The effects of measurement errors on the performances of multivariate charts have not been extensively investigated compared with univariate charts. More specifically, control charts for monitoring the multivariate coefficient of variation (MCV) in the existing literature are not investigated under the assumption that measurement errors are present. This research proposes two one-sided MCV charts in the presence of measurement errors, one for detecting decreasing MCV shifts and another for detecting increasing MCV shifts. The distribu-tional properties of the sample MCV in the presence of measurement errors are derived. Additionally, the for-mulae to compute the control limits and performance measures of the proposed charts are derived. Furthermore, a step-by-step procedure to implement the MCV charts with measurement errors is presented. Finally, an application of the proposed charts is illustrated using real data.

中文翻译：

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带有测量误差的多元变异系数图

与单变量图相比，测量误差对多变量图性能的影响尚未得到广泛研究。更具体地说，没有在假设存在测量误差的情况下研究现有文献中用于监测多变量变异系数 (MCV) 的控制图。本研究提出了两种存在测量误差的单边 MCV 图，一种用于检测减小的 MCV 偏移，另一种用于检测增加的 MCV 偏移。推导出存在测量误差时样品 MCV 的分布特性。此外，还导出了计算建议图表的控制限制和性能度量的公式。此外，还介绍了实施带有测量误差的 MCV 图表的分步程序。最后，