Abstract
Process capability indices such as Cp, k, and Cpk, have been widely used in manufacturing industry to provide numerical measures on process potential and performance. While Cp measures overall process variation, k measures the degree of process departure. In this paper, we consider the index Cp and a transformation of k defined as Ca = 1 - k which measures the degree of process centering. We refer to Cp as the process precision index, and Ca as the process accuracy index. We consider the estimators of Cp and Ca, and investigate their statistical properties. For Cp we obtain the UMVUE and the MLE. We show that this UMVUE is consistent, and asymptotically efficient. For Ca, we investigate its natural estimator. We obtain the first two moments of this estimator, and show that the natural estimator is the MLE, which is asymptotically unbiased and asymptotically efficient. We also propose an efficient test based on the UMVUE of Cp We show that the proposed test is the UMP test.