A Bayesian approach based on multiple samples for measuring process performance with incapability index

Process incapability index, which provides an uncontaminated separation between information concerning the process accuracy and the process precision, has been proposed to the manufacturing industry for measuring process performance. Investigations concerning the estimated incapability index have focused on single sample in existing quality and statistical literatures. However, contributions based on multiple samples have been comparatively neglected. In this paper, investigations based on multiple samples are considered for normally distributed processes. A Bayesian approach to obtain an upper bound for the incapability index is proposed. A computational program using Maple software is proposed to evaluate critical values required to ensure the posterior probability reaching a certain desirable level for the incapability index. A practical example is also provided to illustrate how the proposed reliable Bayesian procedure may be applied in process capability assessment.