Bily, C. and Malak, R., "Composing Tradeoff Studies under Uncertainty based on Parameterized Efficient Sets and Stochastic Dominance Principles," SAE Int. J. Mater. Manf. 5(2):418-429, 2012, doi:10.4271/2012-01-0913.
Tradeoff studies are a common part of engineering practice. Designers conduct tradeoff studies in order to improve their understanding of how various design considerations relate to one another and to make decisions. Generally a tradeoff study involves a systematic multi-criteria evaluation of various alternatives for a particular system or subsystem. After evaluating these alternatives, designers eliminate those that perform poorly under the given criteria and explore more carefully those that remain.One limitation of current practice is that designers cannot combine the results of preexisting tradeoff studies under uncertainty. For deterministic problems, designers can use the Pareto dominance criterion to eliminate inferior designs. Prior work also exists on composing tradeoff studies performed under certainty using an extension of this criterion, called parameterized Pareto dominance. The capability to compose preexisting tradeoff studies is advantageous to the designers of complex systems, such as aircraft, military equipment, and automobiles. For example, automotive systems engineers could combine tradeoff studies from the engine and transmission subsystems quickly to produce a comprehensive tradeoff study for the power train. This level of knowledge reuse is in keeping with good systems engineering practices. However, existing procedures for generating tradeoff studies involve assumptions that preclude the valid composition of tradeoff studies under uncertainty.In this paper we describe a new approach that permits engineers to compose preexisting subsystem-level tradeoff studies under uncertainty into mathematically valid system-level tradeoff studies. The approach is based on two key ideas: the use of stochastic dominance methods to enable the tradeoff evaluation when the values of the design criteria are not known with certainty (i.e., tradeoff studies under uncertainty) and the use of parameterized efficient sets to enable reuse and composition of subsystem-level tradeoff studies. The key ideas and their mathematical validity are described. The overall approach is demonstrated in the context of a tradeoff study for a motor vehicle.