This work focuses on the application of multi-fidelity methods for the robust design optimization of engine components. The robust design optimization approach yields geometric designs that have high efficiencies and are less sensitive to uncertainties from manufacturing and wear. However, the uncertainty quantification techniques required to evaluate the robustness are computationally expensive, which limits their use in robust optimization. Multi-fidelity methods offer a promising solution to reduce the computational cost while maintaining the accuracy in both uncertainty quantification and optimization.A Kriging and a multi-fidelity recursive Cokriging framework are developed, implemented, and applied to a test function. In addition, a multi-fidelity super efficient global optimization algorithm is developed. The optimizer is surrogate model-based and can handle constraints. The developed methods are then applied to a compressor test case of a high pressure compressor blade row with 9 uncertainty and 24 design parameters of the geometry. The 2.5 various uncertainty quantification techniques are analyzed. A multi-fidelity uncertainty quantification approach is developed that combines simplified coarse-grid low-fidelity results with high-fidelity results to reduce the computational cost while maintaining a high accuracy. Uncertainty quantification techniques of three fidelity levels are then developed and used for the multi-fidelity approach in the design space. The robust design optimization of the compressor is performed and the optimal designs obtained from the multi-fidelity approach show superior performance compared to existing robust design optima in the literature.