTTR）。</p>
+<h1 id="可靠性设计">可靠性设计</h1>
+<p>Laprie 等人把提高系统可靠性的方法总结为<a href="https://en.wikipedia.org/wiki/Dependability#Means">四种</a>：</p>
+<ul>
+<li><strong>故障避免（fault avoidonce，简称“避错”）</strong>：在系统的设计和实现过程中使用一些开发方法来减少故障发生，并在系统投入使用之前发现系统中的故障。</li>
+<li><strong>故障排除（fault removal，简称“排错”）</strong>：故障排除可以细分为两个子类别：开发期间的排除和使用期间的排除。在系统使用之前通过<a href="https://zh.wikipedia.org/wiki/%E9%A9%97%E8%AD%89%E5%8F%8A%E7%A2%BA%E8%AA%8D">验证和确认</a>（V&amp;V）来发现和去除系统中的故障；如果系统已经投入使用，通过维护周期将其消除。</li>
+<li><strong>故障容忍（<a href="https://en.wikipedia.org/wiki/Fault_tolerance">fault tolerance</a>，简称“容错”）</strong>：容错是使系统在其某些组件中出现一个或多个故障时能够继续提供服务的能力，尽管该服务可能处于降级级别。容错技术主要是采用<strong>冗余</strong>（<a href="https://en.wikipedia.org/wiki/Redundancy_(engineering)">redundancy</a>）方法来消除故障的影响，冗余的含意是指当系统无故障时取消冗余资源不会影响系统正常运行。</li>
+<li><strong>故障预报（fault forecasting）</strong>：通过收集故障数据，建立可靠性建模，预测可能的故障。</li>
+</ul>
+<p>针对软件可靠性设计，软件故障避免技术，包括采用优秀的软件设计方法、使用强类型的程序设计语言、全面的编译器检查等；软件故障排除技术，主要是代码评审和软件测试；故障预报，能提高硬件可靠性，但是很少应用于软件可靠性。</p>
+<p>系统的资源包括硬件资源、软件资源、信息资源、时间资源，所以冗余区分 4 种方式：</p>
+<ul>
+<li><strong>硬件冗余</strong>（hardware redundancy）：通过配置额外的硬件组件实现冗余</li>
+<li><strong>软件冗余</strong>（software redundancy）：通过配置额外的软件版本实现冗余，例如 N 版本编程（<a href="https://en.wikipedia.org/wiki/N-version_programming">NVP</a>）</li>
+<li><strong>信息冗余</strong>（information redundancy）：通过对信息中外加一部分信息码或将信息存放在多个内存单元或将信息进行备份等实现冗余，例如循环冗余校验码、数据库备份等。</li>
+<li><strong>时间冗余</strong>（time redundancy）：多次执行相同的操作（重试）实现冗余，例如多次执行程序或传输数据的多个副本。</li>
+</ul>
+<p>硬件冗余和软件冗余被合称为结构冗余（structural redundancy）。相对与时间冗余，硬件冗余、软件冗余、信息冗余被合称为空间冗余（space redundancy）。</p>
+<p>在工程领域，利用冗余提高可靠性的例子很多，比如汽车的备胎、大货车的多个轮子、飞机的四台发动机或双台发动机、火箭的多台引擎和多台计算机等。《像火箭科学家一样思考》书中的“为什么冗余不是多余的”小节<sup class="footnote-ref"><a href="#fn19" id="fnref19">[19]</a></sup>中有这样一段阐述：</p>
+<blockquote>
+<p>航天器上的计算机也使用冗余装置。在地球上，电脑往往免不了崩溃或死机，而在有压力的太空环境中，计算机发生故障的概率有增无减，因为计算机在太空中要经历无数振动、冲击、变化的电流和波动的温度。正因为如此，航天飞机的计算机是4倍冗余的，即飞机上有4台计算机在运行着同样的软件。这4台计算机会通过一个多数投票系统就下一步动作进行单独投票。如果其中一台计算机发生故障，开始乱输出数据，其他3台计算机就会投票将其排除在外（没错，伙计们，火箭科学比你想象的更民主）。<br>
+冗余装置要正常工作，就必须独立运行。一架航天飞机配备4台计算机，这听起来非常棒，但由于它们运行着相同的软件，所以只要一个软件出现错误，4台计算机就会同时瘫痪。因此，航天飞机还配备了第5个备用飞行系统。该系统安装有一款不同的软件，而这款软件由不同于其他4款软件的分包商提供。如果某个一般性的软件错误使4台相同的主计算机瘫痪，则备用系统将启动，并会将航天飞机送回地球。</p>
+</blockquote>
+<p>在航天飞机上配备 4 台计算机属于硬件冗余，第 5 个备用飞行系统属于软件冗余。</p>
+<p>IDC 数据中心等级划分（<a href="https://en.wikipedia.org/wiki/Data_centre_tiers">data centre tiers</a>）主要是根据线路、电源、冷却等核心组件的冗余程度而划分的，不同的等级代表不同的可靠性和可用性。按 Uptime Institute 和 TIA-942 标准的建议，数据中心由低到高划分为 T1、T2、T3、T4 共 4 个等级，T1 级为基本型、T2 级为冗余型、T3 级为可并行维护冗余型、T4 级为容错型。4 个等级的冗余程度分别是，T1 级无冗余，T2 级部分 N+1 冗余，T3 级全部 N+1 冗余，T4 级 2N 或 2N+1 冗余。按我国国家标准《GB 50174-2017 数据中心设计规范》，数据中心由高到低划分为 A、B、C 三级，A 级为容错型，B 级为冗余型，C 级为基本型。不同的数据中心等级的对比，如下表所示（表格参考自 <sup class="footnote-ref"><a href="#fn20" id="fnref20">[20]</a></sup>）：</p>
