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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. [ABSTRACT FROM AUTHOR]

Fault tree analysis is one of the most useful techniques in reliability analysis of multistate systems that analyze and handle complex systems via Monte Carlo simulations or mathematical approaches. Traditional fault tree cannot depict the exact evaluation of components and systems failures with respect to simplex analysis. On the other hand, the exact evaluation of system reliability with unknown data owning to components and elements is still difficult. Therefore, in this paper, in order to overcome this problem as for the quantitative analysis of fault trees, the reliability analysis of a multistate system (i.e. Launch Emergency Detection System) based on fault tree analysis and fuzzy failure rates is studied. Accordingly, using fuzzy arithmetic, events time-to-failure are generated and then the Top Event time to failure is calculated. Finally, the results of the analytical solution are compared with the results attained by presented approach and shows that, in spite of less effort and time consuming, this method has more accuracy and suitable for all real industrial and complex systems. This paper has further developed the method of FTA for the most generic case where both the system and the components have multiple failure states. [ABSTRACT FROM AUTHOR]