维修时间受限的单部件系统几何过程维修模型

Geometric process model for a single-unit system with limit repair time

应用几何过程维修理论,研究了一个维修时间受限的单部件系统的最优维修更换策略问题.假定逐次维修后系统工作时间随机递减,逐次维修时间随机递增,分别构成递减和递增的几何过程.系统对维修时间设定一个上限阈值θ,当维修时间超过θ时放弃维修,更换新系统.系统维修N次以后不再维修,下次发生故障时被新系统更换.假定系统工作时间服从一般分布,维修时间服从指数分布,通过分析得到了系统平均可用度、平均故障频度等一些可靠性指标,并给出了系统长期运行平均费用率函数.利用一个数值例子对最优更换策略N*进行了模拟,并分析了维修时间阈值对最优策略的影响.

By applying the geometric process repair theory,the optimal repair replacement policy for a single-unit system with limit repair time is studied.Assume that the operating times of the system after repair decrease stochastically forming a geometric process,while the consecutive repair times constitute an increasing geometric process.An upper threshold θis set for the repair time.If the re-pair is not completed in the given limit repair time θ,the repair is stopped and the system is replaced by a new one.If the system is repaired N times,the system will be replaced at the next failure.As-sume that the working time follows a general distribution,and the repair time is exponentially distrib-uted.Through some analysis,some reliability indices for the system including the average availabili-ty and the average occurrence of failure are obtained.The explicit expression for the long-run aver-age cost rate is also obtained.A numerical example is given to simulate the optimal replacement poli-cy N＊,and the influence of the limit repair time on the optimal replacement policy is also discussed.