In many service and manufacturing industries, process monitoring involves multivariate data, instead of univariate data. In these situations, multivariate charts are employed for process monitoring. Very often when the mean vector shifts to an out-of-control situation, the exact shift size is unknown; hence, multivariate charts for monitoring a range of the mean shift sizes in the mean vector are adopted. In this paper, directionally sensitive weighted adaptive multivariate CUSUM charts are developed for monitoring a range of the mean shift sizes. Directionally sensitive charts are useful in situations where the aim lies in monitoring either an increasing or a decreasing shift in the mean vector of the quality characteristics of interest. The Monte Carlo simulation is used to compute the run length characteristics in comparing the sensitivities of the proposed and existing multivariate CUSUM charts. In general, the directionally sensitive and weighted adaptive features enhance the sensitivities of the proposed multivariate CUSUM charts in comparison with the existing multivariate CUSUM charts without the adaptive feature or those that are directionally invariant. It is also found that the variable sampling interval feature enhances the sensitivities of the proposed and existing charts as compared to their fixed sampling interval counterparts. The implementation of the proposed charts in detecting upward and downward shifts in the in-control process mean vector is demonstrated using two different datasets.

中文翻译：

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方向敏感加权自适应多元 CUSUM 均值图

在许多服务和制造行业，过程监控涉及多变量数据，而不是单变量数据。在这些情况下，多变量图表用于过程监控。很多时候，当平均向量转移到失控状态时，确切的转移大小是未知的；因此，采用了多变量图表来监测平均向量中的一系列平均偏移大小。在本文中，开发了方向敏感的加权自适应多元 CUSUM 图以监测一系列均值偏移大小。方向敏感图表在目标在于监视感兴趣的质量特征的平均向量的增加或减少偏移的情况下很有用。Monte Carlo 模拟用于计算运行长度特性，以比较提议的和现有的多变量 CUSUM 图表的敏感性。一般来说，与没有自适应特征或方向不变的现有多元 CUSUM 图相比，方向敏感和加权自适应特征增强了所提出的多元 CUSUM 图的敏感性。还发现，与固定采样间隔对应物相比，可变采样间隔特征增强了提议和现有图表的敏感性。使用两个不同的数据集演示了所提出的图表在检测受控过程均值向量中向上和向下偏移的实现。与没有自适应特征或方向不变的现有多元 CUSUM 图相比，方向敏感和加权自适应特征增强了所提出的多元 CUSUM 图的敏感性。还发现，与固定采样间隔对应物相比，可变采样间隔特征增强了提议和现有图表的敏感性。使用两个不同的数据集演示了所提出的图表在检测受控过程均值向量中向上和向下偏移的实现。与没有自适应特征或方向不变的现有多元 CUSUM 图相比，方向敏感和加权自适应特征增强了所提出的多元 CUSUM 图的敏感性。还发现，与固定采样间隔对应物相比，可变采样间隔特征增强了提议和现有图表的敏感性。使用两个不同的数据集演示了所提出的图表在检测受控过程均值向量中向上和向下偏移的实现。还发现，与固定采样间隔对应物相比，可变采样间隔特征增强了提议和现有图表的敏感性。使用两个不同的数据集演示了所提出的图表在检测受控过程均值向量中向上和向下偏移的实现。还发现，与固定采样间隔对应物相比，可变采样间隔特征增强了提议和现有图表的敏感性。使用两个不同的数据集演示了所提出的图表在检测受控过程均值向量中向上和向下偏移的实现。