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首页> 外文期刊>International journal of quality, statistics, & reliability >A Nonparametric Shewhart-Type Quality Control Chart for Monitoring Broad Changes in a Process Distribution
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A Nonparametric Shewhart-Type Quality Control Chart for Monitoring Broad Changes in a Process Distribution

机译：非参数Shewhart型质量控制图，用于监视过程分布中的广泛变化

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摘要

This paper develops a distribution-free (or nonparametric) Shewhart-type statistical quality control chart for detecting a broad change in the probability distribution of a process. The proposed chart is designed for grouped observations, and it requires the availability of a reference (or training) sample of observations taken when the process was operating in-control. The charting statistic is a modified version of the two-sample Kolmogorov-Smirnov test statistic that allows the exact calculation of the conditional average run length using the binomial distribution. Unlike the traditional distribution-based control charts (such as the Shewhart X-Bar), the proposed chart maintains the same control limits and the in-control average run length over the class of all (symmetric or asymmetric) continuous probability distributions. The proposed chart aims at monitoring a broad, rather than a one-parameter, change in a process distribution. Simulation studies show that the chart is more robust against increased skewness and/or outliers in the process output. Further, the proposed chart is shown to be more efficient than the Shewhart X-Bar chart when the underlying process distribution has tails heavier than those of the normal distribution.
机译：本文开发了一种无分布（或非参数）Shewhart型统计质量控制图，用于检测过程的概率分布中的广泛变化。拟议的图表是为分组观察而设计的，它要求有过程在受控状态下进行时所获得的参考（或训练）观察样本的可用性。图表统计量是两个样本Kolmogorov-Smirnov试验统计量的修改版本，它允许使用二项式分布精确计算条件平均游程长度。与传统的基于分布的控制图（例如Shewhart X-Bar）不同，所提出的控制图在所有（对称或非对称）连续概率分布的类别上都保持相同的控制极限和控制内平均行程长度。拟议的图表旨在监视过程分布中的广泛而非单一参数的变化。仿真研究表明，该图表在过程输出中增加的偏度和/或离群值方面更具鲁棒性。此外，当基础过程分布的尾部比正态分布的尾部重时，建议的图表显示出比Shewhart X-Bar图表更有效的图表。

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