Failure-mode importance measures in structural system with multiple failure modes and its estimation using copula

In the structural reliability analysis, there exist multiple failure modes. Influence of each failure mode on the structural system reliability needs to be considered, because it is significant for simplifying the system model and improving the performance of the system. By using the concepts of the importance measures(IM) in probability risk assessment (PRA), the importance indices in PRA are extended to measure the failure mode contribution to the structural system reliability, and the analytical solutions of the failure mode importance measure for the parallel and series structural systems are derived firstly. Then, copula method is proposed to estimate the importance indices for the nested hybrid structural systems. At last, one numerical example with a parallel structure and two engineering examples are employed to analyze the failure mode importance and to test the two estimates based on the analytical solution and the copula method. Result indicates that five PRA importance indices can well reflect the failure mode importance. It also shows that the copula method is highly suitable for computing PRA IMs in the intricate structural systems.