Two-dimensional aggregate warranty demand forecasting under sales uncertainty
针对资本密集型产品在二维保修政策下销售过程的不确定性，提出一种聚合维修需求预测方法，用非齐次泊松过程模拟销售，双变量指数分布刻画故障，推导出给定时间段内期望聚合维修需求的解析式。
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.