In reliability-based robust design optimization formulation, the product quality loss function is minimized subject to probabilistic constraints. Since the quality loss function is expressed in terms of the first two statistical moments, mean and variance, several methods have been proposed to accurately and efficiently estimate the statistical moments. However, it is computationally expensive to calculate the statistical moments of the output performance function using the multidimensional integral, especially when the number of the random input variables is relatively high. To overcome the shortcomings, three methods have been recently proposed: univariate dimension reduction method (DRM) [
], performance moment integration (PMI) method [
], and percentile difference method (PDM) [
]. In this paper, a reliability-based robust design optimization method is developed using DRM and compared to PMI and PDM for the robust design part. It is found that PDM cannot estimate the statistical moments of the performance function accurately. The PMI and DRM are also compared in terms of accuracy and efficiency in estimation of statistical moments of the performance function. Several numerical examples are used to compare accuracy and efficiency of these methods. The numerical results show that DRM is effective when the number of random variables is small, whereas PMI is more effective when the number of random variables is relatively large. For the inverse reliability analysis, the enhanced hybrid mean value (HMV+) method is used, whereas the enriched performance measure approach (PMA+) is used for reliability-based design optimization.