The average control chart monitors the shifts in the process. The familiar multivariate control charts are used to detect the mean vector of the process such as multivariate cumulative sum (MCUSUM) and Hotelling's T² control charts. In this paper, the effects of constructing bivariate copulas on multivariate control charts, that is, MCUSUM and Hotelling's T² control charts are intensively investigated when observations are drawn from the exponential distribution. Moreover, the dependence levels of observations are classified to be weak, moderate, and strong in both positive and negative values by Kendall's tau. The numerical results were obtained by Monte Carlo simulation to explore the average run length (ARL). The simulation results show that the performance of Hotelling's T² control chart is superior to the MCUSUM control chart for all shifts in the mean vector of process. Furthermore, from applying the presented control chart to two sets of real data, data set of the strength of 1.5 cm glass fibers measured at the National Physical Laboratory, England and data set of the strength of glass of the aircraft window, it was found that for a small shift ( $\delta \le 0.1$), the MCUSUM control chart is better than Hotelling's T² control chart.

中文翻译：

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构建的双变量 copulas 对多变量控制图有效性的影响

平均控制图监控过程中的变化。熟悉的多元控制图用于检测过程的平均向量，例如多元累积总和 (MCUSUM) 和 Hotelling 的T ²控制图。在本文中，构建双变量 copulas 对多变量控制图的影响，即 MCUSUM 和 Hotelling's T ²当从指数分布中提取观察值时，对控制图进行了深入研究。此外，Kendall's tau 在正值和负值中将观测值的依赖性级别分为弱、中等和强。数值结果是通过蒙特卡罗模拟获得的，以探索平均运行长度 (ARL)。仿真结果表明，Hotelling's T ²的性能对于过程平均向量的所有变化，控制图优于 MCUSUM 控制图。此外，将所提供的控制图应用于两组真实数据，英国国家物理实验室测量的 1.5 厘米玻璃纤维强度数据集和飞机窗户玻璃强度数据集，发现对于小班（$\delta \le 0.1$)，MCUSUM 控制图优于 Hotelling 的T ²控制图。