System Reliability Under Cascading Failure Models

Just with the rapid economic developments, the world has become a unity gradually because of the close connection of different industries, which can be called a complex system. And a small disturbance may cause the failure of the whole system by the connection of the units. Cascading failure models have been studied more recently such as for electric power systems, epidemics and interdependent networks.The current paper presents three cascading failure models in the point-view of system reliability based on the normalized CASCADE model, analyzed the outside disturbance and the stop conditions about the cascading failure propagation process. We considered the cascading model system reliability. We assume that the additional load can be transferred to the working components with some velocity not immediately, or the components will not fail immediately if they exceed the thresholds, i.e. there exists a period of time for cascading failures when a component’s load exceeds its threshold.The main section of the paper is to analysis the system reliability about the three modified cascading failure models. The corresponding system reliability indexes are developed including system reliability, expectation lifetimes of systems, distributions of total number of failures, distributions of cascading failure propagation generations, and other related probabilities. Two numerical examples are discussed, compared the differences between the modified cascading failure models and the normalized CASCADE model, and finally the conclusions are summarized, pointing out the future direction about the research on cascading failure.