+<img width="700" alt="数据中心等级划分" title="数据中心等级划分" src="https://static.nullwy.me/data-centre-tiers.png">
+<p>大多数商业数据中心都介于 T3 级和 T4 级之间，平衡了建设成本和可靠性。金融等行业的数据中心，如银行的数据中心，通常会同时遵循最高等级的国家标准 A 级和 Uptime Institute 的 Tier 4 级标准来建设。</p>
+<p>在生物学中，冗余是生物体的一种重要特征。生物体中的冗余结构和功能可以提高生物体的适应性和生存能力。例如，人体的很多器官是冗余的，比如耳朵、眼睛、肾、肺。冗余的器官如果出现“故障”，虽然不会让人完全失去该器官的机能，但会导致机能降级。其中一个眼睛如果完全失去视力，不会让人失明，不过视觉上无法识别远近。其中一个耳朵如果完全没有听力，不会让人失聪，但无法透过耳朵识别声音的位置。</p>
+<p>尽管冗余是一种很好的提高可靠性的措施，但额外的冗余增加到某种程度之后，就会无谓地增加设备的复杂性和成本，遵循边际效益递减规律。典型的例子是客机，随着发动机本身可靠性的提高，出于安全性和成本之间的权衡，之前的四发动机的客机越来越少见，逐渐被更省油、更低维护成本的双发动机的客机取代。</p>
+<h1 id="参考资料">参考资料</h1>
+<hr class="footnotes-sep">
+<section class="footnotes">
+<ol class="footnotes-list">
+<li id="fn1" class="footnote-item"><p>秦咏红，吕乃基：工程系统可靠性的演进，东北大学学报，2011年第4期295-299，<a href="https://qikan.cqvip.com/Qikan/Article/Detail?id=38777595">cqvip</a> <a href="#fnref1" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn2" class="footnote-item"><p>可靠性概论，工信部电子第五研究所潘勇，2015，<a href="https://book.douban.com/subject/26870237/">豆瓣</a>：第11章 可靠性标准 <a href="#fnref2" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn3" class="footnote-item"><p>2022-09 【标准解读】用标准语言解读装备“六性” <a href="https://mp.weixin.qq.com/s/FqfLL_ovGIZ-GO998HB4uw">https://mp.weixin.qq.com/s/FqfLL_ovGIZ-GO998HB4uw</a> <a href="#fnref3" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn4" class="footnote-item"><p>2021-07 张健：装备通用质量特性关系概述 <a href="https://mp.weixin.qq.com/s/nXmrTrz7c5EnEh4C_h4JEg">https://mp.weixin.qq.com/s/nXmrTrz7c5EnEh4C_h4JEg</a> <a href="#fnref4" class="footnote-backref">↩︎</a> <a href="#fnref4:1" class="footnote-backref">↩︎</a> <a href="#fnref4:2" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn5" class="footnote-item"><p>可靠性工程师手册，中国质量协会，第2版 2017，<a href="https://book.douban.com/subject/10607952/">豆瓣</a> <a href="#fnref5" class="footnote-backref">↩︎</a> <a href="#fnref5:1" class="footnote-backref">↩︎</a> <a href="#fnref5:2" class="footnote-backref">↩︎</a> <a href="#fnref5:3" class="footnote-backref">↩︎</a> <a href="#fnref5:4" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn6" class="footnote-item"><p>2018-01 北航康锐：可靠性的历史与今世 | 可靠性系统工程三部曲（上） <a href="https://mp.weixin.qq.com/s/275pk9Z-V4T3lntI-ZzYCA">https://mp.weixin.qq.com/s/275pk9Z-V4T3lntI-ZzYCA</a> <a href="#fnref6" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn7" class="footnote-item"><p>可靠性工程（Reliability Engineering），Kapur &amp; Pecht，2014，<a