## Node Maps in Engineering Design Complexity Metrics

In engineering, the ability to objectively measure a design or product’s complexity has been long sought after. In their paper, Summers and Shah divide the measurement into three metrics: size, solvability, and coupling. The more complex a design, the larger it is, the more difficult it is to solve, and the more interconnected the components are. To determine the interconnectivity of a design, a node map may be employed.

Sosa, Eppinger, and Rowles present an easy to visualize method for determining component dependencies. Here, the nodes are a product’s components, with the edges dependencies between them. For instance, if the product were a car, the gas tank might form an edge with the engine but maybe not the backseat cup holder. From here, “clusters” of components are formed. These clusters are characterized by closely-connected dependencies within the group of components with more loosely-connected dependencies connecting to other clusters (think you and your high school friends on Facebook vs you and your college friends).  When all components and dependencies have been graphed and clustered, the resulting node map can be used to get an empirical sense of the complexity of a product. It is argued that the more clusters that are observed the less dependent and interconnected the components of the product are. More clusters = less interconnected = less complex. Sosa, et al. continue to describe numeric methods for defining the lack of connectivity (or “modularity”) of a system of components. These methods delve into more advanced graph theory, well beyond the scope of this class.

Summers and Shah present a similar method for determining the “coupling” metric of complexity. They offer up alternative equivalences for nodes and edges (e.g. tasks as nodes with dependencies as edges), but the method for determining interconnectivity mirrors that of Sosa, et al.: measure how decomposable the graph is. This method results in one numerical metric for connectivity. Relations are removed so that disjoint graphs are created, and a running score is kept for the system with points based on the levels and number of relations needed to be removed at that particular level to end up with disjoint graphs. Higher score = more complex.

Knowing levels of complexity for designs is hugely important when making decisions in industry and research. It’s always good to know what you’re getting into before starting to manufacture a jet engine. Through the use of node maps and networks, products and designs are able to objectively be measured for complexity.

Sources:

Summers, J. D. and J. J. Shah (2010). “Mechanical engineering design complexity metrics: size, coupling, and solvability.” Journal of Mechanical Design 132(2): 021004.

Sosa, M. E., Eppinger, S. D., and Rowles, C. M., 2007, “A Network Approach to Define Modularity of Components in Complex Products,” ASME J. Mech. Des., 12911, pp. 1118–1129.