This paper is deals with the preventive replacement for the equipment which fails only when the total amount of damage reaches a prespecified failure level. Most of replacement model use time as their decision variable, but it is not appropriate for the cases in which failures dependent on their cumulative damage levels. In this paper, a new type preventive replacement model is introduced in which an equipment is replaced before failure when the cumulative damage reaches a certain level or replaced on failure, whichever occures first. The optimal replacement damage levels which minimize total expected cost are obtained by the Dynamic programming Method when the number of use of the equipment is finite. A numerical example is also presented. The optimal preventive replacement policy when the equipment will be used for a finite time span is also discussed.