Estimation and Confidence Intervals of Modified Process Capability Index Using Robust Measure of Variability

Abstract The process capability index (PCI), denoted by 𝐼, is a well-known characteristic in quality control analysis. Using Gini’s mean difference, we construct a new PCI, I G I_{G} say, assuming the two-parameter Weibull distribution (WD). In order to estimate the proposed I G I_{G} when the process follows the WD, we use five classical methods of estimation and compare the performance of the obtained estimators with respect to their mean squared errors (MSEs) through a simulation study. Confidence intervals for the proposed PCI are constructed based on five bootstrap confidence intervals (BCIs) methods. Monte Carlo simulation study has been carried out to compare the performance of these five BCIs in terms of average widths and coverage probabilities. Finally, three real data sets from electronic and food industries are employed for illustrating the effectiveness of the proposed study. All these data sets show that the width of bias-corrected accelerated bootstrap interval is minimum among all other considered BCIs.