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