Abstract: To deal with the multi-quality characteristics variation and conflict of the complex equipment products of compliant mechanism under the uncertain engineering conditions, a novel grey-polynomial chaos expansion (PCE) robust optimization design method is proposed which combines the grey relational analysis approach with the PCE robust optimization design approach. Firstly, the PCE approach is adopted to construct multi-quality characteristics surrogate models of the complex equipment products. Then, the PCE six sigma robust optimization design model of the complex equipment products is built by using six sigma robust design method. The solutions set of multi-quality characteristics is acquired from the NSGA-Ⅱ algorithm. Afterward, the grey relational analysis approach is adopt to sequential analyze the solutions set for obtaining the most satisfactory robustness design. Finally, the numerical example of the complex equipment products is provided to illustrate the effectiveness and robustness of the proposed method.