The effect of design variables on the performance measures in the entire design space can be evaluated by global sensitivity analysis (GSA). Therefore, a high-dimensional engineering problem can be transformed to a reduced-dimensional problem by ascertaining important design variables according to GSA. Subsequently, the reduction of design variables helps save computational cost and the duration of design optimization. In this study, GSA was applied to determine the most influential design variable in the design of two reaction hydro turbine components - stay vane and casing. The global sensitivity index technique is selected among GSA methods because it can evaluate both the individual and interaction effects of design variables. Genetic aggregation surrogate models are used to reduce the number of computational fluid dynamics (CFD) analyses for GSA and design optimization. The responses from surrogate models are evaluated to obtain global sensitivity indices for performance measures. The important design variables are selected according to the indices. Using a multiobjective genetic algorithm (MOGA), design optimizations with the selected design variables are performed and the results are compared to the optimum designs with all design variables. The optimum designs using the selected design variables show comparable performances to those of the full-dimensional optimum designs.