Economic modelling and optimisation of SPRT-based quality control schemes for individual observations

Abstract

In many industrial processes, it may not be practical to obtain sample sizes larger than one due to various reasons. As a result, practitioners must rely on control charts based on individual observations for statistical process monitoring and control. The sequential probability ratio test (SPRT) chart is an appropriate solution for such situations. Existing literature predominantly delves into the statistical aspects of designing or optimising an SPRT chart, neglecting the economic and associated design aspects. However, past experience suggests that statistical design may not always be optimal from an economic perspective. This paper aims to bridge this research gap by proposing a two-stage Markov chain approach to develop an economic model for the optimal design of the SPRT chart with individual observations. Following the principles of economic-statistical designs, optimal parameters are determined by solving a mixed-integer non-linear programming problem that minimises the long-run cost per item while ensuring compliance with practical constraints. Through an extensive study, we find that the economic performance of the SPRT chart surpasses that of competing individual control charts in many cases. This indicates that the economic-statistical design of the SPRT chart can yield significant economic benefits while maintaining desirable statistical properties. Moreover, enhancements have been introduced to refine the optimal design of the SPRT chart, retaining excellent overall performance across a wide range of shifts. Finally, we provide two industrial examples to illustrate the effectiveness of the proposed SPRT chart.

KEYWORDS:

• Quality control
• economic modelling
• individual observation
• SPRT chart
• markov chain
• constrained optimisation

Data availability statement

The data that support the findings of this study are available from the author upon request.

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant no 71801179], MOE (Ministry of Education in China) Project of Humanities and Social Sciences [grant no 23YJC630077], Natural Science Foundation of Shaanxi Province, China [grant no 2022JM-421].

Notes on contributors

Chenglong Li

Chenglong Li is an associate professor at the School of Management at Northwestern Polytechnical University. He received his Ph.D. from Xi’an Jiaotong University and City University of Hong Kong in 2017. He received his B.E. in Industrial Engineering from Xi’an Jiaotong University in 2011. Currently, his research interests are mainly on quality engineering, statistical modelling and intelligent decision. His research outcomes have appeared in IISE Transactions, Technometrics, Computers & Industrial Engineering, International Journal of Production Research, among others.

George Nenes

George Nenes is a professor at the Department of Mechanical Engineering at the University of Western Macedonia, Greece, while he is a research associate at the Department of Mechanical Engineering at Aristotle University of Thessaloniki. He has obtained a Diploma (five-year degree) in Mechanical Engineering, an M.Sc. in Management of Production Systems and a Ph.D. in Statistical Quality Control from the Aristotle University of Thessaloniki. He has worked as a Post Doc researcher in Erasmus University of Rotterdam. His work has been published in a variety of journals, including European Journal of Operational Research, IIE Transactions and International Journal of Production Economics. His main research interests are in the area of Statistical Quality Control and Supply Chain Management.