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Sampling-based methods are general but time consuming for solving a Reliability-Based Design Optimization (RBDO) problem. In order to alleviate the computation burden, score function together with the Monte Carlo method was used to compute the stochastic sensitivities of reliability functions. In literature, re-weighting schemes were shown to converge faster than the regular Monte Carlo method. In this paper, a reweighting scheme together with score function is employed to perform sampling-based stochastic sensitivity analysis to improve the computational efficiency and accuracy. An analytical example is used to show the advantages of the proposed method. Comparisons to the conventional methods are made and discussed. Two RBDO problems are solved to demonstrate the use of the proposed method.