Group-wise monitoring of multivariate data with missing values

In this article, we aim to detect the changes in the process that generates multivariate data by monitoring their mean shift. To do this, we utilize a graphical tool known as a multivariate control chart. However, monitoring the mean of multivariate data poses two challenges: the grouped structure of individual observations and the presence of missing values. In this research, we introduce a novel method called HTC for monitoring group-wise multivariate data that includes missing values. HTC offers several advantages over existing methods. First, it is applicable to various types of dependence among individual observations within a group. Second, it provides a unique upper control limit (UCL) regardless of the missing data pattern. Lastly, HTC is computationally more efficient compared to resampling-based techniques. We conduct comprehensive numerical studies to evaluate the performance of the HTC method and compare it with the existing group-wise monitoring method, referred to as HTM. Compared to HTM, HTC achieves a higher true positive rate (TPR) while effectively controlling the in-control false alarm rate (FAR0) at a pre-determined level across various settings considered in our study. To illustrate its effectiveness, we applied HTC to monitoring multivariate environmental data collected from the manufacturing process of a semiconductor company in Korea.