An item undergoes cumulative damage through use. The item fails randomly but the failure rate depends on the accumulated damage. The item is preventively replaced if it survives a certain damage limit at periodic inspections; on failure, it is replaced immediately. The optimal damage limit for preventive replacement which minimizes the long-run expected cost rate is derived. It is unique if an item has increasing damage-dependent failure rate. Numerical example for a stationary gamma process with Weibull distributed failure is given. Copyright (C) 1996 Elsevier Science Ltd.