Monitoring and control of beta-distributed multistage production processes

Abstract

Multistage statistical process control (SPC) is an effective procedure for ensuring quality of products in multistage manufacturing processes. Effective SPC approaches for monitoring and controlling quality in multistage processes are limited. Beta distributed data explained by process input variables are generally prevalent in multistage process industries. In this paper, we propose a generalized linear model for beta-distributed data in multistage processes in order to estimate the distribution parameters and develop two approaches for process monitoring and control: they are model-based SPC charts and a beta regression model. The proposed control charts outperform the existing control charts in terms of the out-of-control average run length for the detection of process mean shifts.

Keywords:

• Beta regression
• deviance residual
• model-based control charts
• multistage statistical process control
• quantile
• Shewhart

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Acknowledgment

The authors are very grateful to the editor and two anonymous referees for their valuable and constructive comments and suggestions which greatly improved the final version of this paper. This paper was made possible by the support of NPRP 5-364-2-142 grant from Qatar National Research Fund (QNRF). The statements made herein are solely the responsibility of the authors. This work is based on an earlier conference paper by Hwang et al: Hwang, W., Al-Khalifa, K.N., Hamouda, A.M.S., Jeong, M.K., & Elsayed, E.A. (2014). Multistage Statistical Process Control for Parametric Variables. International Conference on Quality, Reliability, Risk, Maintenance and Safety Engineering. Dalian, China, July 22-25, 2014.