Estimation of failure probability for parallel system based on simulated annealing method

For the failure probability of parallel system with multiple failure modes, the most probable failure point in the failure domain is defined, and the simulated annealing optimization method is employed to search for this point. The adaptive importance sampling method based on the most probable failure point is presented to estimate the failure probability of the parallel system. The formulae of the failure probability, the variance and the coefficient of variation are derived for the presented adaptive importance sampling method. The presented method is more efficient than Monte Carlo method especially for the small failure probability. And comparing with the successive sequential approximation, the presented method has higher precision and wider applicability. The examples illustrate the feasibility and advantage of the presented method.