In data-scarce scenarios, structural safety faces challenge due to the uncertainty of distribution parameter vector. In case of uncertain distribution parameter vector, the augmented failure probability (AFP) can be used to quantify the safety level of the structure. To enhance the efficiency of estimating AFP, this paper proposes a stochastic collocation algorithm by combining dimensional reduction integration with sparse grids integration. In the proposed algorithm, the AFP is derived as a reduced-dimensional integral of continuous integrands, then the AFP can be efficiently estimated by the integrand values of the sparse grids. The proposed algorithm not only improves the behavior of the integrands of AFP by dimension reduction integration, but also estimates AFP with a small number of performance function estimations at sparse grids. The proposed algorithm is more efficient than the existing methods. The presented examples fully demonstrate the effectiveness of the proposed algorithm.