Bayesian reliability analysis of complex k-out-of-n: ℓ systems under degradation performance

Consider a complex k-out-of-n system consisting of n independent elements each having some dependent components. This paper investigates the reliability of such complex systems based on degradation data systematically. A flexible class of multivariate stochastic processes is proposed to describe the dependence structure of the components by a copula function. Assuming the degradation of each component is modeled by a stochastic process, the reliability of a complex system is derived. A two-step Bayesian approach is used to estimate the unknown parameters of the model and it is implemented with the Hamiltonian Monte Carlo algorithm. Also, Bayesian bootstrap method is applied to estimate system reliability and its credible interval. Moreover, a Markov chain Monte Carlo simulation is conducted to validate our statistical approach. Finally, the applicability of the proposed modeling framework of system reliability is illustrated using two real examples. •The reliability of a new complex k-out-of-n: ℓ system is evaluated.•A multivariate degradation model is proposed to describe the dependence structure.•A two-step Bayesian approach is suggested to estimate the unknown parameters.•A MCMC simulation is conducted to study the performance of the proposed approach.•The results of the paper are illustrated using two real examples.