Structural Complexity Quantification for Engineered Complex Systems and Implications on System Architecture and Design

Abstract

The complexity of today's highly engineered products is rooted in the interwoven architecture defined by its components and their interactions. Such structures can be viewed as the adjacency matrix of the associated dependency network representing the product architecture. To evaluate a complex system or to compare it to other systems, numerical assessment of its structural complexity is essential. In this paper, we develop a quantitative measure for structural complexity and apply the same to real-world engineered systems like gas turbine engines. It is observed that low topological complexity implies centralized architectures and that higher levels of complexity generally indicate highly distributed architectures. We posit that the development cost varies non-linearly with structural complexity. Empirical evidence of such behavior is presented from the literature and preliminary results from simple experiments involving assembly of simple structures further strengthens our hypothesis. We demonstrate that structural complexity and modularity are not necessarily negatively correlated using a simple example. We further discuss distribution of complexity across the system architecture and its strategic implications for system development efforts.