A Bayesian-like estimator of C-pk

Abstract

Bissell (1990) proposed an estimator for the process capability index C-pk assuming the knowledge whether the process mean mu < m or mu greater than or equal to m is available, where m is the mid-point between the upper and lower specification limits. Kotz, Pearn and Johnson (1993) showed that for the index C-pk, the natural estimator gives values for the standard deviation smaller than those of Bissell's. In this paper we show that by adding a well-known correction factor to Bissell's estimator, we obtain an unbiased estimator of C-pk whose standard deviation is smaller than those given in Kotz, Pearn and Johnson (1993). In addition, we propose a Bayesian-like estimator which relaxes Bissell's assumption on the process mean. The distribution of the new estimator is shown to be identical to that of Bissell's estimator.