Abstract: Robust design is a widely used method for design under uncertainty to seek an optimal solution where the design objective is insensitive to the variations of input variables while the design feasibility under the variations is maintained. In this paper, the first four statistical moments, i.e., mean, variance, skewness and kurtosis, are used to measure the robustness of the objective function and probabilistic constraints. With the weighting factor method, a new robust design problem is modeled as a single objective optimization problem on the basic of first four statistical moments. We present moment estimation method as a rigorous method for statistical moment calculation and sensitivity computation with arbitrary input distributions and examine its effectiveness when applied to robust design. Three robust design examples of truss structures are provided to check the feasibility and effectiveness of robust design using moment estimation method and the proposed sensitivity analysis. \vskip 1mm oindent \bf