Abstract: Warranty provides assurance to customers that manufacturers will provide compensation, through repair, replacement or refund, for purchased items that do not perform satisfactorily. To cope with the fierce market competition, attract and hold on customers, manufacturers usually promise to provide long-term and high-quality warranty services, which will entail an additional costto them. Maintenances play an important role in keeping products' performance and making sound decisions on maintenance strategies is an effective way of reducing warranty service costs. In industrial engineering, most products degrade gradually and operate at a lower performance level before complete failure. With the rapid development of computer-based monitoring technologies, condition-based maintenance has been widely used in reliability management and proven effective and economicalin reducing maintenance cost. Furthermore, over a period before the expiration of warranty period, the purpose of the manufacturer's maintenance activities is keeping the operation of the product, instead of improving it. Motivated by the aforementioned engineering practice, this paper focuses on products whose life can be divided into normal and defective stages and proposes an inspection and imperfect condition-based maintenance policy with residual warranty time threshold. Under the policy, the warranty period is divided into two stages: the inspection and preventive maintenance period and the residual warranty period. Over the inspection and preventive maintenance period, periodic inspections are carried outand periodic and imperfect maintenance activities will be performed if the product is identified to be in defective stage. Failures between two successive inspections are rectified using minimal repair. Over the residual warranty period, inspections are not performed and all failures are restored minimally.The virtual age model is used to quantify the level of imperfect maintenance activities. Two cases depending on whether imperfect maintenance activities are performed are discussed. The probabilities and the expected warranty costs for these two cases are derived by probability analysis method and based on them the average warranty cost over the whole warranty period can be obtained. To illustrate the effectiveness of the proposed policy, two comparison modelsare established. Under the first one, inspection and preventive maintenance activities are not performed and the remaining warranty period is not considered. Inspection and preventive maintenance activitiesare performed and the remaining warranty period is also not considered under the second model. Numerical examplesare given to demonstrate the application of the model. From the manufacturer's perspective, the inspection interval, the level of imperfect maintenance activities and the length of residual warranty period are optimized jointly such that the average warranty cost over the whole warranty period is minimized. The results of the numerical examples and contrastive analysis show that the joint optimization cansignifi can tly reduce the cost. The research can throw light on the warranty decision of complex and expensive products.In the current model, failures caused by performance degradations are considered. However, most products are subject to degradation and random shocks simultaneously. Warranty services aiming at external shockshave emerged, such as the “Protection Plus Mobile Elite”launched by Samsung, “iPhone Apple Care+” offered by Apple and so on.We can discuss the condition based warranty decision making for products that experience both degradations and external shocks. The decision analysis in this paper is made from the perspective of manufacturers. For future researches, warranty decision research based on game theory, which may balance the interests between producers and customers, are also worth discussing.

Key words: condition-based maintenance, warranty, inspection, imperfect maintenance, delay time, residual warranty time threshold

摘要： 针对退化服从两阶段故障过程的保修非更新产品,提出了有剩余保修时间阈值的非完美视情维修策略。在该策略下,产品保修期分为两阶段:检测预防维修期和最小维修期。在检测预防维修期内,针对检测时刻系统的状态(正常和缺陷)实施不同的维修策略。在最小维修期内,不进行检测,对发生的故障实施最小维修。以生产商承担的平均保修费用为目标函数,对检测间隔、预防维修水平及剩余保修时间阈值进行了联合优化。通过数值算例及对比分析验证了模型的有效性。

关键词: 视情维修, 保修, 检测, 非完美维修, 延迟时间, 剩余保修时间阈值