Applying Bayesian approach to assess process capability for asymmetric tolerances based on Cpmk″ index

Process capability indices provide numerical measures on process reproduction capability, which are effective tools for quality assurance. They are used to realize current situations of the process, and further improve the process problems to assure of product quality to meet the preset capability requirement. For analyzing process capability, most existing methods for assessing process performance were derived based on the traditional frequentist point of view. However, the sampling distributions of the estimated capability indices are usually so complicated, this makes establishing the exact confidence interval very difficult. In this study, we adopt a Bayesian approach to obtain an interval estimation, particularly for the index Cpmk″. Besides, a testing procedure is developed based on the derived results for practitioners to determine whether their manufacturing processes are capable of reproducing products satisfying the preset capability requirement when the manufacturing tolerance is asymmetric or symmetric.