Failure probability-based global and regional sensitivity analysis using copula

In risk and reliability assessment, the failure probability-based global sensitivity analysis (GSA) and the failure probability-based regional sensitivity analysis (RSA) have attracted much interest. In this article, we deduce the relationship of the failure probability-based GSA importance measure and copula, and point out that the failure probability-based GSA importance measure can be interpreted as the dependence measure between the failure probability and the input variables from copula viewpoint. To calculate the importance measure, the least square fitting copula (LSFC) method is proposed subsequently. The method decouples the double-loop estimating of the conditional failure probability. Additionally, to analyze and identify the effects of the different regions of the input variables on failure probability, a RSA importance measure is proposed, its properties are investigated and proved. At last, an engineering example is employed to demonstrate and validate the effectiveness of the LSFC method and the proposed RSA importance measure.