Pearn et al. proposed the capability index Cpmk, and investigated the statistical properties of its natural estimator Ĉpmk for stable normal processes with constant mean μ. Chen and Hsu showed that under general conditions the asymptotic distribution of Ĉpmk is normal if μ ≠ m, and is a linear combination of the normal and the folded-normal distributions if μ = m, where m is the mid-point between the upper and the lower specification limits. In this paper, we consider a new estimator &Ctilde;pmk for stable processes under a different (more realistic) condition on process mean, namely P(μ≥m)=p, 0≤p≤1. We obtain the exact distribution, the expected value, and the variance of &Ctilde;pmk under normality assumption. We show that for P(μ≥m)=0 or 1, the new estimator &Ctilde;pmk is the MLE of Cpmk, which is asymptotically efficient. In addition, we show that under general conditions &Ctilde;pmk is consistent and is asymptotically unbiased. We also show that the asymptotic distribution of &Ctilde;pmk is a mixture of two normal distributions.
