具有两种失效状态的δ-冲击模型的最优维修策略

针对在运行过程中不断受到冲击且有两种失效状态的系统,提出了一种新的δ-冲击模型.系统在工作过程中不断受到冲击,冲击的到达服从泊松过程,系统发生故障可能有两种原因,一种是由于系统的自然寿命,另一种是冲击造成的.系统逐次故障后的维修时间形成随机递增的几何过程,且逐次维修后的工作时间形成随机递减的几何过程,以系统进行更换前的故障次数N为策略,利用更新过程和几何过程理论求出了系统经长期运行单位时间内期望费用的表达式,并给出了具体例子和数值分析.

Optimal maintenance policy for the δ-shock model which has two types of failures

In this paper, the δ-shock model which has two types of failures is studied, the system suffers shocks in working time, the shocks arrive according to a Poisson process. The failures of the system on the one hand is because of the lifetime of the system, on the other hand is because of the shocks. The successive survival times of the system form a stochastically decreasing geometric process and the consecutive repair times after system failures form a stochastically increasing geometric process, we consider replacement policies N, based on the failure number of the system before replacement. By using the renewal process theory and geometric process theory, the explicit expression of the long-run expected cost per unit time is derived. Finally, a numerical example is given.