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On Bayesian estimation of stress–strength reliability in multicomponent system for two-parameter gamma distribution

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Abstract

This paper deals with multicomponent stress–strength system reliability (MSR) and its maximum likelihood (ML) as well as Bayesian estimation. We assume that \({X}_{1},{X}_{2},\dots ,{X}_{k}\) being the random strengths of k- components of a system and Y is the applied common random stress on them, which independently follows gamma distribution with parameters \(\left({\alpha }_{1},{\lambda }_{1}\right)\) and \(\left({\alpha }_{2},{\lambda }_{2}\right)\) respectively. The system works only if \(s\left(1\le s\le k\right)\) or more of the strengths exceed the common load/stress is called s-out-of-k: G system. Maximum likelihood and asymptotic interval estimators of MSR are obtained. Bayes estimates are computed under symmetric and asymmetric loss functions assuming informative and non-informative priors. ML and Bayes estimators are numerically evaluated and compared based on mean square errors and absolute biases through simulation study employing the Metropolis–Hastings algorithm.

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Authors and Affiliations

  1. Department of Statistics, Rajiv Gandhi University, Itanagar, Arunachal Pradesh, 791112, India

    V. K. Rathaur

  2. Department of Statistics, Pondicherry University, Pondicherry, 605014, India

    N. Chandra

  3. Department of Statistics, Patna University, Patna, 800005, India

    Parmeet Kumar Vinit

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  1. V. K. Rathaur
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  2. N. Chandra
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  3. Parmeet Kumar Vinit
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Correspondence to Parmeet Kumar Vinit.

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Rathaur, V.K., Chandra, N. & Vinit, P.K. On Bayesian estimation of stress–strength reliability in multicomponent system for two-parameter gamma distribution. Int J Syst Assur Eng Manag (2024). https://doi.org/10.1007/s13198-024-02379-8

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