A copula-based approach to modelling the failure process of items under two-dimensional warranty and applications

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.