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Research Papers

# An Investigation Into the Decision Analysis of Design Process Decisions

[+] Author and Article Information
Stephanie C. Thompson

Model-Based Systems Engineering Center, G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332stephaniecthompson@gatech.edu

Christiaan J. J. Paredis

Model-Based Systems Engineering Center, G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332chris.paredis@me.gatech.edu

While we recognize that Howard and Matheson make no distinction between the subjective or objective probabilities, we believe that all probabilities in the context of decision theory are subjective probabilities because they represent the beliefs of the decision maker. This is the case whether or not those beliefs are supported by objective frequency data. Thus, we use the term subjective probability to represent decision maker’s beliefs throughout this paper.

This is the same payoff function used by Ling et al. (19), although we have changed the failure cost from $1 M to$300 M to represent the cost of replacing the vessel when it fails by leaking rather than by bursting.

This definition establishes an analysis as an information source in agreement with the definition of information adopted by Ling et al.  in Ref. 19. Their definition of information differs from that in Ref. 23.

J. Mech. Des 132(12), 121009 (Dec 07, 2010) (9 pages) doi:10.1115/1.4002969 History: Received May 25, 2009; Revised October 28, 2010; Published December 07, 2010; Online December 07, 2010

## Abstract

Although recent work in decision-based design (DBD) recognizes the need for an enterprise perspective in which the expected profit is the primary driver of utility, for the overwhelming majority of contributions in the DBD literature, the emphasis in the problem formulation is exclusively on the design artifact. This formulation of DBD problems is too narrow in scope, because the use of resources during the design and development phase is overlooked, making it impossible to consider the tradeoffs between the quality of the design artifact and the cost of the design process. We aim to establish a new DBD perspective that more accurately represents the tradeoffs under consideration in an enterprise context by studying the design actions with decision analysis. As a first step toward establishing this new perspective, a simple example problem of material selection for a pressure vessel is introduced and analyzed in this paper. Although several simplifying assumptions are made, the intent of this work is to qualitatively explore the impact of relaxing some of the assumptions implicitly made in previous work in DBD, specifically the assumption of ignoring the costs of the design phase and the assumption that the value of a particular analysis is independent of the ability to gain additional information from subsequent analyses. This work confirms that an analysis is worth performing only when the cost is low, the quality is high, and the overlap in the predicted utility of the two concepts is significant. These insights are also compared with the related work in information economics. We show that the decision analysis of design process decisions provides a more comprehensive model of the problem when multiple information sources can sequentially be used.

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## Figures

Figure 1

Trends of (a) expected payoff, (b) vessel wall thickness, and (c) probability of failure versus mean and standard deviation of material strength at the point of maximum expected utility (Eq. 2)

Figure 2

Cumulative distribution functions for materials A and B

Figure 3

Decision tree for the pressure vessel decision problem

Figure 4

Boundary plot comparing (a) full and (b) truncated decision trees; strength of material B∼N(1000,60) MPa

Figure 5

Boundary plots for increasing analysis cost (SA=select A, SB=select B, AA=analyze A, and AB=analyze B)

Figure 6

Boundary plots for decreasing quality of the analysis (SA=select A, SB=select B, AA=analyze A, and AB=analyze B)

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