A Bayesian procedure for process capability assessment

The usual practice of judging process capability by evaluating point estima tes of some process capability indices has a flaw that there is no assessme nt on the error distributions of these estimates. However, the distribution s of these estimates are usually so complicated that it is very difficult t o obtain good interval estimates. In this paper we adopt a Bayesian approac h to obtain an interval estimation, particularly for the index C-pm. The po sterior probability p that the process under investigation is capable is de rived; then the credible interval, a Bayesian analogue of the classical con fidence 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 omega, say 1.33. To make this Bayesian procedure very easy for practitioners to implement on manufacturing floors, we tabulate the mi nimum values of (C) over cap(pm)/omega for which the posterior probability p reaches the desirable level, say 95%. For the special cases where the pro cess mean equals the target value for C-pm and equals the midpoint of the t wo specification limits for C-pk. the procedure is even simpler; only chi-s quare tables are needed. Copyright (C) 1999 John Wiley & Sons, Ltd.