Nowadays, to protect the interests of customers, quite a few warranted products are sold with some kinds of repair thresholds. For example, a mobile phone manufacturer may provide a replacement service if the phone sold still cannot work after several repair attempts or the cumulative repair time reaches 7 days or 1 month. Motivated by this observation, we study a non-renewing replacement warranty policy with a repair number threshold and a repair time threshold, in which the manufacturer has responsibility for replacing a product when the number of failures is beyond the repair number threshold or the cumulative repair time reaches the repair time threshold, whichever occurs first. In addition, an age-based post -warranty maintenance strategy is developed for the non-renewing replacement warranted product, which provides a lower cost rate than the existing ones. Based on the indicator function method and renewal process theory, we derive the product's life cycle cost rate. Finally, considerable numerical experiments are carried out to show the influences of various parameters on the proposed maintenance strategy.& COPY; 2023 Elsevier B.V. All rights reserved.