A new warranty plan combining renewal and a limited number of repair policies

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.