Optimal designs of the omnibus SPRT control chart for joint monitoring of process mean and dispersion

Abstract

The vast majority of control schemes related to the sequential probability ratio test (SPRT) are designed for the purpose of monitoring only the process mean. Nonetheless, most manufacturing processes are vulnerable to external factors that cause the process mean and variability to change simultaneously. It is, therefore, crucial to consider a joint scheme for monitoring both the location and scale parameters of a production process. In this article, we develop a scheme that combines both mean and variance information in a single SPRT, known as the omnibus SPRT (OSPRT) chart. Expressions for the run-length properties of the OSPRT chart are derived by means of the Markov chain approach. We also propose optimal designs for the OSPRT chart based on two different metrics, i.e. by minimising the average time to signal and the average extra quadratic loss. Through a comprehensive analysis, this article reveals that the optimal OSPRT chart outperforms the classical $\overline{X}$-S, weighted-loss cumulative sum, absolute-value SPRT, and two maximum weighted-moving-average-type charts. The optimal OSPRT chart also has the advantage of collecting a small number of samples on average before producing a decision. Finally, the implementation of the OSPRT chart is presented with a wire bonding industrial dataset.

KEYWORDS:

• Average extra quadratic loss
• average time to signal
• joint monitoring scheme
• sequential probability ratio test
• statistical process control

Disclosure statement

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

Data availability statement

The data that supports the findings of this study are available from the corresponding author, W.L. Teoh, upon reasonable request.

Additional information

Funding

This work was supported by the Ministry of Higher Education (MOHE) Malaysia and Heriot-Watt University Malaysia under Fundamental Research Grant Scheme (FRGS), no. FRGS/1/2021/STG06/HWUM/02/1.

Notes on contributors

Jing Wei Teoh

Jing Wei Teoh is a PhD student in the School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia (HWUM). He holds a B.Sc. (Hons) in Actuarial Science from HWUM. His research interest is in statistical process control.

Wei Lin Teoh

Wei Lin Teoh is an Assistant Professor in the School of Mathematical and Computer Sciences, HWUM. She received her PhD in Applied Statistics in 2013 from Universiti Sains Malaysia (USM). Her research interest is in statistical process control. She has authored/co-authored more than 80 papers in peer-reviewed international journals and proceedings of international conferences, including Q1 journals indexed in the Web of Science (WoS) database.

Michael B.C. Khoo

Michael B. C. Khoo is a Professor in the School of Mathematical Sciences, USM. He specialises in Statistical Quality Control. He has published numerous papers in international journals indexed in WoS database. He has also reviewed numerous papers for journals indexed in the WoS database.

Giovanni Celano

Giovanni Celano is an Associate Professor at the University of Catania, Italy. He holds a PhD in production engineering from the University of Palermo, Italy. His current research focuses on developing and implementing statistical process monitoring techniques for on-line quality control with a particular focus on small production runs. He has authored/co-authored more than 130 papers in international journals and in proceedings of national and international conferences. He is a member of the European Network of Business and Industrial Statistics (ENBIS). He is an Advisory Editor of Engineering Reports and an Associate Editor of Quality Technology and Quantitative Management.

Zhi Lin Chong

Zhi Lin Chong is an Assistant Professor in Faculty of Engineering and Green Technology, Universiti Tunku Abdul Rahman. He received his PhD in 2015 from USM. His research interests are statistical process control and nonparametric control charts.