||Consider k (k ≥ 2) manufacturing processes whose mean θi, variance and process capability index Cpw (i), i = 1,…, k, are all unknown. For two given control values Cpw (0) and , we are interested in selecting some process whose capability index is no less than Cpw (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.