Summary: Generalized parameter and tolerance design problems have been formulated as nonlinear optimization problems under a broader set of assumptions. A new approach for parameter design and tolerance design problems is outlined. This approach integrates engineering models and numerical optimization methods so it can work in the early stage of design where a good engineering model is available to simulate the real product or process. The new approach is also able to handle multiple quality characteristics and constraints. Several important theoretical results have been derived by the authors for tolerance design problems that could serve as guidelines for optimal tolerance design and tolerance distribution.