A Bayesian Approach to Quality Control

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Abstract
The general problem of process control is one of maintaining a production process in such a state that the output from the process conforms to design specifications. As the process operates it will be subject to changes which cause the quality of the output to deteriorate. Some amount of deterioration can be tolerated but at some point it becomes less costly to stop and overhaul the process. The problem of establishing control procedures to minimize long-run expected costs has been approached by several researchers using Bayesian decision theory. However, the models used by these researchers have been incomplete. The purpose of this paper is to extend the Bayesian approach to include consideration of the sample size and the sampling interval in the design of the control procedure. Using dynamic programming the analysis will show how the optimal time between samples and the optimal sample size can be found and how the optimal decision can be made based on the outcome of the sample.

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