Abstract

Some key factors in control chart use are associated with the speed of detecting process mean shifts, which are important in minimizing the number of false alarms and cost. Researchers proved that the Fixed Ratio Sampling (FRS) policy has some deficiency in detecting small and moderate shifts. Hence, they improved this issue by proposing the Variable Sample Size (VSS) strategy. They illustrated that this sampling model was more influential in detecting mean shifts. Subsequently, Variable Sample Size with Three-States (3-VSS) was investigated to improve the performance of VSS. It was shown that the performance of the 3-VSS model is more efficient than the VSS policy. In this paper, VSS and 3-VSS are considered in a multivariate Bayesian control chart based on the economic-statistical design. Due to the fact that the distribution of Bayesian statistic is hard to achieve, we apply the Monte Carlo method and employ the artificial bee colony (ABC) algorithm to obtain the optimal design parameters for VSS and 3-VSS models (sample sizes, sampling interval, warning limit(s), and control limit). Hotelling’s \(T^{2}\) and FRS are the most popular multivariate control chart and sampling scheme, respectively. Thus, in order to demonstrate the statistical and economic desirability of VSS and 3-VSS multivariate Bayesian control charts, this case study is compared with VSS and 3-VSS Hotelling’s \(T^{2}\) as well as FRS multivariate Bayesian control charts.

中文翻译：

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基于经济统计设计的样本变量为2和3的多元贝叶斯控制图

摘要

控制图使用中的一些关键因素与检测过程均值移动的速度有关，这对于最大程度地减少错误警报的数量和成本非常重要。研究人员证明，固定比率采样（FRS）策略在检测中小班次时存在一些缺陷。因此，他们通过提出可变样本大小（VSS）策略来改善此问题。他们说明，这种抽样模型在检测均值漂移方面更具影响力。随后，研究了具有三态（3-VSS）的可变样本大小以提高VSS的性能。结果表明，3-VSS模型的性能比VSS策略更有效。本文在基于经济统计设计的多元贝叶斯控制图中考虑了VSS和3-VSS。由于难以获得贝叶斯统计量的分布这一事实，我们采用蒙特卡洛方法，并采用人工蜂群（ABC）算法来获得VSS和3-VSS模型的最佳设计参数（样本大小，抽样间隔）。 ，警告限制和控制限制）。霍特林的\（T ^ {2} \）和FRS分别是最流行的多元控制图和抽样方案。因此，为了证明VSS和3-VSS多元贝叶斯控制图的统计和经济意义，将该案例研究与VSS和3-VSS Hotelling的\（T ^ {2} \）以及FRS多元贝叶斯控制进行了比较。图表。