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

V. K. Rathaur, N. Chandra and Parmeet Kumar Vinit ()
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V. K. Rathaur: Rajiv Gandhi University
N. Chandra: Pondicherry University
Parmeet Kumar Vinit: Patna University

International Journal of System Assurance Engineering and Management, 2024, vol. 15, issue 8, No 19, 3817-3832

Abstract: Abstract This paper deals with multicomponent stress–strength system reliability (MSR) and its maximum likelihood (ML) as well as Bayesian estimation. We assume that $${X}_{1},{X}_{2},\dots ,{X}_{k}$$ X 1 , X 2 , ⋯ , 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 $$\left({\alpha }_{1},{\lambda }_{1}\right)$$ α 1 , λ 1 and $$\left({\alpha }_{2},{\lambda }_{2}\right)$$ α 2 , λ 2 respectively. The system works only if $$s\left(1\le s\le k\right)$$ s 1 ≤ s ≤ k 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.

Keywords: Multicomponent system reliability; Gamma distribution; Bayes estimation; Uniform prior; Jeffreys prior; Squared error loss function; Metropolis–Hastings algorithm (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13198-024-02379-8

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