劣化系统最优维修策略：基于推广累积冲击模型

研究一个遭受累积冲击的劣化系统的最优维修策略. 在系统的工作时间内,任一冲击都将对系统造成损害,其损害效应具有累加性. 当累积冲击损害超过某给定水平时,系统失效. 在每个失效时刻,系统可以维修或者更换. 对一个劣化系统来说,假设引起系统失效的冲击量关于维修次数是几何递减的,并且连续的维修时间构成了一个几何递增过程. 这是一个推广的累积冲击模型,更符合可靠性的客观实际. 采用系统在前N-1次失效后维修,而在第N次失效后被替换的更换策略N,推导了长时间运行后平均费用率的精确表达,并精确地确定了最优维修策略N^*. 最后给出一个数值例子.

Optimal maintenance policy for a deteriorating system based on extended cumulative shock model

The replacement policy for a deteriorating system subject to cumulative shocks is studied. Assume that each shock arriving in the system's operating time can cause a random damage to the system, the damages are additive, and the system fails once the accumulated amount of damages exceeds a prefixed threshold. When a failure occurs, we can repair or replace the system. For such a deteriorating system, we assume that the thresholds are geometrically decreasing in the number of repairs taken, and the consecutive repair times form an increasing geometric process. By adopting the replacement policy N of that the system is maintained after the previous (N-1)th failures and is replaced at the time of the Nth failure, we derive the explicit expression for the long-run average cost rate (ACR), and determine the optimal policy N^* for minimizing the long-run ACR. A numerical example is also given.