System reliability under cascading failure models with different load effect modes

Cascading failure is a phenomenon that minor disturbances trigger a chain reaction failure of the system, causing the disaster to quickly spread in the system and causing part or all of the system to collapse. Traditional cascading models that based on the assumption that the propagation time of cascading failures can be ignored are inadequate for modeling and analyzing all the practical cascading failure systems. It is necessary to develop a general methodology for the cascading failure systems with cascading failure propagation speed and different load effects. This paper derives new models which extend the load effect mode and consider the propagation speed of cascading failure. In the models, the time of the cascading failure propagation is considered. Three load effect modes are proposed that consider the number of remaining working components, the influence range of the failed parts, and the distance between the failed parts and the unfailed components. Additionally, the reliability of the systems with different types of cascading failures is analyzed, and formulas computing reliability indexes are derived. Numerical examples are provided to demonstrate the application of the proposed methodology.