Bayesian Statistical Process Control

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Abstract
This article presents a general Bayesian statistical process control chart. Most previous applications of Bayes' theorem to quality control have either been tied to a rigid optimization model or have used Bayes' theorem to infer the values of structural parameters of the monitored process. The methodology presented differs from both of these approaches. The result is a flexible tool that can be manipulated by decision makers, as is the case with other types of control charts. The Bayesian chart is demonstrated for joint monitoring of the mean and standard deviation of a normal random variable, and compared to both Shewhart and cumulative sum monitoring. The basis for comparison is the expected number of false alarms per expected time in control and the average out-of-control run length. The comparison identifies types of production process where the Bayesian chart has better expected performance than the other two charts and also shows that even though the Bayesian chart requires more detailed knowledge of process structure, acquiring this knowledge can yield real benefits. The article concludes with a practical example.