A sensitivity study on the bootstrap confidence interval of the capability index Cpk

AbstractThe capability index is a simple and quantitative way to describe process capability. The index Cpkis an indicator, involving specifications, process mean and standard deviation, for evaluating the capability of a process. When Cpkis applied to evaluate a process, estimating the confidence interval of Cpkis important for statistical inference on the process. Calculating the confidence interval for a process index usually needs the assumption about the underlying distribution. Bootstrapping is a nonparametric, but computer intensive, estimation method. Several types of bootstrap confidence intervals have been developed over the years. In the present paper we report the results of a simulation study on the behavior of the 95% biased-corrected and accelerated (BCa) percentile bootstrap confidence interval for estimating Cpkwhen the data are correlated and follow a Burr distribution, which is used to represent various probability distributions. Effects of sample size, process capability, non-normality and correlation on the BCabootstrap interval of Cpkare simultaneously studied. A detailed discussion of the simulation results is presented and some conclusions are provided.