Estimating and testing process accuracy with extension to asymmetric tolerances

Pearn et al. (Commun. Stat. Theory Methods, 27(4):985–1000, 1998) introduced the process accuracy index Ca to measure the degree of process centering, the ability to cluster around the center. In this paper, we derive an explicit form of the cumulative distribution function for the estimator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{C}_a }$$\end{document} with the case of symmetric tolerances. Subsequently, the distributional and inferential properties of the estimated process accuracy index Ca are provided. Calculations of the critical values, P-values, and lower confidence bounds are developed for testing process accuracy. Further, a generalization of Ca for the case with asymmetric tolerances is proposed to measure the process accuracy. Based on the results practitioners can easily perform the testing of the process accuracy, and make reliable decisions on whether actions should be taken to improve the process quality. An application is given to illustrate how we test the process accuracy using the actual data collected from the factory.