Jason Matthew Aughenbaugh

The Value of Using Imprecise Probabilities in Engineering Design

Engineering design decisions inherently are made under risk and uncertainty. The characterization of this uncertainty is an essential step in the decision process. In this paper, we consider imprecise probabilities (e.g., 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 designers beliefs. The hypothesis is that, in engineering design decisions, it is valuable to explicitly represent this imprecision by using imprecise probabilities. This hypothesis is supported 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, suggesting that there are design problems for which it is valuable to use imprecise probabilities.

Multi-attribute utility analysis in set-based conceptual design

During conceptual design, engineers deal with incomplete product descriptions called design concepts. Engineers must compare these concepts in order to move towards the more desirable designs. However, comparisons are difficult because a single concept associates with numerous possible final design specifications, and any meaningful comparison of concepts must consider this range of possibilities. Consequently, the performance of a concept can only be characterized imprecisely. While standard multi-attribute utility theory is an accepted framework for making preference-based decisions between precisely characterized alternatives, it does not directly accommodate the analysis of imprecisely characterized alternatives. By extending uncertainty representations to model imprecision explicitly, it is possible to apply the principles of utility theory to such problems. However, this can lead to situations of indeterminacy, meaning that the decision maker is unable to identify a single concept as the most preferred. Under a set-based perspective and approach to design, a designer can work towards a single solution systematically despite indecision arising from imprecise characterizations of design concepts. Existing work in set-based design primarily focuses on feasibility conditions and single-attribute objectives, which are insufficient for most design problems. In this article, we combine the framework of multi-attribute utility theory, the perspective of set-based design, and the explicit mathematical representation of imprecision into a single approach to conceptual design. Each of the component theories is discussed, and their combined application developed. The approach is illustrated using the conceptual design of a fixed-ratio power transmission as an example. Additionally, important directions for future research are identified, with a particular focus on the process of modeling abstract design concepts.

Managing the Collection of Information under Uncertainty using Information Economics

An important element of successful engineering design is the effective management of resources to support design decisions. Design decisions can be thought of as having two phases-a formulation phase and a solution phase. As part of the formulation phase, engineers must decide what information to collect and use to support the design decision. Since information comes at a cost, a cost-benefit tradeoff must be made. Previous work has considered such tradeoffs in cases in which all relevant probability distributions were precisely known. However, engineers frequently must characterize these distributions by gathering sample data during the information collection phase of the decision process. This characterization is crucial in high-risk design problems where uncommon events with severe consequences play a significant role in decisions. In this paper, we introduce the principles of information economics to guide decisions on information collection. We investigate how designers can bound the value of information in the case of distributions with unknown parameters by using imprecise probabilities to characterize the current state of information. We explore the basic performance, subtleties, and limitations of the approach in the context of characterizing the strength of a novel material for the design of a pressure vessel.

Eliminating Design Alternatives Based on Imprecise Information

This paper was presented at the SAE 2006 World Congress, 2006. Reprinted with permission from SAE paper 2006-01-0272

The Role and Limitations of Modeling and Simulation in Systems Design

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.Copyright

APPLYING INFORMATION ECONOMICS AND IMPRECISE PROBABILITIES TO DATA COLLECTION IN DESIGN

One important aspect of the engineering design process is the sequence of design decisions, each consisting of a formulation phase and a solution phase. As part of the decision formulation, engineers must decide what information to use to support the decision. Since information comes at a cost, a cost-benefit trade-off must be made. Previous work has considered these trade-offs in cases in which all relevant probability distributions were precisely known. However, engineers frequently must estimate these distributions by gathering sample data during the information collection phase of the decision process. In this paper, we introduce principles of information economics to guide decisions on information collection. We present a method that enables designers to bound the value of information in the case of unknown distributions by using imprecise probabilities to characterize the current state of information. We illustrate this method with an example material strength characterization for a pressure vessel design problem, in which we explore the basic performance, subtleties, and limitations of the method.Copyright

A COMPARISON OF PROBABILITY BOUNDS ANALYSIS AND SENSITIVITY ANALYSIS IN ENVIRONMENTALLY BENIGN DESIGN AND MANUFACTURE

There is growing acceptance in the design community that two types of uncertainty exist: inherent variability and uncertainty that results from a lack of knowledge, which variously is referred to as imprecision, incertitude, irreducible uncertainty, and epistemic uncertainty. There is much less agreement on the appropriate means for representing and computing with these types of uncertainty. Probability bounds analysis (PBA) is a method that represents uncertainty using upper and lower cumulative probability distributions. These structures, called probability boxes or just p-boxes, capture both variability and imprecision. PBA includes algorithms for efficiently computing with these structures under certain conditions. This paper explores the advantages and limitations of PBA in comparison to traditional decision analysis with sensitivity analysis in the context of environmentally benign design and manufacture. The example of the selection of an oil filter involves multiple objectives and multiple uncertain parameters. These parameters are known with varying levels of uncertainty, and different assumptions about the dependencies between variables are made. As such, the example problem provides a rich context for exploring the applicability of PBA and sensitivity analysis to making engineering decisions under uncertainty. The results reveal specific advantages and limitations of both methods. The appropriate choice of an analysis depends on the exact decision scenario.Copyright

The Value of Imprecise Probabilities in Engineering Design

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 designers 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.

Considering the Info-Gap Approach to Robust Decisions Under Severe Uncertainty in the Context of Environmentally Benign Design

Information-Gap Decision Theory (IGDT), an approach to robust decision making under severe uncertainty, is considered in the context of a simple life cycle engineering example. IGDT offers a path to a decision in the class of problems where only a nominal estimate is available for some uncertain life cycle variable that affects performance, and where there is some unknown amount of discrepancy between that estimate and the variable’s actual value. Instead of seeking maximized performance, the decision rule inherent to IGDT prefers designs with maximum immunity (info-gap robustness) to the size that the unknown discrepancy could take. This robustness aspiration is subject to a constraint of achieving better than some minimal requirement for performance. In this paper, an automotive oil filter selection design example, which involves several types of severe uncertainty, is formulated and solved using an IDGT approach. Particular attention is paid to the complexities of assessing preference for robustness to multiple severe uncertainties simultaneously. The strengths and limitations of the approach are discussed mainly in the context of environmentally benign design and manufacture.Copyright