Two-dimensional aggregate warranty demand forecasting under sales uncertainty

Capital-intensive products, such as automobiles and heavy equipment, are often sold under a two-dimensional warranty policy considering both age and usage. As the products are sold to customers intermittently, the sales process is usually performed under uncertainty. This stochastic nature presents difficulties in predicting the warranty demand over time. The existing literature on two-dimensional warranty only focuses on warranty demand of a single unit, which overlooks the effect of the sales dynamics on the total warranty claims of sold units. To address this issue, from a new warranty analysis perspective, this study develops a general forecasting technique for the aggregate repair demand of all units sold up to a given time period. The stochastic sales process is modeled by a non-homogeneous Poisson process, and the product failures are captured by a two-dimensional failure process with minimal repair. When the first time-to-failure follows a bivariate exponential distribution, the expected aggregate repair demand for a given period of time is derived in an analytical form. Numerical experiments are presented to show the applicability and flexibility of our model in estimating the warranty demands with time-varying sales processes.