Estimation of Moment-Independent Importance Measure on Failure Probability and Its Application in Reliability Analysis

Similar to the definition of the moment-independent importance measure on model failure probability, the authors define the moment-independent importance measure concerning the importance sampling method. After combining the importance sampling procedure, the sampling efficiency is improved and the cost of computation is cheaper. After the moment-independent importance measures of all inputs are obtained, a new method called conditional importance sampling is proposed to calculate the failure probability and those inputs with high importance measures are chosen to be conditional variables. And state-dependent parameter method is employed in the new method. A numerical example and two structural engineering examples are used to demonstrate that the failure probability estimated by the proposed conditional importance sampling method is accurate and converges faster than those estimated by the traditional importance sampling method.