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

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.