Reliability Of Interconnected System Research Based On Copula

Interconnected system is a mainly research object in reliability theory as well as in reliability mathematics. Its importance comes into being for two main reasons, first, it is so practical that it has been widely used in reality; second, the traditional hypotheses of independent components in the system has large gap with the actual state.In the paper, the reliability problems of interconnected system with independent components, and based on relationships among components described by link function in Copula theory, the reliability analysis model is built. Started from the impaired system, through the research of the reliabilities, the average life and the failure rate in an interconnected system with F-G-M function, the paper discusses the relationship between two kinds of average life, respectively with components quadrant dependent and components independent. By examples, it analyses the number of components and the dependence relation to the impact of the average life. Moreover, the Markov repaired system model under Marshall-Olkin copula is further studied.After particularly research, the main results are list as follows:Based on systematic summary of the current studies on reliability system and its development trends, we find that the assumption of dependence among components is insufficient, and this provides a wider thread for the research of reliability system.For the defects in current literature, by systematic study for Copula theory, reliability mathematic, fuzzy math and MATLAB, the author introduces their theory and method into reliability study of interconnected system and provides theoretical evidence for the corresponding research.The main results by particular study include: 1) A systematic study and solution about reliability model of the impaired interconnected system with components FGM dependent, analyses of inf-supremum about the average life of interconnected system, and also a result that can be used to judge the average life is to overestimated or underestimated when the dependent components in system is disposed to be independent for simplicity; 2) Further research about the relationship between the correlation coefficient and the average life in the F-G-M family with identical unit,and also a study for the calculation model of fuzzy system, which is injected with the reliability theory of interconnected system with dependent units; 3) Discussions about the Markov repairable interconnected system reliability model in Marshall-Olkin Copula family, and an application of this model to the repairable parallel system to obtain parallel system repairable model, with the steady-state specification and average specification index also offered.