Incorporating Epistemic Uncertainty in Robust Design

There are two sorts of uncertainty inherent in engineering design, random uncertainty and epistemic uncertainty. Random, or stochastic, uncertainty deals with the randomness or predictability of an event. It is well understood, easily modelled using classical probability, and ideal for such uncertainties as variations in manufacturing processes or material properties. Epistemic uncertainty deals with our lack of knowledge, our lack of information, and our own and others’ subjectivity concerning design parameters. While there are many methods to incorporate random uncertainty in a design process, there are fewer that consider epistemic uncertainty. There are fewer still that attempt to incorporate both sorts of uncertainty, and those that do usually attempt to model both sorts using the same uncertainty model. Two methods, a range method and a fuzzy sets approach, are proposed to achieve designs that are robust to both epistemic uncertainty and random uncertainty. Both methods incorporate preference aggregation methods to achieve more appropriate trade-offs between performance and variability when considering both sorts of uncertainty. The proposed models for epistemic uncertainty are combined with existing models for stochastic uncertainty in a two-step process. An illustrative example incorporating subjectivity concerning design parameters is presented.