Concurrent Modeling Of Positive And Negative Dependencies In The Design Structure Matrix Using Complex Numbers

Abstract

The complexity of an engineering product is based in part on the number of components and their dependencies, where the latter can be desired or undesired. In some cases, where those dependencies exist concurrently, engineers can be misled regarding the design challenge at hand due to ill-adapted representation methods, especially when managing various abstraction levels. To overcome this issue, a new modeling method to concurrently handle positive and negative dependencies is proposed. This paper suggests modeling the dependencies using a complex number notation within a design structure matrix. Using the proposed representation to simultaneously model positive and negative dependencies, shown through an illustrative example, it is possible to differentiate and make use of more information when dealing with different abstraction levels. Finally, the paper discusses implications related to using the modeling method regarding the system analysis.