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

  • Azeem AliEmail author
  • Sanku Dey
  • Haseeb Ur Rehman
  • Zeeshan Ali
Original Article


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 (\(C_{p}\)) 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.


Load-sharing system model Bayes estimate Hazard rate function Bootstrap confidence intervals Modified Burr-III distribution 



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Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2019

Authors and Affiliations

  1. 1.University of Veterinary and Animal SciencesLahorePakistan
  2. 2.Department of StatisticsSt. Anthony’s CollegeShillongIndia
  3. 3.Social Welfare & Bait ul Maal, PunjabLahorePakistan
  4. 4.Department of StatisticsThe University of WarwickCoventryUK

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