In the preventive replacement policies of system that the failure can be detected through only periodic inspection, there is a penalty cost associated with the lapsed time between system failure and its detection. The system under study is replaced if the system fails before $n^{th}$ inspection, otherwise, preventive replacement is performed at the $n^{th}$ inspection. The decision variables are the inspection interval and the period of preventive replacement. This study presents the optimal preventive replacement policy that minimizes the long-run expected cost per unit time.