A graphical approach to obtaining confidence limits of Cpk

The process capability index C_pk has been widely used as a process performance measure. In practice this index is estimated using sample data. Hence it is of great interest to obtain confidence limits for the actual index given a sample estimate. In this paper we depict graphically the relationship between process potential index (C_p), process shift index (k) and percentage non-conforming (p). Based on the monotone properties of the relationship, we derive two-sided confidence limits for k and C_pk under two different scenarios. These two limits are combined using the Bonferroni inequality to generate a third type of confidence limit. The performance of these limits of C_pk in terms of their coverage probability and average width is evaluated by simulation. The most suitable type of confidence limit for each specific range of k is then determined. The usage of these confidence limits is illustrated via examples. Finally a performance comparison is done between the proposed confidence limits and three non-parametric bootstrap confidence limits. The results show that the proposed method consistently gives the smallest width and yet provides the intended coverage probability. © 1997 John Wiley & Sons, Ltd.