Accurate knowledge of the effect of parameter uncertainty on process design and operation is essential for optimal and feasible operation of a process plant. Existing approaches for dealing with uncertainty at the design and process operations level assume the existence of a well-defined model to represent process behavior and, in almost all cases, convexity of the involved equations. However, most of the realistic case studies are described by nonconvex and, more importantly, poorly characterized models. Thus, a new approach is presented in this paper that is based on the development of input-output mapping with respect to a system's flexibility and a design's optimality. High-dimensional model reduction is used as our basic mapping methodology, although different mapping techniques can be employed. The result of the proposed approach is a parametric expression of the optimal objective with respect to uncertain parameters. The proposed approach is general to accommodate black-box models as it does not rely on the nature of the mathematical model of the process. Various examples are presented to illustrate the applicability of the proposed approach.