Abstract: For structural systems involving inputs with distribution parameter uncertainty, the uncertainty in distribution parameters will lead to the uncertainty of failure probability. Consequently, the contributions of the input variables to failure probability are also uncertain. In this case, the three-loop nested Monte Carlo(MC) sampling strategy is considered a natural method to evaluate the influence of input variables on the structural failure., However, the computational cost of the MC method is normally too prohibitive to be accepted for the engineering problem. Therefore, a newly efficient algorithm is proposed in this paper for global reliability sensitivity analysis of the inputs with parameter uncertainty. The proposed method can reduce the three-loop nested MC into a single-loop one by introducing a 'Surrogate Sampling Probability Density Function (SS-PDF)’ and incorporating the single-loop MC theory into the computation, which greatly decreases the computational cost. For the problem with small failure probability, the importance Sampling Procedure (IS) and Truncated Importance Sampling procedure (TIS) are combined with the single-loop sampling method to further improve the calculation efficiency. The efficiency and precision of the proposed methods are verified by several numerical and engineering examples.

Key words: parameter uncertainty, reliability sensitivity indices, surrogate sampling probability density dunction, single-loop Monte Carlo sampling, importance sampling, truncated importance sampling