Competing failure analysis in phased-mission systems with functional dependence in one of phases

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This paper proposes an algorithm for the reliability analysis of non-repairable phased-mission systems (PMS) subject to competing failure propagation and isolation effects. A failure originating from a system component which causes extensive damage to other system components is a propagated failure. When the propagated failure affects all the system components, causing the entire system failure, a propagated failure with global effect (PFGE) is said to occur. However, the failure propagation can be isolated in systems subject to functional dependence (FDEP) behavior, where the failure of a component (referred to as trigger component) causes some other components (referred to as dependent components) to become inaccessible or unusable (isolated from the system), and thus further failures from these dependent components have no effect on the system failure behavior. On the other hand, if any PFGE from dependent components occurs before the trigger failure, the failure propagation effect takes place, causing the overall system failure. In summary, there are two distinct consequences of a PFGE due to the competition between the failure isolation and failure propagation effects in the time domain. Existing works on such competing failures focus only on single-phase systems. However, many real-world systems are phased-mission systems (PMS), which involve multiple, consecutive and non-overlapping phases of operations or tasks. Consideration of competing failures for PMS is a challenging and difficult task because PMS exhibit dynamics in the system configuration and component behavior as well as statistical dependencies across phases for a given component. This paper proposes a combinatorial method to address the competing failure effects in the reliability analysis of binary non-repairable PMS. The proposed method is verified using a Markov-based method through a numerical example. Different from the Markov-based approach that is limited to exponential distribution, the proposed approach has no limitation on the type of time-to-failure distributions for the system components. A case study is given to illustrate such advantage of the proposed method.