In dealing with post-sale warranties, considering only operating time may not be sufficient because products often deteriorate through usage and over time, which both influence product reliability. A two-dimensional warranty is thus more reasonable in practice for both manufacturers and customers. Periodic preventive maintenance within the warranty term seems more prevalent in practice due to its convenience and operability for manufacturers and consumers. However, increases in product deterioration may cause breakdowns to occur more often, even after periodic preventive maintenance has just been performed. In this study, a two-dimensional warranty policy is examined with consideration of non-periodic preventive maintenance to determine the optimal two-dimensional warranty term with a constraint that the product reliability should be above a certain threshold. A numerical application is provided to demonstrate the effectiveness of the proposed approach, with sensitivity analyses being conducted to investigate the robustness of the derived optimal warranty policy.
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