基于PH分布的n中取k系统可靠性模型研究

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.

The reliability analysis of k-out-of-n system based on Phase-type distribution

This research investigates a k-out-of-n system in which the operational, standby and repair time of units follow continuous Phase-type distribution, instead of exponential distribution or other typical distributions. The proposed model provides an analytic reliability model that is more suitable to characterize the real situation. The stationary distribution is built by using matrix analytic methods; and several performance measures of interest, such as the system stationary availability, operational time, mean time between failures (MTBF) and failure arrival rate, are obtained. Finally, the validity and applicability of the model are implemented by numerical applications; and the influences of k on the system reliability laws are demonstrated when the value of n is fixed.