Estimation of stress–strength reliability for generalized Maxwell failure distribution under progressive first failure censoring

Abstract

In this article, the estimation of the stress–strength reliability function $\delta =P(X>Y)$ for generalized Maxwell failure distribution is considered. The Maximum-likelihood and Bayesian estimators for δ based on progressive first failure censoring scheme are developed. The asymptotic confidence, bootstrap p, bootstrap t, Bayesian credible and HPD credible intervals for the stress–strength reliability are derived. A Monte Carlo simulation study is provided for comparing different estimators and various censoring schemes. Finally, a real data study is carried out which illustrate the proposed estimation methods and censoring schemes.

Keywords:

• Progressive first-failure-censoring
• generalized Maxwell failure distribution
• point estimation
• stress–strength reliability
• Bayesian estimator
• Monte Carlo simulation

Mathematics subject classifications:

• 62N05
• 62F10
• 62F15

Acknowledgments

Authors are grateful to the Editor and anonymous referees for their valuable suggestions, which greatly improved this manuscript. The first author, Mr. Shubham Saini is grateful to the Council of Scientific and Industrial Research (CSIR), Ministry of Science and Technology, Government of India for their financial support in the form of Junior Research fellowship (09/045(1614)/2018-EMR-I).

Disclosure statement

No potential conflict of interest was reported by the authors.