Replacement Warranty Research Articles

Optimal burn-in time under cumulative free replacement warranty

In this paper, optimal burn-in time to minimize the total mean cost, which is the sum of manufacturing cost with burn-in and cumulative warranty-related cost, is studied. When the products with cumulative warranty have high failure rate in the early period (infant mortality period), burn-in procedure is considered to eliminate the early product failures. After burn-in, the posterior product life distribution and the cumulative warranty-related cost are dependent on burn-in time; long burn-in period decreases the warranty-related cost, but it increases the manufacturing cost. The paper provides a methodology to obtain the total mean cost under burn-in and cumulative warranty. Properties of the optimal burn-in time are analyzed here. Numerical examples and sensitivity analysis are used to demonstrate the applicability of the methodology derived in the paper.

On bounds for some optimal policies in reliability

Often in the study of reliability and its applications, the goal is to maximize or minimize certain reliability characteristics or some cost functions. For example, burn-in is a procedure used to improve the quality of products before they are used in the field. A natural question which arises is how long the burn-in procedure should last in order to maximize the mean residual life or the conditional survival probability. In the literature, an upper bound for the optimal burn-in time is obtained by assuming that the underlying distribution of the products has a bathtub-shaped failure rate function; however, no lower bound is available. A similar question arises in studying replacement policy, warranty policy, and inspection models. This article gives a lower bound for the optimal burn-in time, and lower and upper bounds for the optimal replacement and warranty policies, under the same bathtub-shape assumption.

A servicing strategy for items sold under warranty

When repairable items sold under warranty fail, the rectification action taken by the manufacturer can be either a repair or a replacement. In this paper a new repair–replacement strategy is proposed for the manufacturer when the items are sold with a non-renewing free replacement warranty policy. The strategy involves splitting the warranty period into two intervals where only repairs are carried out, separated by a third interval with at most one replacement.

Warranty Cost Analysis With Heterogenous Usage Intensity

Models for cost analysis of one‐dimensional warranty policies assume that the usage intensity (or rate) is the same for all users. In real life the usage intensity varies across the population of users. This paper deals with some simple models to study the expected warranty cost for products sold with free replacement warranty with varying usage intensity.

Optimal repair–replace strategies for a warranted product

When a repairable product is sold with a free replacement warranty, the manufacturer has the option of rectifying a failure by either repairing the failed item or replacing it with a new one. In this paper, repairs are assumed to be minimal in the sense that they leave the product in exactly the same condition it was in prior to failure. We discuss the form of the optimal repair–replace strategy that minimises the expected cost of servicing the warranty over the warranty period.

Product risk sharing by warranties in a monopoly market with risk-averse consumers

This paper analyzes the implications of three different warranty rules in a monopoly setting with risk-averse consumers. The necessary condition for the existence of the market is independent of the risk-sharing arrangement. Although the quantity consumed is the highest if the consumer receives no warranty, even if the monopolist is constrained to marginal cost pricing, the replacement warranty is most efficient from a risk allocation point of view. However, the situation with no warranty is Pareto-superior to a money back warranty. Additionally, the producer and the consumers agree on the ranking of the warranty rules.

Algorithms for the free replacement warranty with phase-type lifetime distributions

This paper addresses the stochastic process generated by the cash flows resulting from free replacement warranties. Considering the underlying renewal processes, expressions for the quantities of interest can be obtained in terms of the renewal function which, in general, is very difficult to compute. For this reason most reported results are implemented only for product lifetimes belonging to the exponential family. To date there has been no significant research into the impact of the lifetime distribution on product warranty decisions. In this paper we develop algorithms to evaluate various items of interest in decision making when the lifetimes follow phase-type probability distributions. Extensive numerical results are presented to describe the effect of various model parameters on product warranty decisions.

Two-dimensional combination warranty policies

A combination warranty policy is an extension of two simple warranty policies - the free replacement warranty (FRW) and the pro-rata warranty (PRW) - in the sense that it either contains additional feactures or combines the terms of two simple policies. The paper deals with the cost analysis of five different two dimensional combination policies.

Quality control through lot sizing for items sold with warranty

Due to manufacturing variability, a fraction of the items produced are non-conforming - i.e. they do not meet the design specifications. The performance of a non-conforming item is inferior to that of a conforming item which meets the design specification. When items are sold with warranty, the warranty cost to service non-conforming items is much bigger than that for conforming items. The production of non-conforming items can be controlled through lot sizing. Smaller lot size results in a reduction in the warranty cost per item but this is achieved at the expense of increased manufacturing cost per unit. In this paper, we discuss the optimal lot sizing which achieves a proper trade-off between the two costs for repairable items sold with free replacement warranty (FRW) policy.

Discounted and Per Unit Net Revenues and Costs of Product Warranty: The Case of Phase-Type Lifetimes

In a paper published in this journal, Mamer (1987) 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 repurchase 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, we consider the case of phase-type product lifetimes. Under this assumption, we simplify the computation of the expected cost and revenue functions. Since most distributions can often be represented by phase-type distributions, our simplifications enhance the applicability of Mamer's useful yet computationally unwieldy results. For the per-unit-net-revenue criterion, our results supplement those of Mamer's. There, we also establish an interesting relation pertaining to expected net revenues as a function of consumer loyalty. We 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 one would intuitively conjecture. 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.