Estimation of Upper Confidence Bound for Process Incapability Index in Presence of Gauge Measurement Errors

The process incapability index is a popular tool for assessing the performance of a manufacturing process. The upper confidence bound (UCB) of an incapability index provides a more reliable measure than point estimates due to sampling error. Process observations are often contaminated by gauge measurement errors (GME). In this paper, we examine some effects of measurement error in estimating the UCB for the process incapability index and discuss some remedial approaches to overcome these effects by estimating the adjusted UCB. We discuss two methods, namely, the sampling distribution (SD) approach and the generalized confidence interval (GCI) approach for estimating adjusted UCB. Using simulations, we compare the performance of these two methods in terms of coverage rate (CR) and average value (AV) of the estimated UCB. Our analysis shows that the SD method outperforms the GCI approach in some situations. Two applications are provided to illustrate the usability of the proposed method.