We consider imperfect, periodic preventive maintenance of items with increasing failure rates, and minimal repairs in-between. The imperfect maintenance is performed in accordance with a Kijima II virtual age model. The obtained deterministic asymptotic value of virtual age defines the starting age of an item at the beginning of each cycle in the formulated and analyzed long-run optimization problem. A similar approach is used for the corresponding age-based preventive maintenance, where the starting age of the renewal-type cycle is already a random variable. Some meaningful examples are considered.