Application of Rejection Sampling based methodology to variance based parametric sensitivity analysis

For estimating the effect of uncertain distribution parameter on the variance of failure probability function (FPF), the map from distribution parameters to FPF is built and the high efficient approximation form is extended to solve the parametric variance-based sensitivity index. Then the parametric variance-based sensitivity index can be firstly expressed as the moments of the FPF, and the FPF is approximated by a product of the univariate functions of the distribution parameters, on which the moments of the FPF approximated by the univariate functions can be easily evaluated by the Gaussian integration using the values of the FPF at the Gaussian nodes. Thus the primary task of evaluating the parametric variance-based sensitivity is transformed to calculate the FPF at Gaussian nodes of the univariate functions, for which Monte Carlo (MC), Extended Monte Carlo (EMC) and Rejection Sampling (RS) are employed and compared here. Only one set of samples of inputs are needed in either EMC or RS. Several numerical and engineering examples are presented to verify the accuracy and efficiency of the proposed approximate methods. Additionally, the results also reveal the virtue of RS which can be more accurate and more unlimited than EMC.