# Mathematical reliability model for failure cause analysis of a system with separated derating redundancy

## Abstract

The mathematical reliability model of a repairable system with a separate derating redundancy for the failure causes analysis of such a system is proposed. The model is formed in three stages. An the first stage, the system reliability is mathematically described by a dynamic fault tree, whose main feature is that its logic blocks define not only the failure condition of a system, but also the conditions for load-sharing between the components. At the second stage, based on the dynamic fault tree, the mathematical model of the state and transition graph of the system is constructed and analyzed. At the third stage, the graph model based on the tensor analysis is transformed to a split homogeneous Markov model. According to the calculation results, the probability characteristics of the minimal cut set are determined and the most likely system failure cause is recognized. It is shown that with increasing the duration of usage, the most likely system failure cause changes. Such a behavior of system reliability indices is due to the impact of load-sharing between components whose lives have Weibull distribution.## References

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