Design and Servicing of Product Warranties with Practical Motivations

實踐推動的產品質保設計與保障研究

Student thesis: Doctoral Thesis

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Award date29 Jul 2020

Abstract

In today's highly competitive market, manufacturers are forced not only to provide high quality products timely but also to offer appealing after-sales services for their products. One such kind of after-sales services is product warranty. A warranty is a contractual agreement attached to an item that requires the warrantor (generally the manufacturer) to offer compensation to the consumer according to pre-specified terms when the warranted item fails to perform its intended functions within the warranty period. In general, a warranty contract specifies product performance, contract duration, renewing & extension policy, (preventive) maintenance strategy, compensation mechanism, and buyer responsibilities, etc. However, offering warranty is by no means free from the warrantor's viewpoint. The warranty cost, resulting from the servicing of warranty claims, is a huge financial burden, and can account for as much as 15% of net sales. Optimal design and logistics of product warranties are therefore of great importance for warrantors. 

The thesis aims at developing some new and practical perspectives on the design and servicing of product warranties. In essence, each new perspective either is motivated by the warranty problem facing a company or has been adopted by one or more companies. The thesis consists of five independent studies and each focuses on a specific warranty related problem: The first four studies focus on warranty design issues, i.e., the optimal specification of warranty policies, whereas the last one deals with an operations issue—warranty reserve planning. 

The first work focuses on the warranty renewing policy and studies a new piece-wise renewing free replacement warranty. Under this policy, the whole warranty period is divided into two sub-periods and once an item fails in a specific sub-period, it will be replaced by a new identical one and the warranty period is fully or partially renewed. The proposed model is then modified by involving three sub-periods and a failure limit, respectively. In the latter scenario, when the number of item failures over a warranty cycle exceeds a pre-specified threshold, the manufacturer has to refund the item's purchase price, and consequently the warranty ceases. Case studies show that for a given warranty period, the piece-wise renewing free replacement policy has a better performance than the traditional fully renewing policy, in terms of expected warranty cost, warranty cycle, and cost rate. 

The second work deals with the preventive maintenance policy. An unpunctual preventive maintenance policy, which allows customers to advance or postpone scheduled preventive maintenance activities in a tolerated range, is proposed for repairable items sold with a two-dimensional warranty. The expected total warranty costs of the unpunctual (and punctual) policies are derived under the assumption that customer unpunctuality is governed by a specific probability distribution. The optimization and comparison of the two policies are conducted in different scenarios regarding the product's failure rate function. The impact of customer unpunctuality on the optimization of preventive maintenance policy and the resultant warranty expenses is then examined. Numerical studies show that the expected total warranty cost of the unpunctual policy could be either higher or lower than that of the punctual policy, depending on customer behaviors and the shape of failure rate function. Accordingly, manufacturers could entice customers to adjust their unpunctuality behaviors by modifying preventive maintenance policies or introducing penalty/bonus mechanisms.

The third work proposes a new performance-based warranty for products subject to competing hard and soft failures. A performance-based warranty combines both product and performance warranties, namely, it not only covers the repair or replacement of any defect, but also guarantees the minimum performance level throughout the warranty period. In this work, we propose three compensation policies—that is, free replacement, penalty, and full refund, when an item's performance fails to meet the guaranteed level. The expected warranty servicing costs for the three policies are derived, based on the competing risks concept. A warranty design problem is further formulated to simultaneously determine the optimal product price, warranty length, and performance guarantee level so as to maximize the manufacturer's total profit. Numerical studies show that the full refund policy always leads to the lowest total profit, whereas neither of the other two policies can dominate each other in all scenarios.

The fourth work studies the design and pricing of an extended warranty menu, which offers multiple options with differentiated prices and lengths. The multinomial logit choice model is adopted to describe customer choice behaviors. From a warrantor's perspective, the design and pricing problem is to determine which candidate options to offer and the associated prices so as to maximize the expected warranty profit. We show that the optimal strategy is to offer all candidate options associated with a cost-plus-margin pricing policy, with the same profit margins for all options. In addition, we present three extended models by considering heterogeneous warranty breadths, free preventive maintenance programs, and customers with heterogeneous perceptions of product failure probability. Major findings in the extended models include: i) a free preventive maintenance program should be attached to a warranty option only when it is feasible for that option; and ii) when the customer population is heterogeneous, the equal-margin pricing policy is no longer optimal. 

The last work investigates the warranty reserve planning problem faced by a manufacturer who is responsible for the warranty services of multiple products. Our primary objective is to develop an after-sales demand forecasting model and evaluate the time-varying benefits of risk pooling in warranty reserve management. Inspired by the general pattern of empirical warranty data, we first develop an adaptive aggregate warranty cost model by coupling stochastic product sales and failure processes. Then, the effects of risk pooling on planned reserve levels and expected total losses/costs are analytically investigated via a distributionally robust approach, since the exact distribution of the aggregate warranty cost is generally unknown. We find that the benefits of reserve pooling change over different stages of the warranty life cycle; the relative pooling benefit in terms of expected total losses decreases as the range of standard deviations enlarges. In particular, our case study shows that a dynamic learning mechanism that incorporates real data into the reserve planning model can improve its performance. 

With a series of new and practical perspectives related to the design and servicing of product warranties, the thesis aims to bridge existing gaps that are of interest to researchers and practitioners. The findings offer managerial guidelines on how warrantors should optimally design and support product warranties, so as to attain their business objectives.