A Markov perspective on system-of-systems complexity

The development and acquisition of complex systems remains a challenge, especially in the aerospace/defense sector, due to complexities in both program management and engineering design. The interdependencies between component systems form networks that, while enabling capabilities that are beyond those of individual systems, also increase system complexity and risk since disruptions in the development of one system may propagate to other directly or indirectly dependent systems. This paper presents an approach to measure the complexity of networks in the context of system development time. Development disruption propagation is modeled as a Markov chain, where the states are defined as the constituent systems and the transition probabilities as the interdependency characteristics of systems. A proof-of-concept application shows the approach can distinguish between alternate networks and indicates its applicability for managing risk in design and development of systems with significant interdependencies.