‎We propose an extended two-dimensional warranty policy that combines a renewing free-replacement warranty with a limited number of repairs during the warranty period‎. ‎The system is assumed to experience two types of failures‎: ‎type-I failures‎, ‎which are repairable through minimal repair‎, ‎and type-II failures‎, ‎which are non-repairable or catastrophic and require replacement‎. ‎In the proposed warranty scheme‎, ‎type-II failures are covered by a renewing free-replacement policy during the initial warranty period‎, ‎while type-I failures are subject to an upper limit on the number of allowable occurrences‎. ‎If the number of type-I failures remains below this threshold‎, ‎the warranty is extended up to a predetermined time horizon‎. ‎To identify the optimal warranty strategy‎, ‎an expected total cost function, incorporating the sale price function, is developed as the model\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'s objective function‎. ‎Numerical and graphical analyses are conducted under the assumption that the system lifetime follows a Weibull distribution‎. ‎Finally‎, ‎the applicability of the proposed policy is demonstrated using two real data sets‎.

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