Phase-II dataset for the example.

The coefficient of variation (CV) is employed to develop control charts to measure the relative dispersion of the data. The multivariate coefficient of variation (MCV) chart is used to monitor the CV in Phase-II in a multivariate framework. In this paper, the upward and downward variable sampling interval run sum multivariate coefficient of variation (VSI RS MCV) charts are developed to detect MCV shifts. The developed VSI RS MCV charts are evaluated and compared with their existing MCV and RS MCV counterparts using the average time to signal (ATS), standard deviation of the time to signal (SDTS) and expected average time to signal (EATS) criteria. Optimization programs incorporating the Markov chain methodology are developed in MATLAB to compute the optimal parameters and scores of the developed VSI RS MCV charts that minimize the charts’ out-of-control ATS or EATS value. The findings show that the developed VSI RS MCV charts outperform both the existing RS MCV and MCV charts, for all shift sizes, in terms of the out-of-control ATS, SDTS and EATS criteria. An example is provided to elucidate the implementation of the proposed VSI RS MCV charts.

本文采用变异系数（coefficient of variation, CV）构建控制图以衡量数据的相对离散程度。多元变异系数（multivariate coefficient of variation, MCV）控制图用于多元框架下的第二阶段监测CV。本文构建了双向可变抽样区间游程和多元变异系数（VSI RS MCV）控制图，用于检测MCV偏移。本文采用平均检测时间（average time to signal, ATS）、检测时间标准差（standard deviation of the time to signal, SDTS）与期望平均检测时间（expected average time to signal, EATS）三项指标，对所提出的VSI RS MCV控制图与现有MCV控制图、游程和MCV（RS MCV）控制图进行评估与对比。本文基于马尔可夫链（Markov chain）方法开发优化程序，并通过MATLAB编程计算所提VSI RS MCV控制图的最优参数与评分，以最小化控制图失控状态下的ATS或EATS值。研究结果表明，在所有偏移幅度下，相较于现有RS MCV控制图与MCV控制图，所提VSI RS MCV控制图在失控ATS、SDTS及EATS指标上均表现更优。本文还提供了一个实例，以阐明所提出的VSI RS MCV控制图的实施流程。