Structural Reliability Analysis with Conditional Importance Sampling Method Based on the Law of Total Expectation and Variance in Subintervals

In this paper, a new approach is proposed to estimate the probability of failure in structural reliability analysis. This method is based on the law of total expectation and variance in subintervals, and it combines the conditional Monte Carlo method and the importance sampling method. The conditional input variable can be chosen from the estimates of variance-based sensitivity measures with one set of samples. In addition, the optimal sample size in each subinterval can also be estimated with the same set of samples. The proposed method has a higher rate of convergence compared to the importance sampling method. The numerical and engineering examples show the efficiency of the proposed method.