This thesis deals with a preventive maintenance model for the item whose failure is dependent only on its wear level being checked periodically. In the previous failure models, shocks occur to the item discretely in time. Each shock causes a random wear to the item and these wears accumulate additively, and the item fails when the cumulative wear first exceeds a certain limit. In this model, the wears are considered as accumulated continuously in time. It is assumed that an item will be replaced before failure when the wear has reached some threshold value during periodic inspection or at failure, whichever occurs first. It is also assumed that an item is subject to wear occuring randomly in time as a gamma process. The optimal replacement level which minimizes the expected cost rate for an infinite time span is obtained by the sense of renewal theory.
