Abstract

A control chart for monitoring the multivariate coefficient of variation (MCV) is used when the focus is on monitoring the ratio of relative multivariate variability to the mean of a multivariate process. The MCV chart is useful in process monitoring when practitioners are not interested in the consistency of the mean vector or covariance matrix. This study proposes a one-sided upward variable sampling interval (VSI) exponentially weighted moving average (EWMA) chart to detect increasing shifts in MCV squared $({\mathrm{\gamma }}^2)$ and shows the derivation of formulae to evaluate the performance of the VSI EWMA-${\mathrm{\gamma }}^2$ chart by using the Markov chain approach. Comparative investigations show that the proposed chart outperforms existing MCV charts in detecting shifts in process MCV. A numerical example that uses real data reveals that the proposed chart performs well in actual applications.

摘要

当重点是监控相对多变量变异性与多变量过程均值的比率时，使用用于监控多变量变异系数 (MCV) 的控制图。当从业者对均值向量或协方差矩阵的一致性不感兴趣时​​，MCV 图在过程监控中很有用。本研究提出了一种单边向上变量采样间隔 (VSI) 指数加权移动平均 (EWMA) 图来检测 MCV 平方的增加变化$({\mathrm{\gamma }}^2)$并显示了评估 VSI EWMA 性能的公式的推导-${\mathrm{\gamma }}^2$使用马尔可夫链方法绘制图表。比较研究表明，在检测过程 MCV 的变化方面，建议的图表优于现有的 MCV 图表。使用真实数据的数值示例表明，所提出的图表在实际应用中表现良好。