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

Abstract

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.

Keywords:

• Asymptotic optimality
• Empirical Bayes rule
• Process capability index
• Ranking and selection
• C _pw

Mathematics Subject Classification:

• Primary 62C12
• Secondary 90B50

Acknowledgment

We are grateful to two referees for their patience of careful reading and many helpful comments which greatly lead to improvement of this presentation.