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Run length distribution and percentiles: The Shewhart x chart with unknown parameters

机译：游程长度分布和百分位数：参数未知的Shewhart x图表

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To examine the run length distribution and the percentile of Shewhart X in case the process mean and variance are unknown. The performance of a control chart is judged in terms of certain characteristics associated with its run length distribution. The run length is a random variable defined to be the number of plots on a chart until the first signal is observed indicating an out-of-control situation. Average run length (ARL) is the traditional measure used for this purpose. However, since ARL can take only positive integer values and the run length distribution is significantly rightskewed, other more representative measures are also considered. One such measure is percentile of the two-sided Shewhart X chart for mean when the process particulars are estimated. The paper also examines the run length distribution and its percentiles. (13 refs.)
机译：要检查游程长度分布和Shewhart X的百分位数，以防过程均值和方差未知。根据控制图的运行长度分布的某些特征来判断其性能。行程长度是一个随机变量，定义为图表上的图表数量，直到观察到表示失控情况的第一个信号为止。平均行程长度（ARL）是用于此目的的传统度量。但是，由于ARL只能采用正整数，并且游程长度分布明显偏斜，因此还考虑了其​​他更具代表性的措施。一种这样的度量是当估计过程细节时，在两侧Shewhart X图表中的平均值百分数。本文还研究了游程长度分布及其百分位数。 （13个参考）

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