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This paper investigates the effects of an imperfect renewing free-replacement warranty (RFRW) on the classical age-replacement policy for a product with an increasing failure rate. Under the imperfect RFRW, whenever a product fails during the warranty period, it is replaced by a repaired one from an infinite stock of refurbished items, at no cost to the purchaser, with a new full warranty. We assume that the failure potential of the repaired product is inferior to that of a new product; that is, the repaired product is less reliable than a new one. Long-run expected cost rates for the age-replacement policy are developed for two cases: when the preventive replacement age occurs before, and when it occurs after the warranty expires. The optimal replacement ages that minimize the cost rates are determined, and the impact of an imperfect RFRW on the optimal replacement age is illustrated with a numerical example. We review the literature dealing with warranty and maintenance against this framework, and conclude with some discussions on topics for research in the future. The imperfect RFRW proposed in this paper is practical, and novel; and this study represents a useful extension of Yeh that promises to be of interest to reliability engineers, managers, and theoreticians.