Statistical inference of component lifetimes in a coherent system under proportional hazard rate model with known signature

Document Type : Original Scientific Paper

Authors

Department of Statistics‎, ‎University of Payame Noor‎, ‎Tehran

Abstract

In this paper‎, ‎we discuss the statistical inference of the lifetime distribution of components in a $n$-component coherent system when the system structure is known and the component lifetime follows the proportional hazard rate model‎. ‎Different estimation methods‎, ‎the maximum likelihood estimator‎, ‎approximation of the maximum likelihood estimator‎, ‎and Bayes estimator for the component lifetime parameter are discussed‎. ‎Because the integrals of the Bayes estimates do not possess closed forms‎, ‎the Metropolis-Hastings method and Lindley's approximate method are applied to approximate these integrals‎. ‎Confidence intervals based on the asymptotic distribution of the MLE‎, ‎likelihood ratio test‎, ‎pivotal method‎, ‎and highest posterior density credible are computed‎. ‎Two numerical examples are used to illustrate the methodologies developed in this paper and a Monte Carlo simulation study is used to compare the performance of these estimation methods and recommendations are made based on these results.

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References

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Journal of Statistical Modelling: Theory and Applications
Volume 3, Issue 1
January 2022
Pages 147-167

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History

  • Receive Date: 19 February 2023
  • Revise Date: 09 September 2023
  • Accept Date: 19 October 2023

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