Eliminating Design Alternatives Based on Imprecise Information

In this paper, the relationship between uncertainty and sets of alternatives in engineering design is investigated. In sequential decision making, each decision alternative actually consists of a set of design alternatives. Consequently, the decision-maker can express his or her preferences only imprecisely as a range of expected utilities for each decision alternative. In addition, the performance of each design alternative can be characterized only imprecisely due to uncertainty from limited data, modeling assumptions, and numerical methods. The approach presented in this paper recognizes the presence of both imprecision and sets in the design process by focusing on incrementally eliminating decision alternatives until a small set of solutions remains. This is a fundamental shift from the current paradigm where the focus is on selecting a single decision alternative in each design decision. To make this approach economically feasible, one needs efficient methods for eliminating alternatives-that is, methods that eliminate as many alternatives as possible given the available imprecise information. Efficient elimination requires that one account for dependencies between uncertain quantities, such as shared uncertain variables. In this paper, criteria for elimination with and without shared uncertainty are presented and compared. The set-based nature of design and the presence of imprecision are introduced, elimination criteria are discussed, and the overall set-based approach and elimination criteria are demonstrated with the design of a gearbox as an example problem.