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. [ABSTRACT FROM AUTHOR]