Abstract: A multi-type branching diffusion process with fast transmutations between particles are considered in this paper. The first moment equations for the process are reaction–diffusion equations. As the inverse transmutation rate approaches 0, we derive an averaging principle for these reaction–diffusion equations.
Abstract: With the increasing of system scale and the growing of functional requirements and interactions within and/or among system hierarchies, there are more difficulties for safety engineers to carry out their works. Especially, the research on phased mission system (PMS) with probabilistic common cause failures (PCCFs) is still in the initial stage and has a lot of limitations, because the current researches have not yet considered the dynamic characteristics of PMSs. In this paper, a modular method is proposed as the theoretical basis to construct the components model in the PMS with PCCF. The relationships between common cause events were discussed…and the probabilistic model of CCFs is extended, so that the model can fit for different statistical relations, and a module-based modeling and analysis method using binary decision diagram (BDD) and Markov model were proposed to deal with static and dynamic module in PMS respectively. Moreover, a standardization of description method for modular method using extensible markup language (XML) is given, based on which the system reliability model can be constructed by computer aided. Finally, the proposed method is demonstrated through a case study.
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Keywords: Probabilistic common cause failure, phased-mission system, Markov method, XML, standardization, automatic generation of model