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A phase I nonparametric Shewhart-type control chart based on the median

机译：基于中位数的阶段I非参数Shewhart型控制图

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摘要

Purpose:To propose a nonparametric Shewhart-type control chart for monitoring the location of a continuous variable in a Phase I process control setting. Summary: The proposed chart is based on the pooled median of the available Phase I samples and the charting statistics are the counts in each sample that are less than the pooled median. An exact expression for the false alarm probability (FAP) is given in terms of the multivariate hypergeometric distribution and this is used to provide tables for control limits for specified nominal FAP value of 0.01,0.05 or 0.10 and for some sample sizes (n) and the number of Phase I samples (jri). Some approximations are discussed in terms of univariate hypergeometric and normal distributions. A simulation study shows that the proposed chart performs at least as well as existing Shewhart-type charts. Numerical examples for the proposed chart are included. (14 refs.)
机译：目的：提出一个非参数Shewhart型控制图，用于监视第一阶段过程控制设置中连续变量的位置。摘要：建议的图表基于可用的第一阶段样本的汇总中位数，而图表统计信息是每个样本中小于汇总中位数的计数。根据多元超几何分布给出了误报概率（FAP）的精确表达式，用于为指定的FAP标称值为0.01、0.05或0.10以及某些样本量（n）和第一阶段样本数（jri）。根据单变量超几何分布和正态分布讨论了一些近似值。仿真研究表明，所提出的图表的性能至少与现有的Shewhart型图表相同。建议的图表的数值示例包括在内。 （14篇参考文献）

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