Statistical monitoring of the covariance matrix in multivariate processes: A literature review

Abstract

Monitoring several correlated quality characteristics of a process is common in modern manufacturing and service industries. Although a lot of attention has been paid to monitoring the multivariate process mean, not many control charts are available for monitoring the covariance matrix. This paper presents a comprehensive overview of the literature on control charts for monitoring the covariance matrix in a multivariate statistical process monitoring (MSPM) framework. It classifies the research that has previously appeared in the literature. We highlight the challenging areas for research and provide some directions for future research.

Keywords:

• covariance matrix
• multivariate control charts
• Phase I and Phase II
• statistical process monitoring (SPM)

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Mohsen Ebadi

Mohsen Ebadi is currently a postdoc fellow at the department of Statistics & Actuarial Science, University of Waterloo. He received his B.S., M.S., and PhD degrees in Industrial Engineering from Iran University of Science and Technology, Khajeh Nasir University of Technology, and Amirkabir University of Technology (Tehran Polytechnic), respectively. His research interests are in the areas of statistical process monitoring, applied statistics, and data analytics.

Shojaeddin Chenouri

Dr. Shojaeddin Chenouri is a Professor of Statistics at the Department of Statistics and Actuarial Science, University of Waterloo. His research focuses on developing nonparametric and robust statistical procedures to analyze various data structures arising from a broad range of disciplines such as engineering, health, environmental studies, and humanities. He has extensive consulting experience and publishes on a wide range of statistical and data science topics.

Dennis K. J. Lin

Dr. Dennis K. J. Lin is a Distinguished Professor and Head in Department of Statistics at Purdue University. His research interests are quality assurance, industrial statistics, data mining, and response surface. He has published more than 250 SCI/SSCI papers in a wide variety of journals. He currently serves or has served as an associate editor for more than 10 professional journals. Dr. Lin is an elected fellow of ASA, IMS, ASQ, and RSS, an elected member of ISI, and a lifetime member of ICSA. His recent awards include, the Youden Address, the Shewell Award, the Don Owen Award, the Loutit Address Award, the Hunter Award, the Shewhart Medal, the SPES Award, and the Deming Lecturer Award at 2020 JSM.

Stefan H. Steiner

Stefan H. Steiner is a Professor/Department Chair in the Department of Statistics and Actuarial Science. He holds a Ph.D. in Business Administration (Management Science/Systems) from McMaster University. His primary research interests include quality improvement, process monitoring, experimental design and measurement system assessment.