According to the flexibility relationships of the 3-RRR compliant parallel micromotion platform along the X, Y direction and the rotation around the Z axis, using the Taguchi Design and Monte Carlo Simulation methods, considering the strong robustness of the flexibility in X direction and the existence of errors of the flexible hinge geometrical sizes, the flexibility iterative optimization for the compliance of the micromotion platform along the translation in Y-direction and the rotation around the Z axis are carried out respectively, the best geometry sizes of flexible hinge are find out, which provides a new solution of robust optimization design with multiple response problems of compliant mechanism consider uncertainty disturbance situation. Finally the correctness and validity of the method are verified with an example.