Reliability analysis of system with timing functional dependency using fuzzy-bathtub failure rates

Dependency among system elements impress the system performance and efficiency, thus dependencies have to be modeled and analyzed. The aim of this paper is introducing and studying a specified dependence in reliability analysis of fault trees with dynamic dependencies; named Timing Functional Dependency (TFDEP) gate. In most systems with functional dependency constructions equipped with known FDEP gate, event failures occur in particular order and their dependencies are only usual and sequentially without any time considerations. However, in some specific systems, the events in addition to the predefined order, are also time-dependent and for each occurrence, a specific event’s activation/deactivation time should be considered. This timing requirement necessitates inventing a new TFDEP gate. On the other hand, in order to exact simulation, the Fuzzy-bathtub distributions are used as the time-to-failure parameter and Fuzzy Monte Carlo technique throughout the predetermined operating time is considered to the simulation process. Finally, the proposed approach is implemented in an air/space system as an application example and the simulation results demonstrated that the presented technique is a valid approach in the analysis of system reliability with timing dependencies and events that have unknown failure occurrence probabilities.