Development of robust confidence intervals for the cost-based process capability index

Abstract

We consider the process capability index Cpmc when a tolerance cost function is introduced. It is well known that Cpmc performs well under the general assumption that the data is not contaminated. Under this assumption, the standard sample mean and sample variance are used to estimate Cpmc. However, it is also well known that this estimate is extremely sensitive to data contamination since the sample mean and sample variance have a zero breakdown point. This in turn makes any constructed confidence interval (CI) also very sensitive to data contamination. In this paper, we develop robust estimators of the process capability index along with robust CIs. We compare the performance of the proposed estimators of Cpmc using the notion of statistical power and receiver operating characteristic curves. Finally, we investigate the use of bootstrapping approaches for improving power of associated hypothesis tests. The results clearly indicate that, when data contamination exists, the methods together with bootstrapping outperform the conventional method.