A Graph Theory Approach to Functional Failure Propagation in Early Complex Cyber-Physical Systems (CCPSs)

This paper presents a framework to quantify failure propagation potential for complex, cyber-physical systems (CCPSs) during the conceptual stages of design. This method is referred to as the Function Failure Propagation Potential Methodology (FFPPM). This research is motivated by recent trends in engineering design. As systems become increasingly connected, an open area of research for CCPSs is to move reliability and failure assessments earlier in the engineering design process. This allows practitioners to make decisions at a point in the design process where the decision has a high impact and a low cost. Standard methods are limited by the availability of data and often rely on detailed representations of the system. As such, they have not addressed failure propagation in the functional design prior to selecting candidate architectures. To develop the metrics, graph theory is used to model and quantify the connectedness of the functional block diagram (FBD). These metrics quantify (1) the summation of the reachability matrix and (2) the summation of the number of paths between nodes (functions within system models) i and j for all i and j. From a practical standpoint, these metrics quantify the reachability between functions in the graph and the number of paths between functions defines the failure propagation potential of that failure. The unique contribution of this research is to quantify failure propagation potential during conceptual design prior to selecting candidate architectures. The goal of these metrics is to produce derived system requirements, based on an analysis, that focus on minimizing the impact of failures.