A Bayesian Approach to Obtain a Lower Bound for the C p m Capability Index

The Taguchi capability index C p m , 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 C p m for normal processes have been investigated extensively. However, the investigation was restricted to processes with symmetric tolerances. Recently, a generalized C p m , 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 r th 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.