A Bayesian-like estimator of the process capability index C-pmk

Abstract

Pearn et al. (1992) proposed the capability index C-pmk, and investigated the statistical properties of its natural estimator (C) over cap (pmk) for stable normal processes with constant mean mu. Chen and Hsu (1995) showed that under general conditions the asymptotic distribution of (C) over cap (pmk) is normal if munot equalm, and is a linear combination of the normal and the folded-normal distributions if mu=m, where m is the mid-point between the upper and the lower specification limits. In this paper, we consider a new estimator (C) over tilde (pmk) for stable processes under a different (more realistic) condition on process mean, namely, P (mugreater than or equal tom)=p, 0less than or equal topless than or equal to1. We obtain the exact distribution, the expected value, and the variance of (C) over tilde (pmk) under normality assumption. We show that for P (mugreater than or equal tom)=0, or 1, the new estimator (C) over tilde (pmk) is the MLE of C-pmk, which is asymptotically efficient. In addition, we show that under general conditions (C) over tilde (pmk) is consistent and is asymptotically unbiased. We also show that the asymptotic distribution of (C) over tilde (pmk) is a mixture of two normal distributions.