A Systems Complexity-based Assessment of Risk in Acquisition and Development Programs

Abstract

Development and acquisition programs of cyber-physical systems can often encounter cost or schedule overruns due to the complexity of the system. It has been shown that certain amount of system complexity is related to the system functionalities (effective complexity), whereas excessive complexity is related to unnecessary intricacies in the design (apparent complexity). While the former is necessary, the latter can be removed through precise local redesign. One of the major challenges of systems engineering today is the development of tools, quantitative measures, and models for the identification of apparent complexity within the system. This technical report has the goal of presenting our research results during last year on evaluating and measuring the structural complexity of the engineered system, and does it through the analysis of its graph representation. The objective of this research has been to mathematically formulate and manage the relationship between the quantitative complexity level of an acquisition or engineering development program (at any point in lifecycle) and its relationship to the increased actual technical as well as programmatic risk respectively. The use of the concepts of graph energy and other spectral invariant quantities allow for the definition of an innovative complexity metric. This metric can be applied knowing the design of the system, to understand which areas are more in need of redesign so that the apparent complexity can be reduced. Considering the positive correlation between complexity and risk, and complexity and cost, this technical research report presents quantitative measures of the complexity of the system of interest. A set of 12 metrics has been developed and applied to a software system and a defense system of systems. Validation of the metrics has been achieved through human experiments.