Bayesian estimation of the change point in a gamma process using control chart

Abstract

The process personnel always seek the opportunity to improve the processes. One of the essential steps for the process improvement is to recognize the starting time or the change point of a process disturbance quickly. Different from the traditional normally distributed assumption for a process, this study considers a process that follows a gamma distribution. The proposed approach combines the commonly used control chart with the Bayesian estimation technique to estimate the change point. Two Bayes estimators corresponding to an informative and a noninformative prior along with maximum likelihood estimation (MLE) are considered. Their efficiency is compared through a series of simulations. The results show that the Bayes estimator with the informative prior is more accurate and more precise when the means of the process before and after the change point time are not too closed. Additionally, the efficiency of the Bayes estimator with the informative prior increases as either the sample size increases or the change point goes away from the origin.

KEYWORDS:

• Bayesian estimation
• Change point
• Gamma process
• Maximum likelihood estimation
• control chart.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15
• 62F10

Acknowledgments

The authors want to thank anonymous referees and editor for their comments to strengthen the presentation of their results. The authors also thank the Persian Gulf University for financial support.