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This paper presents the effects of a renewing free-replacement warranty (RFRW) on the age-replacement policy in a discrete time process. Consider a product that should be operating over an indefinitely long operation cycle n (n=1,2,...); under the discrete age-replacement policy, a product is replaced at cycle N (N=1,2,...) after its installation, or at failure, whichever occurs first. The cost models from the customer's perspective are developed for both warranted, and non-warranted products. The corresponding optimal replacement age N* (i.e., the optimal number of operation cycles for a preventive replacement) is derived such that the long-run expected cost rate is minimized. Under the assumption of the discrete time increasing failure rate, the existence and uniqueness of the optimal N* are shown, and the impacts of a RFRW on the optimal replacement policies are investigated analytically. The optimal N* for a warranted product is closer to the end of the warranty period than for a non-warranted product. Finally, a numerical example is demonstrated for the optimal policy illustration and verification. The observations from the technical analysis and numerical results provide valuable information for a buyer (user) to adjust the optimal age-replacement policy if a product is operating in discrete time under a RFRW.