To improve the sensitivity of a Shewhart control chart, it is common among practitioners to use supplementary runs rules. The performance of such runs rules charts is studied in the presence of positive autocorrelation caused by a first-order discrete autoregressive process. This type of data-generating process allows to compute the chart’s run length properties exactly and efficiently, by utilizing the finite Markov chain embedding technique. Explicit formulae are derived for common types of runs rules. Afterwards, a detailed performance study about runs rules charts under serial dependence is presented.

中文翻译：

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在序列依赖性下具有补充运行规则的个人图表

为了提高Shewhart控制图的敏感性，从业人员通常会使用补充运行规则。在存在由一阶离散自回归过程引起的正自相关的情况下研究这种运行规则图的性能。通过使用有限的马尔可夫链嵌入技术，这种类型的数据生成过程可以准确高效地计算图表的游程长度属性。明确的公式是针对运行规则的常见类型得出的。然后，对串行依赖下的运行规则图进行了详细的性能研究。