A copula-based approach to modelling the failure process of items under two-dimensional warranty and applications
针对现有二维保修预防性维护研究的两个局限（简化年龄与使用量关系、假设对所有产品进行维护都划算），提出基于Copula的方法建模年龄与使用量的关系，推导多产品用户的最优维护策略，并融入维护效果。
Hundreds of scholarly papers on optimisation of preventive maintenance policies for items under warranty have been published in the reliability related literature. They typically have two limitations: they make a simplified assumption on the relationship between age and usage for items under two-dimensional warranty and they assume that it is cost-effective to conduct preventive maintenance (PM) on each sold product item. These assumptions may not reflect the reality. This paper therefore proposes a copula-based approach to modelling the relationship between age and usage of items under two-dimensional (2D) warranty. It investigates the probabilistic properties of the bivariate failure rate functions of age and usage and derives optimal PM policies for users who bought multiple product items. It also proposes approaches to incorporating maintenance effectiveness in bivariate copulas for depicting the dependence between age and usage. A case study and numerical examples are provided to illustrate the findings.