Warranty and optimal redundancy with uncertain quality

The expected warranty servicing cost is critically dependent on the reliability of the product. One way of improving product reliability is through redundancy but this is achieved at the expense of increased manufacturing cost. Redundancy is worthwhile if the reduction in expected warranty servicing cost exceeds the increase in the manufacturing cost. This paper examines optimal strategies with quality uncertainty where nonconforming items have inferior performance characteristics relative to conforming ones. It also examines the effect of life testing on the optimal strategies.     

Warranty and optimal reliability improvement through product development

For products sold with warranty, the warranty servicing cost can be reduced by improving product reliability through a development process. However, this increases the unit manufacturing cost. Optimal development must achieve a trade-off between these two costs. The outcome of the development process is uncertain and needs to be taken into account in the determination of the optimal development effort. The paper develops a model where this uncertainty is taken into account.     

Product warranty logistics: Issues and challenges

Warranty is an important element of marketing new products. The servicing of warranty results in additional costs to the manufacturer. Warranty logistics deals with various issues relating to the servicing of warranty. Proper management of warranty logistics is needed not only to reduce the warranty servicing cost but also to ensure customer satisfaction as customer dissatisfaction has a negative impact on sales and revenue. Unfortunately, warranty logistics has received very little attention. The paper links the literature on warranty and on logistics and then discusses the different issues in warranty logistics. It highlights the challenges and identifies some research topics of potential interest to operational researchers.     

Maintenance models in warranty: A literature review

Along with increasing the warranty period for complex systems, reducing the warranty servicing costs has become an issue of great importance to the manufacturers. One possible way to reduce the expected warranty servicing cost is by making sound decision on the product warranty and maintenance strategies. Therefore, warranties (basic warranty and extended warranty) and maintenance (corrective and preventive) are strongly interlinked and of great interest to both manufacturers and customers. This paper is the first identifiable academic literature review to deal with warranty and maintenance. It provides a classification scheme for the articles that link warranty and maintenance published between 2001 and 2011 covering 44 journals and proposes a taxonomy scheme to classify these articles. Nine hundred articles were identified for their relevance to warranty and were carefully reviewed. One-hundred and twenty-two articles were subsequently selected for their relevance to maintenance and included in the classification.     

An imperfect repair strategy for two-dimensional warranty

The objective of this study is to develop a warranty servicing strategy, based on imperfect and minimal repairs, that minimises the total warranty servicing cost. For pre-specified degrees of repair, the expected warranty servicing cost is minimised by optimally partitioning a two-dimensional rectangular warranty region into n disjoint subregions. We numerically illustrate the imperfect repair strategy and provide a comparison with previously studied warranty repair strategies.     

A new preventive maintenance strategy for items sold under warranty

When products are sold under warranty, the manufacturer incursadditional costs for warranty servicing. Preventive maintenanceactions can be used to reduce this cost and these are worthwhileonly if the extra cost incurred is less than the reduction achieved.In this paper we propose a new preventive maintenance policywhere the parameters are selected optimally to minimize thetotal warranty servicing cost.     

Warranty cost analysis: Increasing warranty repair times

In this study, we model the warranty servicing costs under nonrenewing and renewing free repair warranties. We assume nonzero increasing repair times with the warranty cost depending on the length of the repair time. An increasing geometric process is used to model the consecutive repair times. We introduce the generalised alternating renewal process, which is an alternating process with cycles consisting of an item's operational time followed by the corresponding repair time. We derive analytical results for a generalised alternating renewal process with a finite time horizon and use them to evaluate the warranty costs over the warranty period and over the life cycle of the product under the nonrenewing free repair warranty and renewing free repair warranty. Properties of the model are demonstrated through a simulation study and through the application to warranty claims data from an automotive manufacturer.     

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.     

