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Research Papers

Mechanical Engineering Design Complexity Metrics: Size, Coupling, and Solvability

[+] Author and Article Information
Joshua D. Summers

 Clemson University, Clemson, SC 29634-0921joshua.summers@ces.clemson.edu

Jami J. Shah

 Arizona State University, Tempe, AZ 85287-6106jami.shah@asu.edu

J. Mech. Des 132(2), 021004 (Jan 14, 2010) (11 pages) doi:10.1115/1.4000759 History: Received January 25, 2009; Revised December 04, 2009; Published January 14, 2010; Online January 14, 2010

Developing objective measures for evaluating and measuring the complexity of design would facilitate (1) empirical studies that require the use of equivalent but different design problems, (2) the development of design curriculums, and (3) the comparison of computer aided design automation tools. This paper surveys and evaluates different approaches to defining complexity in design for the design problem, process, and product. Three fundamental aspects to complexity are identified, size, coupling, and solvability, and expanded with respect to the three elements of design, problem, process, and product. Alternative methods for measuring these characteristics of the design are based on computational, information, and traditional design views of complexity. A method of measuring size as it relates to complexity is proposed for measuring the information content of design. A second method is proposed for decomposing a graph-based representation of design that provides a measure of the interconnectedness as it relates to complexity. Finally, two methods are proposed for determining the solvability complexity of design based on the effort involved and the degree of freedom of design. These measures are developed specifically for parametric and geometric problems as found in the embodiment design, but these principles may be applied beyond this.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Relations between problem, process, and product

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Figure 2

Entity-relationship graph: (a) initial graph and (b) removed unary constraints

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Figure 3

Level 3; set size 2; number sets 4: (a) graph with removed constraints highlighted and (b) resulting graph

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Figure 4

Graph with removed constraints highlighted level 3; set size 2; number sets 4

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