Making decisions in assessing process capability index C-pk

Abstract

Process capability indices C-p, C-pk and C-pm have been used in manufacturing industries to provide a quantitative measure of process potential and performance. The formulae for these indices are easy to understand and straightforward to apply. However, since sample data must be collected in order to calculate these indices, a great degree of uncertainty may be introduced into capability assessments owing to sampling errors. Currently, most practitioners simply look at the value of the index calculated from the sample data and then make a conclusion on whether the given process meets the capability (quality) requirement. This approach is not reliable, since sampling errors are ignored. Cheng (Qual. Engng., 7, 239-259 (1994)) has developed a procedure involving estimators of C-p and C-pm for practitioners to use to determine whether a process meets the capability requirement or not. However, no procedure for C-pk was given, because difficulties were encountered in calculating the sampling distribution of the estimator of C-pk. In this paper we use a newly proposed estimator of C-pk to develop a procedure for practitioners to use so that decisions made in assessing process capability are more reliable. Copyright (C) 1999 John Wiley & Sons, Ltd.