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

Abstract

The capability index is a simple and quantitative way to describe process capability. The index C_pk is an indicator, involving specifications, process mean and standard deviation, for evaluating the capability of a process. When C_pk is applied to evaluate a process, estimating the confidence interval of C_pk is 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 C_pk when 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 BCa bootstrap interval of C_pk are simultaneously studied. A detailed discussion of the simulation results is presented and some conclusions are provided.

Keywords:

• Autocorrelation coefficient
• Bootstrap
• Capability index
• Non-normality