A GRAPHICAL APPROACH TO OBTAINING CONFIDENCE-LIMITS OF C-PK

The process capability index Cpk has been widely used as a process per formance measure. In practice this index is estimated using sample dat a. Hence it is of great interest to obtain confidence limits for the a ctual index given a sample estimate. In this paper we depict graphical ly the relationship between process potential index (C-p), process shi ft 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 com bined using the Bonferroni inequality to generate a third type of conf idence limit. The performance of these limits of C-pk in terms of thei r coverage probability and average width is evaluated by simulation. T he most suitable type of confidence limit for each specific range of k is then determined. The usage of these confidence limits is illustrat ed via examples. Finally a performance comparison is done between the proposed confidence limits and three nonparametric bootstrap confidenc e limits. The results show that the proposed method consistently gives the smallest width and yet provides the intended coverage probability . (C) 1997 John Wiley & Sons, Ltd.