Calculating the Reserve for a Time and Usage Indexed Warranty

Many products carry a warranty that offers protection for the consumer against low quality. These warranties are often two dimensional, such as an automobile warranty that guarantees repair up to a certain time and mileage after sale. This paper considers the problem of assessing the size of a reserve needed by the manufacturer to meet future claims for such a two-dimensional warranty. To do this, a class of failure models that describe failure by two scales—time and mileage, for example—must be developed. The first half of the paper is devoted to this development. Then the warranty reserve problem is considered in more detail. The problem is described and a decision-theoretic solution, making use of the newly developed reliability model, is proposed.