Estimation of multi-stress strength reliability under progressive first failure censoring using generalized inverted exponential distribution

Abstract

We investigate the estimation of multi-stress strength reliability under progressively first failure censoring for the generalized inverted exponential distribution using classical and Bayesian approaches. Classical estimation employs maximum likelihood estimators with the Expectation-Maximization algorithm to handle incomplete data. Bayesian estimation utilizes Markov Chain Monte Carlo (MCMC) techniques and Tierney-Kadane's approximation to approximate the posterior distribution. Furthermore, A generalized entropy loss function is employed to measure estimation accuracy. Finally, Validation is provided through Monte Carlo simulations and real-world applications. Findings highlight the robustness and accuracy of Bayesian methods, particularly with informative priors, and underscore the strengths of MCMC techniques and Bayesian Credible Intervals in specific aspects of estimation.

Keywords:

• Reliability
• generalized inverted exponential distribution
• censoring
• EM algorithm
• Bayesian estimation
• MCMC techniques

Mathematics subject classifications:

• 62N05
• 62F15

Acknowledgments

The authors are grateful to the editor-in-chief, associate editor, and learned reviewers for their critical comments and valuable suggestions, which led to a fine version of the manuscript.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.