Two-dimensional failure-free warranty policies: Two-dimensional point process models

A two-dimensional warranty policy is characterized by a region in a two-dimensional plane with the horizontal axis representing time and the vertical axis the usage. In this paper, we study two-dimensional failure-free warranty policies for nonrepairable items that require the manufacturer to replace all items which fail under warranty by new ones at no cost to the buyer. We derive expressions for the expected warranty cost per item sold and for the expected life cycle cost for four different warranty regions. We illustrate these by numerical examples and discuss some resulting implications for the consumer and the manufacturer.