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On Bayesian reliability estimation of a 1-out-of-k load sharing system model of modified Burr-III distribution

Author

Listed:
  • Azeem Ali

    (University of Veterinary and Animal Sciences)

  • Sanku Dey

    (St. Anthony’s College)

  • Haseeb Ur Rehman

    (Social Welfare & Bait ul Maal, Punjab)

  • Zeeshan Ali

    (The University of Warwick)

Abstract

This article deals with classical and Bayesian estimation of the parameters of a 1-out-of-k load-sharing parallel system model in which each component’s lifetime follows modified Burr-III distribution. In the classical set up, the maximum likelihood estimates of the load-share parameters, system reliability and hazard rate functions with their bias, standard errors (SEs), average absolute bias (AABias) and width of the confidence interval along with coverage probability are obtained. Besides, two bootstrap confidence intervals for the parameters of the model are also obtained. Further, by assuming both gamma and non-informative priors for the unknown parameters, Bayes estimates of the parameters, system reliability and hazard rate functions with their bias, SEs, AABias and width of the Bayes credible interval along with coverage probability ( $$C_{p}$$ C p ) are obtained. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. Finally, we analyze one real data set to illustrate the results derived.

Suggested Citation

  • Azeem Ali & Sanku Dey & Haseeb Ur Rehman & Zeeshan Ali, 2019. "On Bayesian reliability estimation of a 1-out-of-k load sharing system model of modified Burr-III distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 1052-1081, October.
    • Handle: RePEc:spr:ijsaem:v:10:y:2019:i:5:d:10.1007_s13198-019-00835-4
    DOI: 10.1007/s13198-019-00835-4
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    References listed on IDEAS

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