Bootstrap Confidence Intervals of the Modified Process Capability Index for Weibull distribution

Abstract

The objective of the paper is to modify the existing process capability index (PCI) for a Weibull distribution and to construct bootstrap confidence intervals (BCIs) for the newly proposed index. Three BCIs that consist of standard, percentile and bias-corrected percentile bootstrap (BCPB) confidence intervals are constructed for the newly proposed index and the existing Pearn and Chen index. The efficiency of the newly proposed index \(C_{\mathrm{GPK}} \) is compared with Pearn and Chen index using their coverage probabilities and average widths. The coverage probabilities and average width of three BCIs were calculated using Monte Carlo simulation studies. The newly proposed index shows better performance than Pearn and Chen index. The results indicate that BCPB confidence interval was more efficient in both cases and outperform other two confidence intervals in all situations. The comparison of average width of BCPB apparently shows that the proposed index performed better in all cases. A real-life example is also provided for a practical application.