Warranty data contain useful information on the product reliability, and should be carefully analyzed for deploying an appropriate warranty policy as well as for the improvement of product reliability. For some product, warranty data are two-dimensional. For instance, automobile manufacturers give a warranty on the vehicles in terms of the amount of usage time and mileage. That is, only the vehicle which fails within the time and mileage limits is repaired without any charge to the owner. Analyzing such two-dimensional warranty data is difficult in that censoring occurs due to the time or mileage limit. Therefore, many sophisticated statistical methods have been proposed. However, these statistical methods are usually not capable of dealing with a complicated nonlinear relationship between the product reliability and vehicle's attributes. In this thesis, an approach based on the neural network is developed and is applied to simulated warranty data. The proposed approach is versatile and yields an accurate prediction of the product reliability. It can be also used to predict the product reliability when the warranty limits are expanded. In summary, this thesis shows that the proposed neural network approach is a promising alternative to other statistical methods.