Probability distributions of cost,revenue and profit over a warranty cycle

A warranty cycle starts with the sale of a new item and terminates when the warranty servicing obligation of the manufacturer created by this sale ends. Cost and profit measures over a warranty cycle are of interest with regards to accounting, pricing, product quality, warranty policy design, and other issues. For most predictive and decision making purposes, these variables cannot be described adequately by their means alone. In this paper, we obtain the probability distributions of the manufacturer's rebate, cost, revenue and profit during a cycle, under a (combination) freereplacement/pro-rata warranty policy, with the incorporation of the customer repurchase behavior under warranty. We first derive the joint distribution of the numbers of free and pro-rata replacements during a cycle. We then construct and compute the distributions of interest by conditioning on the numbers of such replacements. In so doing, we take into account the warranty policy, in terms of the lengths of the free and pro-rata periods, the cost and rebate profiles, customer repurchase probabilities during a pro-rata period, and the failure time distribution of the product. We provide several numerical examples, using data that are typical of battery warranties.     

The role of repair strategy in warranty cost minimization: An investigation via quasi-renewal processes

Most companies seek efficient rectification strategies to keep their warranty related costs under control. This study develops and investigates different repair strategies for one- and two-dimensional warranties with the objective of minimizing manufacturer’s expected warranty cost. Static, improved and dynamic repair strategies are proposed and analyzed under different warranty structures. Numerical experimentation with representative cost functions indicates that performance of the policies depend on various factors such as product reliability, structure of the cost function and type of the warranty contract.     

新产品定价决策的影响因素分析

新产品的成功销售取决于两个重要的因素:一是具有生产特性的工程变量,比如产品的可靠性水平;一是具有市场特征的影响因素,比如价格和保障机制。为了实现收益,制造商必须认真审视价格、产品可靠性和保障机制的选择。因此,本文将价格作为外生变量,将保障机制与可靠性作为决策变量,建立了以最大化为目标的收益模型,分析可靠性与保障机制的最优策略。另外,探讨当不同变量的敏感性参数发生变化时,最优保障机制与产品可靠性的变化规律。最后,通过算例分析收益函数的基本特性,结论显示消费者总是从产品保障机制的信号中判断产品的可靠性水平,这对新产品销售有一定的借鉴意义。     

Game theoretic modelling of service agent warranty fraud

When a warranty provider outsources warranty servicing to an external service agent this agent may act in a fraudulent manner. In this paper we consider a special case of service agent fraud—with the service agent overbilling the warranty provider for some of the warranty claims. A detailed inspection of a claim may be made to identify whether or not the service agent has committed fraud, but this inspection involves an additional cost to the warranty provider. This cost may be recovered by imposing a penalty on the service agent whenever a fraud is committed and it is detected. This penalty is specified in the maintenance service contract. A game theoretic approach is used to find the optimal overbilling strategy for the service agent and the optimal inspection strategy for the warranty provider. The optimal solution is the mixed strategy Nash equilibrium of a static game between the two parties.     

Repair-replace strategies for two-dimensional warranty policies

For repairable items sold with free replacement warranty, the actions available to the manufacturer to rectify failures under warranty are to

1. (1) repair the failed item or

2. (2) replace it with a new one.

A proper repair-replace strategy can reduce the expected cost of servicing the warranty. In this paper, we study repair-replace strategies for items sold with a two-dimensional free replacement warranty.     

Lot sizing and testing for items with uncertain quality

We consider the problem where items are produced in lots and sold with warranty. Due to manufacturing variability, some items do not conform to the design specifications and their performance is inferior (for example, have higher failure rate). The warranty servicing cost for these is much higher than for those which conform. Two approaches have been advocated for reducing the warranty cost per item released and in both it is achieved at the expense of increased manufacturing cost. The first involves life testing to weed out nonconforming items and the second involves strategies to reduce nonconforming items being produced. In this paper, the authors develop a model which combines both approaches and quality control decisions are made optimally to minimize the total (manufacturing and warranty) cost. It extends the earlier models of the authors which deals with quality decisions based solely on either the first or the second approach.     

