Distributional and inferential properties of the estimated precision C-p based on multiple samples

Abstract

Process precision index C-p has been widely used in the manufacturing industry to provide numerical measures on process potential. Pearn et al. ( 1998) considered an unbiased estimator of C-p for one single sample. They showed that the unbiased estimator is the UMVUE. They also proposed an efficient test for C-p based on one single sample, and showed that the test is the UMP test. In this paper, we consider an unbiased estimator of C-p for multiple samples. We show that the unbiased estimator is the UMVUE of C-p, which is asymptotically efficient. We also consider an efficient test for C-p, and show that the test is the UMP test for multiple samples. The practitioners can use the proposed test on their in-plant applications to obtain reliable decisions.