Multivariate process dispersion monitoring without subgrouping

Abstract

The memory-type adaptive and non-adaptive control charts are among the best control charts for detecting small-to-moderate changes in the process parameter(s). In this paper, we propose the Crosier CUSUM (CCUSUM), EWMA, adaptive CCUSUM (ACCUSUM) and adaptive EWMA (AEWMA) charts for efficiently monitoring the changes in the covariance matrix of a multivariate normal process without subgrouping. Using extensive Monte Carlo simulations, the length characteristics of these control charts are computed. It turns out that the ACCUSUM and AEWMA charts perform uniformly and substantially better than the CCUSUM and EWMA charts when detecting a range of shift sizes in the covariance matrix. Moreover, the AEWMA chart outperforms the ACCUSUM chart. A real dataset is used to explain the implementation of the proposed control charts.

Keywords:

• Average run length
• ACCUSUM
• AEWMA
• control chart
• CUSUM
• EWMA
• Monte Carlo simulation
• statistical process control
• covariance matrix

Acknowledgments

The authors are thankful to the associate editor and two anonymous reviewers for providing useful comments that led to an improved version of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.