A Bayesian procedure for process capability assessment

Abstract

The usual practice of judging process capability by evaluating point estimates of some process capability indices has a flaw that there is no assessment on the error distributions of these estimates. However, the distributions of these estimates are usually so complicated that it is very difficult to obtain good interval estimates. In this paper we adopt a Bayesian approach to obtain an interval estimation, particularly for the index Cpm. The posterior probability p that the process under investigation is capable is derived; then the credible interval, a Bayesian analogue of the classical confidence interval, can be obtained. We claim that the process is capable if all the points in the credible interval are greater than the pre-specified capability level ω, say 1.33. To make this Bayesian procedure very easy for practitioners to implement on manufacturing floors, we tabulate the minimum values of Ĉpm/ω, for which the posterior probability p reaches the desirable level, say 95%. For the special cases where the process mean equals the target value for Cpm and equals the midpoint of the two specification limits for Cpk, the procedure is even simpler; only chi-square tables are needed. Copyright © 1999 John Wiley & Sons, Ltd.