An Empirical Fitting-Adaptive Approach to Importance Sampling in Reliability Analysis

Abstract

This paper presents a fitting-adaptive approach to importance sampling, in which a fitting density function is introduced to calculate the failure probability instead of the importance sampling density function. The approach improves the accuracy of the importance sampling technique when the sample size is relatively small. Therefore, it is very useful to problems that have high reliability and consume much CPU time in a single Monte Carlo run. Furthermore, the adaptive operation is performed if the fitting density function is not satisfactory. When the design point is used, the proposed approach yields even better results. Numerical examples demonstrate that a significant reduction in variance of the failure probability can be achieved by use of this approach.