Multivariate Control Charts for Monitoring Covariance Matrix: A Review

Abstract

In this paper, we review multivariate control charts designed for monitoring changes in a covariance matrix that have been developed in the last 15 years. The focus is on control charts developed for multivariate normal processes, assuming that independent subgroups of observations or independent individual observations are sampled as process monitoring proceeds. Control charts developed between 1990 and 2005 are reviewed according to the types of the control chart: multivariate Shewhart chart, multivariate CUSUM chart and multivariate EWMA chart. In addition to these developments, a new multivariate EWMA control chart is proposed. We also discuss comparisons of chart performance that have been carried out in the literature, as well as the issue of diagnostics. Some potential future research ideas are also given.

Key Words:

• Conditional entropy
• Decomposition
• generalized variance
• likelihood ratio test
• moving ranges
• phase II process monitoring
• projection pursuit

Additional information

Notes on contributors

Arthur B. Yeh

Arthur B. Yeh received Ph.D. in statistics from Rutgers University in 1993. He is a Professor of Statistics in the Department of Applied Statistics and Operations Research at Bowling Green State University. Dr. Yeh has conducted and published research in several areas of industrial statistics, including optimal experimental designs, univariate and multivariate control charts, multivariate process capability indices, and multivariate run-by-run process control. He has also worked as a consultant for various local and international companies in both traditional and modern high-tech manufacturing environments. He had served in the past as the President of the Northwest Ohio Chapter of the American Statistical Association, and the Chair of the Toledo Section of the American Society for Quality. He currently serves as an Associate Editor for The American Statistician and as a director for the Toledo Section of the American Society of Quality. Dr. Yeh is a member of the American Statistical Association and the Institute of Mathematical Statistics, and a senior member of the American Society for Quality.

Dennis K. J. Lin

Dennis K. J. Lin is a University Distinguished Professor of Supply Chain and Statistics at the Penn State University. His research interests are quality engineering, industrial statistics, data mining and response surface. He has published over 100 papers in a wide variety of journals. He serves (or served) as associate editor for Statistica Sinica, American Statisticians, Journal of Data Science, Quality Technology & Quality Management, Journal of Quality Technology; and Taiwan Outlook. Dr. Lin is a Fellow of the American Statistical Association (ASA), an elected member of International Statistical Institute (ISI), a Fellow of American Society of Quality (ASQ), a lifetime member of International Chinese Statistical Association (ICSA), and a Fellow of the Royal Statistical Society. He is an honorary chair professor for various universities, including National Chengchi University (Taiwan), Remin University of China and XiAn Statistical Institute.

Richard N. McGrath

Richard N. McGrath is an Associate Professor in the Department of Applied Statistics and Operations Research at Bowling Green State University. His research interests include all areas of industrial statistics with a special interest in analysis of dispersion. Dr. McGrath is a member of the American Statistical Association and the Institute of Mathematical Statistics, and a senior member of the American Society for Quality.