Reliability evaluation of a k-out-of-n(G)-subsystem based multi-state phased mission system with common bus performance sharing subjected to common cause failures

Multi-state phased mission systems (MS-PMSs) with common bus performance sharing widely exist in practice. Their subsystems are often designed as redundant k-out-of-n(G) systems to ensure the reliable operation of the whole system, such as power generating systems. However, common cause failures (CCFs) of components can decrease the reliability of such redundant subsystems. Considering the above two factors, we propose a new reliability model for the MS-PMS with k-out-of-n(G) subsystems and performance sharing subject to CCFs. Each subsystem contains multiple multi-state components, whose behaviors are analyzed using the Markov chain. Components in each subsystem may belong to a CCF group, and each CCF group suffers multiple independent CCF modes. We propose a Binary Indicator Universal Generating Function (BIUGF) method to evaluate the system reliability by adding an indicator variable and a pointer vector in the traditional universal generating function method, and the impacts of CCFs are taken into account using an implicit analysis method. The method is illustrated and validated through applications to power supply systems, which justify the effectiveness of the proposed method.