Statistical Inference on the Generalized Lifetime Performance Index of the Odd Lindley Half-Logistic Distribution

Abstract

Performance capability indices are valuable measures to evaluate the quality of a product. We consider inference on the Generalized Lifetime Performance Index when the product’s lifetime follows the Odd Lindley Half-Logistic distribution. The maximum likelihood estimator of the GLPI is derived, and its asymptotic variance is established. Asymptotic confidence intervals are considered, and a uniformly most powerful test for process capability is developed. A Monte Carlo simulation study is conducted to compare the bias and mean squared error of the proposed estimator. Two real datasets on the breaking stress and strength of carbon fibers are used to illustrate the proposed methods.