Selecting the Best Process Based on Capability Index via Empirical Bayes Approach

Consider k (k ≥ 2) manufacturing processes whose mean θ i , variance and process capability index C pw (i), i = 1,…, k, are all unknown. For two given control values C pw (0) and , we are interested in selecting some process whose capability index is no less than C pw (0) and is the largest in the qualified subset in which each process variance is no larger than . Under a Bayes framework, we consider the normally distributed manufacturing processes taking normal-gamma as its conjugate prior. A Bayes approach is set up and an empirical Bayes procedure is proposed which has been shown to be asymptotically optimal. A simulation study is carried out for the performance of the proposed procedure and it is found practically useful.