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The generalized process incapability index has been developed in the manufacturing industry to provide numerical measures on evaluating process performance. Contributions on the estimated incapability index in existing quality assurance and statistical literature are almost from the frequentist point of view. In this paper, a Bayesian approach is developed under a non-informative prior to obtain the interval estimation for the generalized process incapability index . Useful maximum values required to ensure the posterior probability reaching a certain desirable level based on are tabulated. A Bayesian procedure for judging whether the process satisfies the preset quality reliability requirement is proposed. A practical example is also presented to illustrate how the proposed procedure may be applied.