Bootstrap confidence intervals for bias corrected quantile based capability indices using gamma distribution

Process capability, analysis plays an important role in evaluating the performance of manufacturing processes. The conventional process capability indices (PCIs) usually assume normality of data and thus cannot be applied in processes with skewed quality characteristics. This study proposes a Gamma-specific non-conformance-based process capability indices (NC-PCI) corresponding to $${C}_{p}$$ and $${C}_{pk}$$ for gamma distributed quality characteristics. The proposed indices are unit-free and directly proportional to the percentage of non-conforming items. In order to derive these indices with sufficient accuracy, a revised approximate skewness correction (MASC) algorithm has been used to calculate Gamma quantiles. Moreover, a bias-corrected form, CMASC, is proposed to minimize bias in small samples. Extensive simulation findings indicate that proposed the CMASC estimator generates smaller values of bias and root mean square error (RMSE) compared to the other estimators used in the study, especially in highly skewed situations. Bootstrap confidence interval analysis also shows that the CMASC estimator has better coverage probabilities and smaller interval widths on various sample sizes. A real-life dataset further supports the simulation findings.