href="https://book.douban.com/subject/30619305/">豆瓣</a>：第1章 21世纪的可靠性工程 <a href="#fnref7" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn8" class="footnote-item"><p>2002-03 褚善元：failure和fault的定名问题 <a href="http://www.term.org.cn/CN/abstract/abstract10076.shtml">http://www.term.org.cn/CN/abstract/abstract10076.shtml</a> <a href="#fnref8" class="footnote-backref">↩︎</a> <a href="#fnref8:1" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn9" class="footnote-item"><p>2002-03 朱美娴：关于failure和fault定义的研讨 <a href="http://www.term.org.cn/CN/abstract/abstract10081.shtml">http://www.term.org.cn/CN/abstract/abstract10081.shtml</a> <a href="#fnref9" class="footnote-backref">↩︎</a> <a href="#fnref9:1" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn10" class="footnote-item"><p>System Reliability Theory, Rausand, etc., 3rd 2020，<a href="https://book.douban.com/subject/35473900/">豆瓣</a>：3 Failures and Faults, Figure 3.3 Illustration of the difference between failure and fault for a degrading item. <a href="#fnref10" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn11" class="footnote-item"><p>2021-09 揭秘：SSD 的“可靠性”到底可不可靠 <a href="https://memblaze.com/innovate/technical-articles/169.html">https://memblaze.com/innovate/technical-articles/169.html</a> <a href="#fnref11" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn12" class="footnote-item"><p>实用可靠性工程（Practical Reliability Engineering），O'Connor, etc.，第5版2012，<a href="https://book.douban.com/subject/35263950/">豆瓣</a> <a href="#fnref12" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn13" class="footnote-item"><p>陈光宇，黄锡滋：软件可靠性学科发展现状及展望，电子科技大学学报社科版，2002年第3期99-102，<a href="https://qikan.cqvip.com/Qikan/Article/Detail?id=6859748">cqvip</a> <a href="#fnref13" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn14" class="footnote-item"><p>SRE：Google运维解密，Beyer, etc. 2016，<a href="https://book.douban.com/subject/26875239/">豆瓣</a>：序言 <a href="#fnref14" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn15" class="footnote-item"><p>SRE原理与实践：构建高可靠性互联网应用，张观石，2022，<a href="https://book.douban.com/subject/36202918/">豆瓣</a>：第1章 互联网软件可靠性概论 <a href="#fnref15" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn16" class="footnote-item"><p>软件工程：实践者的研究方法，Pressman，第8版2014，<a href="https://book.douban.com/subject/26918148/">豆瓣</a>：第21章 软件质量保证，21.7 软件可靠性 <a href="#fnref16" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn17" class="footnote-item"><p>2010-07 John Allspaw: Thoughts on systems safety, software operations, and sociotechnical systems <a href="https://www.kitchensoap.com/2010/11/07/mttr-mtbf-for-most-types-of-f/">https://www.kitchensoap.com/2010/11/07/mttr-mtbf-for-most-types-of-f/</a> <a href="#fnref17" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn18" class="footnote-item"><p>2023-07 LigaAI：研发质量指标大 PK：MTTR vs MTBF，谁是靠谱王？ <a href="https://segmentfault.com/a/1190000043971564">https://segmentfault.com/a/1190000043971564</a> <a href="#fnref18" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn19" class="footnote-item"><p>像火箭科学家一样思考，Ozan Varol，2020，<a href="https://book.douban.com/subject/35228079/">豆瓣</a>：第1章 与不确定性共舞，为什么冗余不是多余的 <a href="#fnref19" class="footnote-backref">↩︎</a></p>
+</li>
+<li id="fn20" class="footnote-item"><p>2020-12 艾瑞咨询：2020年中国数据中心行业研究报告 <a href="https://report.iresearch.cn/report/202012/3699.shtml">https://report.iresearch.cn/report/202012/3699.shtml</a> <a href="#fnref20" class="footnote-backref">↩︎</a></p>
+</li>
+</ol>
+</section>
+]]></content>
+      <categories>
+        <category>架构</category>
+      </categories>
+      <tags>
+        <tag>架构</tag>
+        <tag>可靠性</tag>
+        <tag>SRE</tag>
+      </tags>
+  </entry>
 </search>
diff --git a/sitemap.txt b/sitemap.txt
index 14f9e053..7644e1c1 100644
--- a/sitemap.txt
+++ b/sitemap.txt
@@ -36,15 +36,15 @@ https://nullwy.me/tags/MySQL/
 https://nullwy.me/tags/%E6%95%B0%E6%8D%AE%E5%BA%93/
 https://nullwy.me/tags/%E4%B9%A6%E7%B1%8D/
 https://nullwy.me/tags/CS/
-https://nullwy.me/tags/InnoDB/
-https://nullwy.me/tags/%E9%94%81/
-https://nullwy.me/tags/MVCC/
 https://nullwy.me/tags/ELK/
 https://nullwy.me/tags/Elastic/
 https://nullwy.me/tags/%E6%97%A5%E5%BF%97/
-https://nullwy.me/tags/Java/
+https://nullwy.me/tags/InnoDB/
+https://nullwy.me/tags/%E9%94%81/
+https://nullwy.me/tags/MVCC/
 https://nullwy.me/tags/%E5%B7%A5%E5%85%B7/
 https://nullwy.me/tags/%E4%BB%A3%E7%A0%81/
+https://nullwy.me/tags/Java/
 https://nullwy.me/tags/IO/
 https://nullwy.me/tags/%E6%9C%8D%E5%8A%A1%E5%99%A8/
 https://nullwy.me/tags/%E7%BD%91%E7%BB%9C/
@@ -65,10 +65,10 @@ https://nullwy.me/tags/Nginx/
 https://nullwy.me/tags/OpenResty/
 https://nullwy.me/tags/%E7%BD%91%E5%85%B3/
 https://nullwy.me/tags/%E8%AF%AD%E8%A8%80/
-https://nullwy.me/tags/MyBatis/
 https://nullwy.me/tags/%E7%BC%96%E8%AF%91%E5%99%A8/
 https://nullwy.me/tags/javac/
 https://nullwy.me/tags/Lombok/
+https://nullwy.me/tags/MyBatis/
 https://nullwy.me/tags/binlog/
 https://nullwy.me/tags/ZooKeeper/
 https://nullwy.me/tags/%E5%88%86%E5%B8%83%E5%BC%8F/
diff --git a/sitemap.xml b/sitemap.xml
index 71cc2163..0bcf2a40 100644
--- a/sitemap.xml
+++ b/sitemap.xml
@@ -326,63 +326,63 @@
   </url>
   
