Expected warranty cost of two-attribute free-replacement warranties based on a bivariate exponential distribution

Many warranty policies offered by manufacturers are limited by two factors, typically time since purchase, and usage of the product. Such policies are referred to as two-attribute (or two-dimensional) warranty policies and can be described in terms of regions in a plane with one axis representing time and the other axis the usage. In this paper, we consider two-attribute warranty policies for non-repairable items. The item failures are described in terms of a bivariate exponential distribution. Analytical expressions are derived for the resulting two-dimensional renewal function and the cost of warranty. An illustratve numerical example is presented to study the effect of correlation between the warranty variables on the cost of warranty.