Constructing Bootstrap Confidence Intervals of Process Capability Indices for a Three Parameter Weibull Distribution

Abstract

Statistical Quality Control (SQC) technique is used in investigating the quality improvement features in a manufacturing process. One of the important tools in SQC is the process capability indices (PCIs), for measuring and comparing the characteristics of a production
process to engineering specifications. This article evaluates the performance of the PCIs for a three parameter Weibull distribution which is commonly employed in almost all fields of studies, such as reliability, stability and breakage data. In this article, three different techniques of constructing bootstrap confidence intervals (BCIs) of PCIs are investigated using simulations for the three parameterWeibull distribution. The three different techniques considered are percentile bootstrap, bias-corrected percentile bootstrap and normal  bootstrap techniques. By using simulation, the authors investigate the average widths of the BCI of each of the three different techniques. It is found that the average widths of the bias-corrected percentile bootstrap technique are shorter than that of the other two techniques.