Semiparametric control schemes for dynamically monitoring profiles with count data and arbitrary design

Abstract

Many existing studies on profile monitoring focus on parametric profiles or normally distributed responses, and usually assume that the design points within different profiles are deterministic. In practice, however, profiles with count responses are common, and different profiles often have different within-profile sample sizes and design points. Furthermore, it is difficult to fit models to complex profiles with multiple explanatory variables either parametrically or nonparametrically. This article aims to monitor small-sample size profiles with count response and arbitrary design using a semiparametric model. Two novel control schemes with dynamic control limits are proposed based on the weighted likelihood ratio test and the weighted F test, respectively. Numerical simulations are conducted to investigate the performance of the proposed control charts. The performance between the control chart with constant and dynamic control limits is also compared, and the effect of model misspecification is explored. Finally, a real-data example of automobile warranty claims is presented to illustrate the implementation of the proposed control charts.

Keywords:

• Arbitrary design
• count data
• dynamic control limits
• profile monitoring
• semiparametric model
• small within-profile sample size

Acknowledgments

The authors would like to thank the editors and reviewers for their comments and suggestions.

Data availability statement

The data that support the findings of this study are available from the corresponding author, Yanfen Shang, upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under grant numbers 72032005, 71872123, 71902138, 71902139, 71672122, 71902180.

Notes on contributors

Lisha Song

Lisha Song received her PhD degree in business administration from Tianjin University, China, in Jan. 2022. She received her MS degree in statistics from Nanjing Normal University, China, in Jun. 2017. Her research interests include statistical process control and profile monitoring.

Shuguang He

Shuguang He is a Professor in College of Management and Economics, Tianjin University, China. He received his PhD degree in management science and engineering from Tianjin University, China, in 2002. His research interests focus on quality management, warranty data analysis, and statistical quality control. He has published more than 50 papers in research journals, such as International Journal of Production Research, Journal of Quality Technology, Reliability Engineering & System Safety, Annals of Operations Research, International Transactions in Operations Research.

Ting Li

Ting Li is a PhD candidate in the College of Management and Economics at Tianjin University, China. She received her MS degree from Southwestern University of Finance and Economics, China. Her research interests include reliability engineering and degradation data analysis.

Yanfen Shang

Yanfen Shang is an Associate Professor of the College of Management and Economics at Tianjin University, China. She received her BS and MS degrees from Tianjin University, and PhD degree from Hong Kong University of Science and Technology (HKUST), Hong Kong. Her research interests include quality management and statistical process control.