Date of Award


Document Type


Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering

Committee Chair/Advisor

Summers, Joshua D

Committee Member

Mocko , Gregory M

Committee Member

Goddard , Wayne D


Complexity is an aspect of engineering design that is often addressed directly with the principle that 'designs should be simple'. However, such a principle fails to offer an effective means of quantifying the complexity of a given design for comparison and decision making. The measurement of complexity within a specific representations and domains has been well established. However, such measurements are inherently limited in their applicability and not always clear in their implications. This research presents a method of measuring complexity from different engineering representations in a consistent manner and explores the application of these measures.
The development of a measurement method has suggested that complexity is the effort required to understand a given system and that this effort is based on a collection of attributes rather than a single value. These attributes are derived from graph-based representations and are divided into classes of size, interconnection, centrality, and decomposition. Each of these classes contains two measurement subtypes composed of multiple metrics each for a total of 29 dimensions of complexity. While this set is not exhaustive, it is considered to be sufficient for application.
These complexity measurements are used in three application cases. The first of these cases applies complexity measurement to product connectivity graphs and establishes a model mapping these measurements to assembly time. The variability of the model are within one standard deviation of that observed between different designers conducting the same assembly time analysis. This demonstrates that it is possible to use complexity metrics as a surrogate mapping to design performance measures.
The second application case addresses function structures and product market value. Complexity measurements are used as the input to neural networks to develop a mapping which gives a predicted probability density function over a range of market values. This mapping is shown to be accurate, while the precision is limited to the general product range due to a limited training set size. The success of this approach suggests that a formalized method to establishing complexity mappings can be established.
The final application case develops a protocol for capturing the connective information in a design process. This protocol uses email, meeting minutes, and engineering documents to create a temporal hypergraph representation of the process. The application of complexity measurements to the data created by this protocol shows the ability to identify design process properties such as work habits, group dynamics, and critical points. (9116 kB) (6165 kB)
JMATHIE_MS_Defense.pptx (4095 kB)



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