Two-dimensional warranty policy design with the consideration of protection term

Abstract

In practice, car products are sold with 2-dimensional (2D) warranty policies, on which existing literature usually assumes that the products are repaired upon failures throughout the warranty period. However, this is not always the case in real life; for example, car manufacturers may need to replace defective cars during an early period of warranty, when the total time on repairing the failures reaches a specified repair time constraint or the number of repair attempts reaches a specified repair number constraint. Motivated by this, this paper divides a warranty period into two stages: the initial protection term and the subsequent repair stage. During the initial protection term, the manufacturer needs to provide a replacement service when a specified replacement condition is satisfied; while during the subsequent repair stage, the manufacturer should provide repair services upon product failures. Taking the warranty servicing cost into account, a profit model is built. The expected total profit of the product is derived, and the optimal warranty period and product price are designed to maximize the manufacturer’s profit. Finally, numerical experiments on car examples are provided to illustrate the considered warranty policy with protection term.