A Bayesian Approach to Obtain a Lower Bound for the Cpm Capability Index

Abstract

Abstract The Taguchi capability index Cpm, which incorporates the departure of the process mean from the target value, has been proposed to the manufacturing industry for measuring manufacturing capability. A Bayesian procedure has been considered for testing process performance assuming $\mu =T$ , which was generalized without assuming $\mu = T$ . Statistical properties of the natural estimator of the index Cpm for normal processes have been investigated extensively. However, the investigation was restricted to processes with symmetric tolerances. Recently, a generalized Cpm, referred to as $C''_{{\rm p}m}$ , was proposed to cover processes with asymmetric tolerances. Under the normality assumption, the statistical properties of the estimated $C''_{{\rm p}m}$ including the exact sampling distribution, the rth moment, expected value, variance, and the mean‐squared error were obtained. In this paper, we use a Bayesian approach to obtain the interval estimation for the generalized Taguchi capability index $C''_{{\rm p}m}$ . Consequently, the manufacturing capability testing can be performed for quality assurance. Copyright © 2005 John Wiley & Sons, Ltd.

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