Bayesian and classical estimation of reliability in a multicomponent stress-strength model under adaptive hybrid progressive censored data

  • Akram Kohansal
  • Shirin ShoaeeEmail author
Regular Article


The statistical inference of multicomponent stress-strength reliability under the adaptive Type-II hybrid progressive censored samples for the Weibull distribution is considered. It is assumed that both stress and strength are two Weibull independent random variables. We study the problem in three cases. First assuming that the stress and strength have the same shape parameter and different scale parameters, the maximum likelihood estimation (MLE), approximate maximum likelihood estimation (AMLE) and two Bayes approximations, due to the lack of explicit forms, are derived. Also, the asymptotic confidence intervals, two bootstrap confidence intervals and highest posterior density (HPD) credible intervals are obtained. In the second case, when the shape parameter is known, MLE, exact Bayes estimation, uniformly minimum variance unbiased estimator (UMVUE) and different confidence intervals (asymptotic and HPD) are studied. Finally, assuming that the stress and strength have the different shape and scale parameters, ML, AML and Bayesian estimations on multicomponent reliability have been considered. The performances of different methods are compared using the Monte Carlo simulations and for illustrative aims, one data set is investigated.


Adaptive Type-II hybrid progressive censored Approximation maximum likelihood estimation MCMC method Multicomponent stress-strength reliability Weibull distribution 

Mathematics Subject Classification

62F10 62F15 62N02 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsImam Khomeini International UniversityQazvinIran
  2. 2.Department of Actuarial Science, Faculty of Mathematical SciencesShahid Beheshti UniversityTehranIran

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