This study considers an item that can be operated over an indefinitely long run operation cycle n (n = 1, 2, 3, …), where each operation period causes a random amount of damage to the item, where the damage is accumulated over time, and where the item fails when the cumulated damage/wear exceeds a failure level ξ₀. For such an item, a warranty policy in a discrete-time form is considered. It is suggested that the discrete-type warranty policy that consists of a renewable free-replacement and one-inspection service can increase the probability of warranty success and decrease the costs due to the warranty contract. Under such a warranty policy, with a coverage period of N, items from a mixed population are inspected at an intermediate operation cycle M (< N), and if the observed level of the cumulated damage/wear exceeds the predetermined value ξ (< ξ₀), it is screened out and replaced by a new one and the warranty is renewed, without any cost to the customer. Probabilistic and cost analyses of the model are performed, the optimal ξ* and M* that minimize the warranty costs are calculated, and illustrative examples are presented and discussed.

本研究考虑了一个可以在无限长的运行周期n ( n  = 1, 2, 3, ...) 中运行的项目，其中每个运行周期都会对该项目造成随机数量的损坏，其中损坏随着时间的推移而累积，以及当累积损坏/磨损超过故障级别 ξ ₀时，该项目发生故障。对于此类项目，应考虑离散时间形式的保修政策。建议由可续期免费更换和一次检查服务组成的离散型保修政策可以增加保修成功的可能性并降低由于保修合同而产生的成本。在这样的保修政策下，保修期为N，来自混合总体的项目在中间操作周期M (< N )进行检查，如果观察到的累积损坏/磨损水平超过预定值 ξ (< ξ ₀ )，则将其筛选出来并由新的替换一并更新保修，客户无需支付任何费用。对该模型进行了概率和成本分析，计算了使保修成本最小化的最佳 ξ* 和M *，并给出和讨论了说明性示例。