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本文以n中取k系统为研究对象,采用Phase-type(PH)分布代替指数分布等典型分布,假设部件在工作状态、储备状态和维修状态停留时间均为连续时间PH分布;建立了一种描述能力更强的系统可靠性解析模型,利用矩阵解析方法获得了系统稳态概率,推导出系统稳态可用度、工作时间、平均故障间隔时间和维修台故障件到达率的解析表达式;并通过算例验证了模型的正确性和适用性,演示了给定n值后,k值变化对系统可靠性规律的影响.
In this paper, we take the n-k system as the research object, and use the Phase-type (PH) distribution instead of the typical distribution such as the exponential distribution. Assuming that the part residence time in the working state, the reserve state and the maintenance state are the continuous-time PH distributions, Describing a more robust system reliability analysis model, using the matrix analysis method to obtain the steady-state probability of the system, and deriving the analytic expression of the system steady-state availability, working time, mean time between failures and arrival rate of the fault on the maintenance station; An example is given to verify the correctness and applicability of the model. The effect of the change of k value on the reliability of the system after a given value of n is demonstrated.