Stress–strength reliability estimation in a system with p-type non-identical multicomponents from PRHR family based on records

Abstract

In this article, we estimate stress-strength reliability of a system containing K components of type p when non-identical strength variates and common stress variate follow proportional reversed hazard rate (PRHR) family of distribution for lower records. The maximum likelihood estimator, an asymptotic distribution and logit-scale transformed asymptotic confidence intervals of the stress-strength reliability are studied for unknown and known θ. Further, the Bayes estimates of stress-strength reliability with squared error loss function are obtained for unknown and known θ. In the deficiency of the explicit forms of the Bayesian estimators, the Lindley's approximation method and Markov Chain Monte Carlo methods are followed. Further, the credible interval with the highest posterior density is obtained through Markov Chain Monte Carlo methods. The performance of the estimators is carried out through simulation technique. A presentation of two real data is done here to exhibit the application of the derived results.

Keywords:

• Stress–strength reliability
• PRHR family of distribution
• records
• Bayes estimator
• squared error loss function
• Lindley approximation method
• Markov Chain Monte Carlo methods
• highest posterior density credible interval

Acknowledgements

The authors are thankful to the editor and anonymous referees for their constructive and helpful comments which have significantly improved the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author would like to thank Science and Engineering Research Board, DST, Government of India [MATRICS Grant: MTR/2018/000084] for providing financial support.