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In this paper, a three-state system with preventive maintenance is studied. Assume that the system have one working state and two different failure states. The preventive maintenance is performed as soon as the hazard rate reaches to the critical value 0 r before the system fails. The successive repair times form an increasing geometric process. A generalized replacement policy ( N r , 0 ) is adopted. The explicit expression of the long-run expected cost per unit time is determined. Finally, a numerical example is given where the working time of the system yields a Weibull distribution. The corresponding optimal policycan be determined numerically. We also provide numerically some comparisons with two existing policies. Keywords-geometric process, renewal process, replacement policy, multistate system, preventive maintenance component. Wang [18] presented a more reasonable assumption for a geometric process repair model, that is, they assumed that the interval of the preventive repair depends on the reliability of the system R . The time interval between two preventive repairs is geometrically decreasing with of the failure numbers. Considering that most systems need more