For structural systems with both epistemic and aleatory uncertainties, research on quantifying the contribution of the epistemic and aleatory uncertainties to the failure probability of the systems is conducted. Based on the method of separating epistemic and aleatory uncertainties in a variable, the core idea of the research is firstly to establish a novel deterministic transition model for auxiliary variables, distribution parameters, random variables, failure probability, then to propose the

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... improved importance sampling (IS) to solve the transition model. Furthermore, the distribution parameters and auxiliary variables are sampled simultaneously and independently; therefore, the inefficient sampling procedure with an "inner-loop" for epistemic uncertainty and an "outer-loop" for aleatory uncertainty in traditional methods is avoided. Since the proposed method combines the fast convergence of the proper estimates and searches failure samples in the interesting regions with high efficiency, the proposed method is more efficient than traditional methods for the variance-based failure probability sensitivity measures in the presence of epistemic and aleatory uncertainties. Two numerical examples and one engineering example are introduced for demonstrating the efficiency and precision of the proposed method for structural systems with both epistemic and aleatory uncertainties.