Random periodic replacement models after the expiry of 2D-warranty

The rapid development of advanced sensor technologies makes it possible to monitor the working cycle of products, which enables manufacturers to design warranty policies by monitoring working cycle during the warranty period and facilitates consumers to carry out post-warranty maintenance by tracking the post-warranty working cycle. The optimal warranty and maintenance policies considering random working cycles is rarely studied in existing literature. In this article, we make contribution by incorporating the limited number of random working cycle into a warranty term and proposing two types of two-dimensional warranty, which guarantees the product reliability performance by monitoring working cycle during the warranty period. Based on the proposed warranty policy, we further investigate the optimal post-warranty random maintenance policies from consumers' perspective, including the random periodic replacement first and replacement last policies, which enhances the post-warranty reliability by monitoring the post-warranty working cycle. The warranty cost model is established under each proposed warranty policy, and the cost rate is evaluated under each post-warranty random maintenance policy. Some special cases of the established models are provided and discussed. By numerical experiments, we conduct sensitivity analysis of the proposed warranty and post-warranty random maintenance polices.