Universal failure model for multi-unit systems with shared functionality

A Universal Failure Model (UFM) is proposed for complex systems that rely on large number of entities for performing a common function. Economy of scale or other considerations may dictate the need to pool resources for the common purpose, but the resulting strong coupling precludes the grouping of those components into modules. Existing system-level failure models rely on modularity for reducing modeling complexity, so the UFM will fill an important gap in constructing efficient system-level models. Conceptually, the UFM resembles cellular automata (CA) infused with realistic failure mechanisms. Components’ behavior is determined based on the balance between their strength (capacity) and their load (demand) share. If the load exceeds the components’ capacity, the component fails and its load share is distributed among its neighbors (possibly with a time delay and load losses). The strength of components can degrade with time if the load exceeds an elastic threshold. The global load (demand) carried by the system can vary over time, with the peak values providing shocks to the system (e.g., wind loads in civil structures, electricity demand, stressful activities to human bodies, or drought in an ecosystem). Unlike the models traditionally studied by CA, the focus of the presented model is on the system reliability, and specifically on the study of time-to-failure distributions, rather than steady-state patterns and average time-to-failure characteristics. In this context, the relationships between the types of failure distributions and the parameters of the failure model are discussed.