一般δ-冲击模型及其最优更换策略

General δ-Shock Model and Its Optimal Replacement Policy

本文讨论了一种具有一般δ-冲击的可修系统,我们不仅给出了该系统的一些可靠性指标,如系统的可靠度,系统平均工作时间,系统工作时间的极限分布等,而且对该可修系统的分布性质也进行了研究.在Poisson冲击下,我们证明了该系统的寿命分布是NBU的.在该系统为”修复非新”时,我们利用几何过程考虑了以系统的故障次数N为更换策略,以长期运行单位时间内的期望费用为目标函数,通过目标函数最小化确定了最优更换策略.最后我们给出了一个数值例子.

In this paper, a repairable system with general δ-shock is studied. We not only obtain some reliability indices of the system such as the system reliability, the mean working time of the system, and the limiting distribution of system working time etc. but also study the distribution property. We prove that the system life distribution is NWU under Poisson shock source. Assume that the system after repair is not 'as good as new', by using geometric processes we consider a replacement policy N based on the failure number of the system. The problem is to choose the optimal replacement policy N such that the long-run average cost per unit time is minimized. Finally, a numerical example is given.