Multivariate time-between-events monitoring: An overview and some overlooked underlying complexities

Abstract

We review methods for monitoring multivariate time-between-events (TBE) data. We present some underlying complexities that have been overlooked in the literature. It is helpful to classify multivariate TBE monitoring applications into two fundamentally different scenarios. One scenario involves monitoring individual vectors of TBE data. The other involves the monitoring of several, possibly correlated, temporal point processes in which events could occur at different rates. We discuss performance measures and advise the use of time-between-signal based metrics for the design and comparison of methods. We re-evaluate an existing multivariate TBE monitoring method, offer some advice and suggest some directions for future research.

Keywords:

• Average time-to-signal
• control charts
• high-quality processes
• inter-arrival time distribution
• multivariate time-between-events
• renewal process

Additional information

Notes on contributors

Inez M. Zwetsloot

Inez M. Zwetsloot is 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. Her email address is [email protected].

Tahir Mahmood

Tahir Mahmood got his degree of BS (Hons.) in Statistics with distinction (Gold Medalist) from the Department of Statistics, University of Sargodha, Sargodha, Pakistan, in 2012. In April 2017, he received his MS (Applied Statistics) degree from Department of Mathematics and Statistics, KFUPM. Now, he is student of PhD in the Department of Systems Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong. His current research interests include statistical process monitoring and applied statistics. His e-mail addresses are [email protected] and [email protected].

William H. Woodall

William H. Woodall is a Professor Emeritus in the Department of Statistics at Virginia Tech. He is a former editor of the Journal of Quality Technology (2001–2003) and associate editor of Technometrics (1987–1995). He is the recipient of the Box Medal (2012), Shewhart Medal (2002), William G. Hunters Award (2019), Jack Youden Prize (1995, 2003), and Brumbaugh Award (2000, 2006). He is a Fellow of the American Statistical Association, a Fellow of the American Society for Quality, and an elected member of the International Statistical Institute. His email address is [email protected].