Control Charts for One-sided Capability Indices

There are many industrial product characteristics are desired to be the bigger the best and the smaller the best. The two well-know processes capability indices Cpl and Cpu, which measure larger-the-better and smaller-the-better process capabilities. Obviously, the formulae for the two indices Cpl and Cpu are easy to understand and straightforward to apply. Thus, indices Cpl and Cpu have been utilized by a number of Japanese companies and the U.S. automotive industry by Ford Motor Company. Boyles (1991, Journal of Quality Technology. 23: 17–26) and Spring (1995, Total Quality Management 6(3): 427–438.) point out that as soon as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{X}$$\end{document} and S control charts are in statistical control, the control charts of process capability indices can be used to monitor the quality of process. In the previous, we know that if the process is not in control, the process capability index control chart can be used to monitor the differences of process capability, and as soon as the process is in control the stable process capability can be identified. Therefore, process capability index control chart not only can be used to monitor the stability of process’s quality but also can be used to monitor the quality of process. Since Boyles (1991, Journal of Quality Technology 23: 17–26.) and Spiring (1995, Total Quality Management 6(1): 21–33.) had had research about control chart of the bilateral specification index Cpm., but there are many kinds of products, which meet unilateral quality specification. Therefore, we will construct the control chart of unilateral specification index Cpl and Cpu to monitor and evaluate the stability of process and process capability.