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.

Keywords:

• process accuracy index
• process precision index
• process yield
• process mean
• process standard deviation