Estimating process capability index C"(pmk) for asymmetric tolerances: Distributional properties

Abstract

Pearn et al. (1999) considered a capability index C"(pmk), a new gener alization of C-pmk, for processes with asymmetric tolerances. In this paper, we provide a comparison between C"(pmk), and other existing generalizations of C-pmk PM on the accuracy of measuring process performance for processes with asymmetric tolerances. We show that the new generalization C"(pmk) is superior to other existing generalizations of C-pmk. Under the assumption of normality, we derive explicit forms of the cumulative distribution function and the probability density function of the estimated index (C) over cap "(pmk). We show that the cumulative distribution function and the probability density function of the estimated index (C) over cap "(pmk) can be expressed in terms of a mixture of the chi-square distribution and the normal distribution. The explicit forms of the cumulative distribution function and the probability density function considerably simplify the complexity for analyzing the statistical properties of the estimated index (C) over cap "(pmk).