Inference on the lifetime performance index of gamma distribution: point and interval estimation

Abstract

Performance capability indices are valuable measures to evaluate the quality of a product. In this paper, we consider inference on a lifetime performance index when the product’s lifetime follows a gamma distribution with unknown parameters. The bias and mean square error of the maximum likelihood estimator and other proposed estimators are compared. Also, an asymptotic confidence interval using the maximum likelihood estimator, thirteen bootstrap confidence intervals, and four generalized pivotal quantities are derived for the performance capability index. A Monte Carlo simulation is provided to investigate the accuracy of expected lengths and coverage probabilities of the confidence intervals. An actual data set is used to illustrate the estimators and confidence intervals.