   <url>
-    <loc>https://nullwy.me/tags/InnoDB/</loc>
+    <loc>https://nullwy.me/tags/ELK/</loc>
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     <changefreq>weekly</changefreq>
     <priority>0.2</priority>
   </url>
   
   <url>
-    <loc>https://nullwy.me/tags/%E9%94%81/</loc>
+    <loc>https://nullwy.me/tags/Elastic/</loc>
     <lastmod>2023-12-07</lastmod>
     <changefreq>weekly</changefreq>
     <priority>0.2</priority>
   </url>
   
   <url>
-    <loc>https://nullwy.me/tags/MVCC/</loc>
+    <loc>https://nullwy.me/tags/%E6%97%A5%E5%BF%97/</loc>
     <lastmod>2023-12-07</lastmod>
     <changefreq>weekly</changefreq>
     <priority>0.2</priority>
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   <url>
-    <loc>https://nullwy.me/tags/ELK/</loc>
+    <loc>https://nullwy.me/tags/InnoDB/</loc>
     <lastmod>2023-12-07</lastmod>
     <changefreq>weekly</changefreq>
     <priority>0.2</priority>
   </url>
   
   <url>
-    <loc>https://nullwy.me/tags/Elastic/</loc>
+    <loc>https://nullwy.me/tags/%E9%94%81/</loc>
     <lastmod>2023-12-07</lastmod>
     <changefreq>weekly</changefreq>
     <priority>0.2</priority>
   </url>
   
   <url>
-    <loc>https://nullwy.me/tags/%E6%97%A5%E5%BF%97/</loc>
+    <loc>https://nullwy.me/tags/MVCC/</loc>
     <lastmod>2023-12-07</lastmod>
     <changefreq>weekly</changefreq>
     <priority>0.2</priority>
   </url>
   
   <url>
-    <loc>https://nullwy.me/tags/Java/</loc>
+    <loc>https://nullwy.me/tags/%E5%B7%A5%E5%85%B7/</loc>
     <lastmod>2023-12-07</lastmod>
     <changefreq>weekly</changefreq>
     <priority>0.2</priority>
   </url>
   
   <url>
-    <loc>https://nullwy.me/tags/%E5%B7%A5%E5%85%B7/</loc>
+    <loc>https://nullwy.me/tags/%E4%BB%A3%E7%A0%81/</loc>
     <lastmod>2023-12-07</lastmod>
     <changefreq>weekly</changefreq>
     <priority>0.2</priority>
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   <url>
-    <loc>https://nullwy.me/tags/%E4%BB%A3%E7%A0%81/</loc>
+    <loc>https://nullwy.me/tags/Java/</loc>
     <lastmod>2023-12-07</lastmod>
     <changefreq>weekly</changefreq>
     <priority>0.2</priority>
@@ -529,28 +529,28 @@
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   <url>
-    <loc>https://nullwy.me/tags/MyBatis/</loc>
+    <loc>https://nullwy.me/tags/%E7%BC%96%E8%AF%91%E5%99%A8/</loc>
     <lastmod>2023-12-07</lastmod>
     <changefreq>weekly</changefreq>
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   <url>
-    <loc>https://nullwy.me/tags/%E7%BC%96%E8%AF%91%E5%99%A8/</loc>
+    <loc>https://nullwy.me/tags/javac/</loc>
     <lastmod>2023-12-07</lastmod>
     <changefreq>weekly</changefreq>
     <priority>0.2</priority>
   </url>
   
   <url>
-    <loc>https://nullwy.me/tags/javac/</loc>
+    <loc>https://nullwy.me/tags/Lombok/</loc>
     <lastmod>2023-12-07</lastmod>
     <changefreq>weekly</changefreq>
     <priority>0.2</priority>
   </url>
   
   <url>
-    <loc>https://nullwy.me/tags/Lombok/</loc>
+    <loc>https://nullwy.me/tags/MyBatis/</loc>
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     <changefreq>weekly</changefreq>
     <priority>0.2</priority>