Bayesian inference for dependent stress–strength reliability of series–parallel system based on copula

In this paper, we investigate the inferential procedures for dependent stress-strength reliability within a series-parallel system, utilizing the Clayton copula to characterize the dependence structure between stress and strength variables, which follow proportional reversed hazard rate model. We establish maximum likelihood estimations for model parameters and system reliability, along with improved approximate confidence intervals based on Fisher information. Bayesian estimations are performed using the highly flexible Gamma-Beta prior distribution under different loss functions, and the highest posterior density interval is obtained via the Metropolis-Hastings algorithm. To assess the performance of the proposed methods, Monte Carlo simulations are conducted. Finally, an original data set, the general dam occupancy rate of Istanbul, is analyzed for illustrative purposes.