Copula-Based Efficient Estimation for Global Reliability Sensitivity Analysis

The global reliability sensitivity index (GRSI) is defined as the average difference between the unconditional failure probability and the conditional one on fixing an input at its realization, which reflects the effect of the fixed input on the failure probability. In this paper, two aspects of the GRSI are concerned, one is the interpretation of the GRSI in terms of copula, the other is the estimation methods of the GRSI based on copula. Firstly, the relationship between GRSI and copula is constructed from copula viewpoint. Secondly, two methods based on copula, i.e., copula-MCS and copula-AK method, are proposed to estimate the GRSI. In contrast to the direct copula-MCS based on the nonparametric estimation, the copula-AK method is more efficient by embeding the adaptive Kriging (AK) model. At last, two engineering examples are provided to verify the proposed methods.