This research project will extend the illustrative and informal models of iteration in engineering design that are available at present. Formal methods for guiding the refinement of engineering designs at each iteration will be developed that permit the designer to make better decisions during the design process. The set-based representation and manipulation of uncertainties in engineering design developed previously will be extended to combine the imprecise results from each design step to guide the next step. Since engineering design informally converges to a solution (in most cases) now, we believe that developing a formalism for guiding the design refinement will also produce an understanding of the conditions under which the iterations are convergent. This, of course, has profound implications for design, in that very early indications of the possibility of convergence of several different candidate designs may be able to guide the designer to pursue (at least initially) those candidates with the best indications of convergence.
