Estimation of the process incapability index

Greenwich and Jahr-Schaffrath (1995) introduced a new index C _pp a simple transformation of the index C _pm , which provides an uncontaminated separation between information concerning process accuracy and process precision. Under the assumption of normality, we first show that the estimators of C _pp proposed by Greenwich and Jahr-Schaffrath (1995) are UMVU estimators. We also show that for the inaccuracy index, the variance of the unbiased estimator is smaller than the mean squared error (MSE) of the natural (biased) estimator for n > 3. In addition, we obtain the r-th moment and the probability density function of these estimators.