Confidence interval for the process capability index based on the bootstrap-t confidence interval for the standard deviation

Abstract

This paper proposes a confidence interval for the process capability index based on the bootstrap-t confidence interval for the standard deviation. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence interval with the existing confidence interval based on the confidence interval for the standard deviation. Simulation results show that the proposed confidence interval performs well in terms of coverage probability in case of more skewed distributions. On the other hand, the existing confidence interval has a coverage probability close to the nominal level for symmetrical or less skewed distributions. The code to estimate the confidence interval in R language is provided.