Expected Warranty Cost Research Articles

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.

How long should a producer offer full refund?

Almost all consumer products are associated with a certain warranty time as stipulated by the manufacturer. Such a statement of warranty provides the buyer with an assurance on the performance of the product in the stated period. On the other hand, manufacturers use warranties for promotional and protectional purposes. In most cases, the type of warranty offered is linear pro-rata. This means that the rebate offered to the customer decreases linearly, from the price of the product to zero, as the time of product failure varies between zero and the warranty time. However, in some products, better promotional characteristics are observed if a full refund of the product price is made up to a certain period and linear pro-rata takes place thereafter. The purpose of this paper is to determine the time up to which a full refund is to be made. The conditions under which this time for full refund is found is based on maximizing the market share of the product subject to the constraint that the proportional increase in expected warranty costs, when compared to a linear pro-rata plan, does not exceed a chosen value.

Approximating Expected Warranty Costs

In this paper, we survey a portion of the literature in the analysis of warranty costs. In order to compare the price of different warranty policies, we review a framework which leads to expressing the expected costs in terms of complex functions arising in renewal theory. These functions and several approximations are discussed. In particular, a straight line approximation performs well.

Estimating the Cost of a Warranty

The cost of certain types of warranties is closely related to functions that arise in renewal theory. The problem of estimating the warranty cost for a random sample of size n can be reduced to estimating these functions. In an earlier paper, I gave several methods of estimating the expected number of renewals, called the renewal function. This answered an important accounting question of how to arrive at a good approximation of the expected warranty cost. In this article, estimation of the renewal function is reviewed and several extensions are given. In particular, a resampling estimator of the renewal function is introduced. Further, I argue that managers may wish to examine other summary measures of the warranty cost, in particular the variability. To estimate this variability, I introduce estimators, both parametric and nonparametric, of the variance associated with the number of renewals. Several numerical examples are provided.

An Optimal Policy for Servicing Warranty

In this paper we study a policy for servicing items sold with warranty. We obtain the optimal policy to minimize the expected warranty cost per unit sold.

A General Model for Estimating Warranty Costs for Repairable Products

For a product sold with a warranty period T, the manufacturer must pay all repair costs for failures in [O, T]. This paper presents a model to estimate warranty liability associated with this type of warranty policy. The quantities estimated are: (i) the expected total warranty cost and prediction interval for a fixed lot size of sales, and (ii) the expected number of units returned for repair and the expected warranty costs incurred in any time interval during the product life cycle, when sales occur continuously. The results are applicable for any failure time distribution and for various types of repair. A numerical example is given to illustrate the application of the model.