A novel second‐order mixture importance sampling strategy for system reliability analysis

Reliability analysis and evaluation of systems with multiple failure modes is extremely challenging. In this paper, a novel, efficient, and accurate system reliability method is proposed based on the second‐order approximation and the mixture important sampling (mixture‐IS) method. The proposed method does not require the construction of surrogate models and integrates the advantages of second‐order approximation and mixture‐IS strategies, which can greatly reduce the computational effort of estimating the system failure probability as well as ensuring the accuracy. The accuracy and efficiency of the proposed method are verified by several numerical and engineering problems, and comparisons are made against other existing reliability methods. The results indicate that the method can effectively reduce the number of limit state function calls and achieve high computational accuracy.