Distributional and inferential properties of the process accuracy and process precision indices

Abstract

Process capability indices such as C-p, k, and C-pk, have been widely used in manufacturing industry to provide numerical measures on process potential and performance. While C-p measures overall process variation, k measures the degree of process departure. In this paper, we consider the index C-p and a transformation of k defined as C-a = 1 - k which measures the degree of process centering. We refer to C-p as the process precision index, and C-a as the process accuracy index. We consider the estimators of C-p and C-a, and investigate their statistical properties. For C-p, we obtain the UMVUE and the MLE. We show that this UMVUE is consistent, and asymptotically efficient. For C-a, 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 C-p. We show that the proposed test is the UMP test.