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Keywords
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Bayesian estimation, Change point, Gamma process, Maximum likelihood estimation, Xbar control chart.
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Abstract
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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 which follows a gamma distribution. The
proposed approach combines the commonly used ˉX 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 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.
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