Statistical inference for component lifetime distribution from coherent system lifetimes under a proportional reversed hazard model

Abstract

Proportional reversed hazard model and exponentiated distributions have received considerable attention in the statistical literature due to its flexibility. In this paper, we develop the tools for statistical inference of the lifetime distribution of components in a n-component coherent system while the system lifetimes are observed, the system structure is known and the component lifetime follows the proportional reversed hazard model. Different point and interval estimation procedures based on frequentist and Bayesian approaches are developed. The existence and uniqueness of the maximum likelihood estimator are discussed. In addition, two statistical testing procedures, a pivotal quantity approach and a likelihood ratio test, to test whether the exponentiated parameter equals to a particular value are proposed. A numerical example is used to illustrate the methodologies developed in this paper and a Monte Carlo simulation study is employed to evaluate the performance of the statistical inferential procedures.

Keywords:

• Coherent system
• generalized exponential distribution
• maximum likelihood estimator
• Bayes estimator
• MCMC

Acknowledgements

We would like to thank the anonymous referees and the editor for their constructive comments which improved the paper. The authors gratefully acknowledge the high performance computing center of University of Mazandaran for providing computing resource and time.