1 SAE 06B-233 Eliminating Design Alternatives Based on Imprecise Information

In this paper, we investigate the relationship between uncertainty and set-based design. In set-based design the focus is on incrementally eliminating design alter-natives until a small set of satisficing solutions re-mains. This is a fundamental shift from the current paradigm where the focus is on selecting a single best decision alternative in each design decision. The main principle in set-based design is that one should only eliminate design alternatives that are known to be dominated by other alternatives. However, due to the imprecision in the behavioral models, in the models of the decision maker’s preferences, and in the specifica-tions of the design alternatives themselves, eliminating the dominated designs results in a set of mutually non-dominated designs rather than in a single design solu-tion. To make the set-based design method economi-cally feasible, one needs efficient methods for eliminat-ing dominated alternatives—that is, methods that eliminate as many alternatives as possible given the currently available information. We will show in this paper that efficient elimination requires considering the difference in performance between two design alterna-tive, because it allows taking into account the depend-ence between uncertain quantities, as for instance in shared uncertain variables. We will derive the criteria for elimination with and without shared uncertainty, and illustrate with a gearbox design problem how these criteria can be used. KEYWORDS Set-based design, imprecise probabilities, probability bounds analysis, decision making under uncertainty, dependent uncertainty