Bayesian process control for the Phase II Shewart-type p-chart

Abstract

The binomial distribution is often used in quality control. The usual operation of the p-chart will be extended by introducing a Bayesian approach. We will consider a beta type I prior distribution with six different parameter combinations. Control chart limits, average run lengths (ARLs) and false alarm rates (FARs) will be determined by using a Bayesian method. These results will be compared to the results obtained when using the classical method. A predictive density based on a Bayesian approach will be used to derive the control limits in Phase II. The proposed method gives wider control limits than those obtained from the classical method. The Bayesian method gives larger values for the ARL and smaller values for the FAR. A smaller value for the FAR is desired.

Keywords:

• Average run length
• Bayesian analysis
• beta-binomial distribution
• false alarm rate
• p-chart
• predictive density

Acknowledgements

The authors would like to thank the referees and the editor for their valuable suggestions and comments which have improved this paper. The second author would like to thank the National Research Foundation of South Africa for their support.

Notes

No potential conflict of interest was reported by the authors.