Abstract： An orderreplacement model was developed for a repairable deteriorating system. The policy N was adopted where the system would be replaced after the the Nth failure and the spare system was ordered at the end of the (N-1)th failure. The deterioration process of the system was modeled by the delayed geometric process. The longrun average availability and the average cost rate were derived by using the renewal reward theory. The optimal policy was obtained under the premise of meeting the availability requirement. Finally, a numerical example was given to illustrate the proposed model.