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Statistical Papers

, Volume 60, Issue 6, pp 2185–2224 | Cite as

On estimation of reliability in a multicomponent stress-strength model for a Kumaraswamy distribution based on progressively censored sample

  • Akram KohansalEmail author
Regular Article

Abstract

Based on progressively Type-II censored samples, this paper deals with the estimation of multicomponent stress-strength reliability by assuming the Kumaraswamy distribution. Both stress and strength are assumed to have a Kumaraswamy distribution with different the first shape parameters, but having the same second shape parameter. Different methods are applied for estimating the reliability. The maximum likelihood estimate of reliability is derived. Also its asymptotic distribution is used to construct an asymptotic confidence interval. The Bayes estimates of reliability have been developed by using Lindley’s approximation and the Markov Chain Monte Carlo methods due to the lack of explicit forms. The uniformly minimum variance unbiased and Bayes estimates of reliability are obtained when the common second shape parameter is known. The highest posterior density credible intervals are constructed for reliability. Monte Carlo simulations are performed to compare the performances of the different methods, and one data set is analyzed for illustrative purposes.

Keywords

Kumaraswamy distribution Progressive Type-II censoring Multicomponent stress-strength Maximum likelihood estimator Bayesian estimator Monte Carlo simulation 

Mathematics Subject Classification

62F10 62F15 62N02 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of StatisticsImam Khomeini International UniversityQazvinIran

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