A graph theory approach to predicting functional failure propagation during conceptual systems design

An open area of research for complex, cyber-physical systems is how to adequately support decision making using reliability and failure data early in the systems engineering process. Having meaningful reliability and failure data available early offers information to decision makers at a point in the design process where decisions have a high impact to cost ratio. When applied to conceptual system design, widely used methods such as probabilistic risk analysis (PRA) and failure modes effects and criticality analysis (FMECA) are limited by the availability of data and often rely on detailed representations of the system. Further, existing methods for system reliability and failure methods have not addressed failure propagation in conceptual system design prior to selecting candidate architectures. Consideration given to failure propagation primarily focuses on the basic representation where failures propagate forward. In order to address the shortcomings of existing reliability and failure methods, this paper presents the function failure propagation potential methodology (FFPPM) to formalize the types of failure propagation and quantify failure propagation potential for complex, cyber-physical systems during the conceptual stage of system design. Graph theory is leveraged to model and quantify the connectedness of the functional block diagram (FBD) to develop the metrics used in FFPPM. The FFPPM metrics include (i) the summation of the reachability matrix, (ii) the summation of the number of paths between nodes (i.e., functions) i and j for all i and j, and (iii) the degree and degree distribution. In plain English, these metrics quantify the reachability between functions in the graph, the number of paths between functions, and the connectedness of each node. The FFPPM metrics can then be used to make candidate architecture selection decisions and be used as early indicators for risk. The unique contribution of this research is to quantify failure propagation potential during conceptual system design of complex, cyber-physical systems prior to selecting candidate architectures. FFPPM has been demonstrated using the example of an emergency core cooling system (ECCS) system in a pressurized water reactor (PWR).