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Complexity Measure for Engineering Systems Incorporating System States and Behavior

Complex engineering systems have structures characterized by a large number of components, interconnections, and elaborated configurations. Time-dependent functionality and multiple system states defy accurate predictions of complex systems behavior. Although many measures exist to quantify complexity, most of them consider either structure or function only. States and behavior are critical aspects to consider simultaneously with structure and function when assessing the complexity of modern systems as all of them have a profound impact on system design and future system performance. A more complete understanding of system complexity could improve the accuracy of scheduling and cost estimates during system development. This article proposes an objective, dynamic, and comprehensive complexity measure derived from molecular quantum mechanics and signal processing principles to quantify engineering system complexity. The proposed measure formalizes complexity as a single quantifiable system property that incorporates structure, functionality, and behavior, enabling unbiased comparisons of different conceptual designs, identification of complex elements, and analysis of complexity management. It provides systems architects and systems engineers with a strong basis for evaluating and communicating complexity during system design and architectural modeling. The formulation of the measure and methodology to calculate system complexity is illustrated through test cases using model-based systems engineering.