System Reliability and Component Importance Under Dependence: A Copula Approach

System reliability and component importance are of great interest in reliability modeling, especially when the components within the system are dependent. We characterize the influence of dependence structures on system reliability and component importance in coherent systems with discrete marginal distributions. The effects of dependence are captured through copula theory. We extend our framework to coherent multi-state system. Applications of the derived results are demonstrated using a Gaussian copula, which yields simple interpretations. Simulations and two examples are presented to demonstrate the importance of modeling dependence when estimating system reliability and ranking of component importance. Proofs, algorithms, code, and data are provided in supplementary materials available online.