A review of dispersion control charts for multivariate individual observations

Abstract

A multivariate control chart is designed to monitor process parameters of multiple correlated quality characteristics. Often data on multivariate processes are collected as individual observations, i.e., as vectors one at a time. Various control charts have been proposed in the literature to monitor the covariance matrix of a process when individual observations are collected. In this study, we review the literature on control charts based on individual observations from multivariate continuous processes, where we find 30 relevant articles from the period 1987–2019. We group the articles into five categories. We observe that less research has been done on CUSUM, high-dimensional and non-parametric type control charts for monitoring the process covariance matrix. We describe each proposed method, state their advantages, and limitations. Finally, we give suggestions for future research.

Keywords:

• CUSUM
• EWMA
• high-dimensional
• individual observations
• multivariate dispersion control chart
• non-parametric
• Shewhart

Additional information

Notes on contributors

Jimoh Olawale Ajadi

Jimoh Olawale Ajadi is a PhD student in the Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong. He received his MSc in Applied Statistics from King Fahd University of Petroleum & Minerals, Saudi Arabia, and BSc in Mathematics/Statistics from University of Lagos, Nigeria. His research interests include statistical process monitoring and applied statistics.

Zezhong Wang

Zezhong Wang is PhD student supervised by Dr. Inez Maria Zwetsloot in the Department of Systems Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong. Her current research focuses on statistical process monitoring.

Inez Maria Zwetsloot

Inez Maria Zwetsloot is an assistant professor in the Department of Systems Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong. She is also affiliated faculty member of the Data Science School at City University of Hong Kong, Kowloon, Hong Kong. Her current research focuses on statistical process monitoring, applied statistics and statistical engineering.