A replacement policy for a repairable system with its repairman having multiple vacations

This paper considers a replacement policy for a repairable system with a repairman, who can have multiple vacations. If the system fails and the repairman is on vacation, it will wait for repair until the repairman is available. Assuming that the system can not be repaired “as good as new” and a repair upon failure can be performed immediately with a probability of p, we optimise replacement policy using geometric processes. The explicit expression of the expected cost rate is derived, and the corresponding optimal policy can be determined analytically or numerically. Finally, a numerical example is given to illustrate the theoretical results of the model.