Vine copula-based parametric sensitivity analysis of failure probability-based importance measure in the presence of multidimensional dependencies

In this paper, we propose derivative-oriented parametric sensitivity indices to investigate the influence of parameter uncertainty on a previously proposed failure probability-based importance measure in the presence of multidimensional dependencies. Herein, the vine copula function, a powerful mathematical tool for modeling variable dependencies, is utilized to establish the joint probability density function (PDF) for multidimensional dependencies. Based on the properties of the copula function, the developed parametric sensitivity indices are decomposed into independent and dependent parts. Using these parts, different types of contributions to the failure probability are identified. By computing the kernel function for each marginal PDF and the copula kernel function for each pair-copula PDF involved in the vine factorization, a general numerical algorithm is developed for estimating separated parametric sensitivity indices. Finally, the feasibility of the proposed indices and numerical solutions is verified through a numerical example and by solving two engineering problems.