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In the present academic and engineering fields, every measure function of product reliability is modeled and estimated from the statistical perspective. These indicate that there universally exist differences in the reliabilities of new identical products that survive the burn-in test. On the basis of the differences in the reliabilities of new identical products, designing through-life maintenance models for managing the different reliabilities is a very practical topic for engineering fields. In this study, a random warranty model and a random maintenance model are designed by screening product reliabilities to manage the through-life reliabilities of products. In the random warranty model, the coverage areas of the warranty are set as the different areas for applying flexibility to them to control the warranty costs of new identical products with different reliabilities, and thus this warranty is called a flexible random free repair warranty (FRFRW) model. In the random maintenance model, two random replacement actions are customized by setting different replacement ranges for controlling maintenance costs and lengthening service life. This random maintenance model is called a customized random replacement (CRR), which is used to manage product reliabilities after the FRFRW expiration. These two random models are characterized from the mathematical perspective, and some derivatives of both are provided to model other maintenance problems. The characteristics of every model and the performance of the CRR are explored and illustrated through numerical experiments. The results show that the CRR is superior to random age replacement.

With the help of advanced digital technologies, product managers can use monitored mission cycles to sustain product reliability. In this study, a random warranty model and a random replacement next (RRN) model are designed to sustain the through-life reliability of the product with monitored mission cycles. The designed random warranty, called a two-stage two-dimensional free repair warranty (2DFRW), can be carried out to sustain the reliability of the product during the warranty stage. In this warranty, ‘whichever occurs first and last’ is used to distinguish the coverage ranges of the latter stage warranties, which is to maintain the warranty fairness by removing the inequity of the former stage warranty. The RRN can be performed to sustain post-warranty reliability, which defines that if the limited number of mission cycles is completed before a working time, then the product will be replaced at next mission cycle completion to extend remaining service life; otherwise, the product will be replaced at a working time. Under the case of the two-stage 2DFRW, the cost rate of the RRN is constructed based on the renewable reward theorem. By simplifying the parameters, some derivative models of the cost rate are presented. Numerical analysis is performed to explore characteristics.