An optimal preventive maintenance scheduling model for deteriorating structures is presented. The random initial damage and the cumulative damages are quantitatively measured with the statistical distribution of a dominant fatigue crack size in the structure. The preventive main tenance for the structure in service is assumed to be possible only at a series of discrete times. By taking into account the costs of structure failure and preventive maintenance, a minimum cost rate criterion is established to determinate the optimal time for preventive maintenance. Finally, an illustrative example i...