This paper introduces models for preventive maintenance policies and considers periodic preventive maintenance policy with minimal repair when the failure of system occurs. It is assumed that minimal repairs do not change the failure rate of the system. The failure rate under prevention maintenance received an effect by a previously prevention maintenance and the slope of failure rate increases the model where it considered. Also the start point of failure rate under prevention maintenance considers the degradation of system and that it increases quotient, it assumed. Per unit time it bought an expectation cost from under this prevention maintenance policy. We obtain the optimal periodic time and the number for the periodic preventive maintenance by using Nakagawa''s Algorithm, which minimizes the expected cost per unit time.