On Empirical Bayes Procedures for Selecting the Best Manufacturing Process Based on Process Capability Index

Consider k (k ges 2) manufacturing processes whose process capability indices C_pw are denoted by C_pw(i), i = 1, ldrldrldr, k all unknown. For a given control value C_pw(0), we are interested in selecting some manufacturing process whose process capability index is the largest in the qualified subset in which each process capability index is no less than C_pw(0). In this paper, under a Bayes framework, we focus on 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 satisfactory.