Confidence intervals for the process capability index CP based on confidence intervals for variance under non-normality

One of the indicators for evaluating the capability of a process is the process capability index Cp. The confidence interval of Cp is important for statistical inference on the process. Usually, the calculation of the confidence interval for a process capability index requires an assumption about the underlying distribution. Therefore, three confidence intervals for based on the confidence intervals for the variance under non-normality were proposed in this paper. The confidence intervals considered were the adjusted degrees of freedom (ADJ) confidence interval, large-sample (LS) confidence interval, and augmented-large-sample (ALS) confidence interval. The estimated coverage probability and expected length of 95% confidence intervals for Cp were studied by means of a Monte Carlo simulation under different settings. Simulation results showed that the ALS confidence interval performed well in terms of coverage probability for all conditions. The LS and ADJ confidence intervals had much lower coverage probability than the nominal level for skewed distributions