The performance of process capability index C-s on skewed distributions

Abstract

Wright (1995) considered a new process capability index C-s, which extends the most useful index to date for processes with two-sided specification limits, C-pmk proposed by Pearn, Kotz and Johnson (1992). The new index C-s not only takes into account the process variation as well as the location of the process mean relative to the specification limits, but also considers the asymmetry of the distribution by incorporating a penalty for skewness. Wright(1995) investigated an estimator of C-s and studied its bias and variance by simulation. The simulation study, however, was restricted to normal distributions where skewness is not present. In this paper, we extend Wright's simulation study to cover some skewed distributions including chi-square, lognormal, and Weibull distributions for some parameter values. The results show that the percentage bias of the estimator increases as the skewness coefficient mu(3)/sigma(3) increases. Extensive simulation results, comparisons, and analysis are provided.