δ-冲击模型及其最优更换策略  

δ-Shock Model and the Optimal Replacement Policy

作　　者：王冠军[1] 张元林[1] 

机构地区：[1]东南大学应用数学系,南京210096

出　　处：《东南大学学报（自然科学版）》2001年第5期121-124,共4页Journal of Southeast University：Natural Science Edition

摘　　要：讨论了一种特殊的冲击模型———δ冲击模型 ,在Poisson冲击流下 ,给出了单部件系统的一些可靠性指标 :系统可靠度函数和首次故障前平均时间 .进一步 ,假定系统是可修的 ,逐次故障后的维修时间构成随机递增的几何过程 ,而逐次维修后的系统性能指标成比例劣化 ,相应系统工作时间是按一定方式随机递减 .我们以系统故障次数N为策略 ,以长期运行单位时间内的期望费用为目标函数 ,导出了目标函数的解析表达式C(N) ,并通过最小化目标函数C(N) ,找到几何维修下可靠性系统的最优更换策略N .A special kind of shock model named δ -shock model is studied. The reliability function and the mean time to first failure of the system under δ -shock model are deduced. Furthermore, we assume that the system is repairable, but the system cannot be 'as good as new' after repair. The successive survival time of the system after repair decrease stochastically, while the consecutive repair time of the system constitute an increasing geometric process. The problem is to determine the optimal replacement policy N * such that the long-run average cost per unit time is minimized. The explicit expression of the long-run average cost per unit time C(N) is derived, and the corresponding optimal replacement policy N * can be determined analytically or numerically.

关 键 词：Δ-冲击模型 可靠度函 几何过程 最优更换策略 可靠性 系统故障 目标函数 寿命分布 

分 类 号：O213.2[理学—概率论与数理统计]