Tolerance design is becoming increasingly important for electromechanical products. Reasonable tolerance design can reduce production costs and improve product performance. However, as the complexity of the coupling of tolerances and performance increases, it becomes difficult for designers to establish accurate tolerance design models, leading to experience-based design. This study proposes a novel performance-oriented tolerance design method. First, the main tolerance variables affecting the product performance are rapidly determined based on the proposed locally inferred sensitivity analysis method. Then, based on the improved approximate polynomial chaos expansion, a surrogate model of the product performance and main tolerance variables is established. Finally, the geometric tolerances of the electromechanical products are optimized based on the surrogate model with performance requirements. The proposed tolerance design method is computationally efficient and accurate, and it can be implemented with a small number of samples. To demonstrate its performance, the proposed method is validated with a spaceborne active phased array antenna. The optimal tolerance design of the antenna for the electrical performance requirements is performed successfully.