Design variables and design parameters are rarely deterministic in practice. Robust optimal design takes into consideration of the uncertainties in the design variables and parameters. Robust optimization methodology with probability constraints requires a lot of system analyses fer calculating failure probability of each constraint. By introducing an envelope function to reduce the number of constraints, efficiency of robust optimization techniques can be considerably improved. Through four illustrative examples, it is shown that the number of system analyses is greatly decreased while little differences in the optimum results are observed.