Truncated importance sampling method based on optimization of mixed genetic algorithm

A truncated importance sampling method is employed for the failure probability of parallel system with multiple failure modes. The mixed genetic optimization algorithm is chosen to search for the most probable failure point in the failure domain, and solve the approximate reliability index β of the parallel system. A β-sphere truncated importance sampling method for the failure probability of parallel system is consisted of β-sphere truncation and importance sampling probability function. Comparing with the successive sequential approximation approach and FORM, the presented method performs much more efficiently than Monte-Carlo method with higher accuracy, especially for the small failure probability.