Hotelling T² control chart based on minimum vector variance for monitoring high‐dimensional correlated multivariate process

Abstract

Abstract Multivariate control charts are practical tools that simultaneously monitor several correlated quality characteristics in a process. Monitoring high‐dimensional data structures is challenging because, in most cases, the process sample size for monitoring parameters is greater than the number of process characteristics. Many researchers have used the multivariate Hotelling's T 2 chart to monitor high‐dimensional data using the maximum‐likelihood methods (MLM) to estimate the covariance matrices. However, the multivariate Hotelling's T 2 chart based on MLM suffers from low statistical performance. In this paper, we proposed a multivariate Hotelling's T 2 chart based on the minimum vector variance (MVV) and some regularized methods for monitoring high‐dimensional data structures. The performance of the proposed chart is evaluated in terms of the average run length ( ARL ). The results reveal the superiority of the proposed MVV Hotelling's T 2 chart over the existing Hotelling's T 2 charts for high‐dimensional correlated processes.