Discounted and per unit net revenues and costs of product warranty: The case of phase-type lifetimes

In a previously published paper, Mamer studies the expected costs to producers and benefits to consumers of three types of product warranty: the ordinary free replacement warranty, the unlimited free replacement warranty, and the pro-rata warranty. In addition to assuming a random product lifetime, Mamer’s models allow for randomness in consumer re-purchase behavior and for the possibility of an independent damage process acting on products sold under warranty. The criteria for evaluating warranty policies are discounted costs and net revenues over an infinite horizon, and per unit costs and net revenues. In this paper, the authors consider the case of phase-type product lifetimes. Under this assumption, they simplify the computation of the expected cost and revenue functions. Since most distributions can often be represented by phase-type distributions, the present simplifications enhance the applicability of Mamer’s useful yet computationally unwieldy results. For the per-unit-net-revenue criterion, the results supplement those of Mamer’s. There, the authors also establish an interesting relation pertaining to expected net revenues as a function of consumer loyalty. They find that under the per-unit-net-revenue criterion, from the producer’s perspective, repeated purchases by the same customer are not as profitable as would be intuitively conjectured. Such a counter-intuitive relation makes the need for being able to compute various cost and revenue functions more compelling-particularly when lifetimes are not exponential.