Engineering design decisions inherently are made under uncertainty. In this paper, we consider imprecise probabilities (i.e. intervals of probabilities) to express explicitly the precision with which something is known. Imprecision can arise from fundamental indeterminacy in the available evidence or from incomplete characterizations of the available evidence and designer's beliefs. Our hypothesis is that, in engineering design decisions, it is valuable to explicitly represent this imprecision by using imprecise probabilities. We support this hypothesis with a computational experiment in which a pressure vessel is designed using two approaches, both variations of utility-based decision making. In the first approach, the designer uses a purely probabilistic, precise best-fit normal distribution to represent uncertainty. In the second approach, the designer explicitly expresses the imprecision in the available information using a probability box, or p-box. When the imprecision is large, this p-box approach on average results in designs with expected utilities that are greater than those for designs created with the purely probabilistic approach. In the context of decision theory, this suggests that there are design problems for which it is valuable to use imprecise probabilities.
Engineering design decisions inherently are made under uncertainty. In this paper, we consider imprecise probabilities (i.e. intervals of probabilities) to express explicitly the precision with which something is known. Imprecision can arise from fundamental indeterminacy in the available evidence or from incomplete characterizations of the available evidence and designer’s beliefs. Our hypothesis is that, in engineering design decisions, it is valuable to explicitly represent this imprecision by using imprecise probabilities. We support this hypothesis with a computational experiment in which a pressure vessel is designed using two approaches, both variations of utility-based decision making. In the first approach, the designer uses a purely probabilistic, precise best-fit normal distribution to represent uncertainty. In the second approach, the designer explicitly expresses the imprecision in the available information using a probability box, or p-box. When the imprecision is large, this p-box approach on average results in designs with expected utilities that are greater than those for designs created with the purely probabilistic approach. In the context of decision theory, this suggests that there are design problems for which it is valuable to use imprecise probabilities.
To design today’s complex, multi-disciplinary systems, designers need a design method that allows them to systematically decompose a complex design problem into simpler sub-problems. Systems engineering provides such a framework. In an iterative, hierarchical fashion systems are decomposed into subsystems and requirements are allocated to these subsystems based on estimates of their attributes. In this paper, we investigate the role and limitations of modeling and simulation in this process of system decomposition and requirements flowdown. We first identify different levels of complexity in the estimation of system attributes, ranging from simple aggregation to complex emergent behavior. We also identify the main obstacles to the systems engineering decomposition approach: identifying coupling at the appropriate level of abstraction and characterizing and processing uncertainty. The main contributions of this paper are to identify these short-comings, present the role of modeling and simulation in overcoming these shortcomings, and discuss research directions for addressing these issues and expanding the role of modeling and simulation in the future.
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 setbased 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.
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