6.4 Universal Generating Function–Based Method
This section presents a universal generating function (u‐function) based approach for the reliability analysis of nonrepairable series‐parallel systems with CCFs caused by propagation of failures of system components. The failure propagation may have selective effects, meaning that CCFs originating from different components can cause failures of different subsets of system components [21]. Moreover, the failure propagation can take time to take effect. For example, infection, fire, or corrosion takes time to propagate; some component failures cause factors (e.g. overheating or humidity) that affect other components, but not immediately [22]. In this section, the failure propagation time is assumed to be a random value following a certain given distribution. The set of components that can generate CCFs and the set of components affected by the CCFs are disjoint. Also, any system component can be affected by at most one...