Nonparametric monitoring of multiple count data

Abstract

Process monitoring of multiple count data has recently received considerable attention in the statistical process control literature. Most existing methods on this topic are based on parametric modeling of the observed process data. However, the assumed parametric models are often invalid in practice, leading to unreliable performance of the related control charts. In this article, we first show the consequence of using a parametric control chart in cases where the underlying parametric distribution is invalid. Then, we thoroughly investigate the performance of some parametric and nonparametric control charts in monitoring multiple count data. Our numerical results show that nonparametric methods can provide a more reliable and effective process monitoring in such cases. A real-data example about the crime log of the University of Florida Police Department is used for illustrating the implementation of the related control charts.

Keywords:

• Distribution-free
• log-linear modeling
• multiple count data
• nonparametric procedures
• Poisson distribution
• statistical process control

Acknowledgments

The authors thank the editors and referees for many helpful comments and suggestions, which improved the quality of the paper greatly.

Notes on contributors

Peihua Qiu received his Ph.D in statistics from the Department of Statistics at the University of Wisconsin at Madison in 1996. He worked as a senior research consulting statistician of the Biostatistics Center at the Ohio State University between 1996 and 1998. Then, he worked as an assistant professor (1998–2002), an associate professor (2002–2007), and a full professor (2007–2013) of the School of Statistics at the University of Minnesota. He is an elected fellow of the American Statistical Association, an elected fellow of the Institute of Mathematical Statistics, an elected member of the International Statistical Institute, a senior member of the American Society for Quality, and a lifetime member of the International Chinese Statistical Association. He served as associate editor for a number of top journals in statistics, including Journal of the American Statistical Association, Biometrics, and Technometrics. He was the editor of Technometrics between 2014 and 2016 and has been the founding chair of the Department of Biostatistics at the University of Florida since July 1, 2013. Peihua Qiu has made substantial contributions in the areas of jump regression analysis, image processing, statistical process control, survival analysis, and reliability. So far, he has published over 100 research papers in top refereed journals, including Technometrics, Journal of the American Statistical Association, Annals of Statistics, Annals of Applied Statistics, Journal of the Royal Statistical Society (Series B), Biometrika, Biometrics, IEEE Transactions on Pattern Analysis and Machine Intelligence, and IISE Transactions. His research monograph titled Image Processing and Jump Regression Analysis (2005, Wiley) won the inaugural Ziegel prize in 2007, for its contribution in bridging the gap between jump regression analysis in statistics and image processing in computer science. His second book titled Introduction to Statistical Process Control was published in 2014 by Chapman & Hall/CRC.

Zhen He is a professor in the College of Management and Economics, Tianjin University. He received his Ph.D. in management science and engineering from Tianjin University, China, in 2001. He is the recipient of the Outstanding Research Young Scholar Award of the National Natural Science Foundation of China. His research interests include statistical quality control, design of experiment, and Six Sigma management.

Zhiqiong Wang received his Ph.D. degree in 2018 from the College of Management and Economics of the Tianjin University in China. He is currently an assistant professor of the School of Management at the Tianjin University of Technology. His major research interests include quality control and management, change-point detection, and various quality-related applications. This paper was written during his one-year visit at the Department of Biostatistics of the University of Florida.

Additional information

Funding

This research is supported in part by the National Science Foundation grant DMS-1405698 in US, by the Natural Sciences Foundation of China grants 71532008, 7161147003, and 71672122 and by Tianjin Municipal Education Commission of China under grant 2018SK031.