Estimation and Confidence Intervals of a New PCI C N p m c for Logistic-Exponential Process Distribution

Abstract

The process capability index has been introduced as an effective tool used in industries to aid in the assessment of process performance as well as to measure how much the product meets the costumer expectations. We are aware that classical process capability indices provide better results when the quality characteristic of the processes follows normal distribution. However, these classical indices may not provide accurate results for evaluating nonnormally distributed process which in turn may hinder the decision-making. In this article, we consider a new process capability index $C_{Npmc}$ which is based on cost function and is applicable both for normally and nonnormally distributed processes. In order to estimate the process capability index $C_{Npmc}$ when the process follows logistic-exponential distribution, we have used ten classical methods of estimation, and the performances of these classical estimates of the index $C_{Npmc}$ are compared in terms of their mean squared errors through a simulation study. Next, we construct five bootstrap confidence intervals of the process capability index $C_{Npmc}$ and compare them in terms of their average width and coverage probabilities. Finally, two data sets related to electronic industries are reanalyzed to show the applicabilities of the proposed methods.