<p>The distribution parameters of random inputs often possess randomness due to the lack of input information. For this case, the augmented failure probability can be used to quantify the safety level of structures, and the augmented failure probability based global reliability sensitivity (A-GRS) can measure the effect of the randomness of both inputs and their distribution parameters on the safety level. However, estimating A-GRS is time-demanding due to the twofold uncertainties from the inputs and their distribution parameters. To efficiently estimate A-GRS, this paper proposes a stochastic collocation algorithm by combining dimension reduction integral and high-dimension model representation. The main innovation includes two aspects. Firstly, in the augmented input space by the distribution parameters, the proposed algorithm converts the A-GRS estimation into the integral of continuous integrands by dimension reduction integral, then the stochastic collocation algorithm can be used to combine with the truncation models of the continuous integrands for efficiently estimating the A-GRS. Secondly, the proposed algorithm designs an information-sharing strategy of stochastic collocation node to enhance the efficiency of estimating the A-GRS. Additionally, the Kriging surrogate model of performance function is adaptively trained in the stochastic collocation node set to further improve the efficiency. These innovations are validated by the presented examples.</p>