The Value of Using Imprecise Probabilities in Engineering Design

[+] Author and Article Information
Jason Matthew Aughenbaugh

Systems Realization Laboratory, G. W. Woodruff School of Mechanical Engineering,  Georgia Institute of Technology, Atlanta, GA 30332-0405jaughenbaugh.me03@gtalumni.org

Christiaan J. Paredis

Systems Realization Laboratory, G. W. Woodruff School of Mechanical Engineering,  Georgia Institute of Technology, Atlanta, GA 30332-0405chris.paredis@me.gatech.edu

J. Mech. Des 128(4), 969-979 (Dec 21, 2005) (11 pages) doi:10.1115/1.2204976 History: Received September 13, 2005; Revised December 21, 2005

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 designer’s 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.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 5

A computational experiment for determining the value of using imprecise probabilities

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Figure 6

Forming bounds of the p-box

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Figure 8

Variation of value with imprecision

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Figure 9

Histogram of value of p-box approach

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Figure 10

Example expected utility functions, V(B)<0

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Figure 11

Example expected utility functions, V(B)>0

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Figure 12

Example expected utility functions, V(B)=0

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Figure 13

Variation in value with imprecision for midpoint policy

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Figure 14

Midpoint policy results

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Figure 1

Characteristics of uncertainty (adapted from Ref. 10)

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Figure 2

Dimensions of uncertainty

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Figure 3

Example p-box and distributions

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Figure 4

Pressure vessel schematic and design variables




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