Two-dimensional warranty repair strategy based on minimal and complete repairs

For repairable products, the warrantor has options in choosing the degree of repair applied to an item that has failed within the warranty period. We focus on a particular warranty repair strategy, related to the degree of the warranty repair, for non-renewing, two-dimensional, free of charge to the consumer warranty policy. We consider a rectangular warranty region and divide it into three disjoint subregions, so that each of these subregions has a preassigned degree of repair for a faulty item. Our main goal is to determine the subregions, so that the associated expected warranty servicing cost per item sold is minimised. A comparison between our strategy and previously studied, more restrictive, ones is provided.     

Optimal maintenance strategy under renewable warranty with repair time threshold

In this paper, we consider a periodic preventive maintenance model, from the manufacturer's perspective, which can be implemented to reduce the maintenance cost of a repairable product during a given warranty period. The product is assumed to deteriorate with age and the warranty policy we adopt in this paper takes into account the two factors of failure time and repair time of the product when the product failure occurs. Under the proposed two-factor warranty, a repair time threshold is pre-determined and if the repair takes more time than that of the threshold, the failed product is replaced with a renewed warranty policy. Otherwise, the product is only minimally repaired to return to the operating state. During such a renewable warranty period, preventive maintenance is conducted to reduce the rate of degradation periodically while the product is in operation. By assuming certain cost structures, we formulate the expected warranty cost during the warranty period from the manufacturer's perspective when a periodic preventive maintenance strategy is adapted. Although more frequent preventive maintenance increases the warranty cost, the chance of product failures would be reduced. The main aim of this paper is to accomplish the optimal trade-off between the warranty cost and the preventive maintenance period by determining the optimal preventive maintenance period that minimizes the total expected warranty cost during the warranty period. Assuming the power law process for the product failures, we illustrate our proposed maintenance model numerically and study the impact of relevant parameters on the optimal preventive maintenance policy.     

基于视情维修的质保政策设计研究

随着产品同质化程度不断提升,完善的质保服务已成为厂商提升品牌形象、刺激用户购买需求和全面反馈市场信息的主要途径。本文以具有退化特性的耐用品为研究对象,建立了视情维修条件下性能退化的维纳过程模型,考虑产品价格、质保期长度和维修费用承担比例对产品需求的影响,以最大化厂商利润为目标,确定了最优的质保期长度和维修费用承担比例。结合算例,比较了无视情维修和提供视情维修两种情形下对应的厂商利润,并分析了产品退化速率、成本参数和产品价格对利润的影响。研究结果表明,在质保服务范围内提供合理的视情维修服务既可将产品可靠性维持在一个较高水平,又可显著提升厂商利润。     

Cost analysis on renewable full-service warranties for multi-component systems

This paper presents a novel warranty policy named ‘full-service warranty’ (FSW) for repairable multi-component systems under which the failed component(s) or subsystem(s) will be replaced, in addition, a (perfect) maintenance action will be performed to reduce the chance of future system failure, both free of charge to consumers. Such a policy is desirable for both consumers and manufacturers since consumers receive better warranty service compared to the traditional free repair policy, at the same time, manufacturers may enjoy increase in sale as well as cost-saving due to improved product reliability by the maintenance action. Under the renewable FSW policy, from manufacturers’ point of view, cost models for complex systems with series, parallel, series–parallel (s–p) and parallel–series (p–s) structure are developed. Exact expressions for the first and second centered moments of warranty cost per product sold are obtained. Sensitivity analysis is performed based on a numerical example.     

A general age-replacement model with minimal repair under renewing free-replacement warranty

A general age-replacement model in which incorporates minimal repair, planned and unplanned replacement, is considered in this paper for products under a renewing free-replacement warranty policy. For both warranted and non-warranted products, cost models from the user’s perspective are developed, and the corresponding optimal replacement ages are derived such that the long-run expected cost rate is minimized. The impacts of a product warranty on the optimal replacement model are investigated analytically. Furthermore, we show that the optimal replacement age for a warranted product is closer to the end of the warranty period than for a non-warranted product. Finally, numerical examples are given for illustration.     

Optimal warranties,reliabilities and prices for durable goods in an oligopoly

This paper addresses the problem of durable goods manufacturers in an oligopoly seeking optimal values for three decision variables: product warranty, reliability and price. Each firm seeks a warranty-reliability-price combination that maximizes expected profit subject to quite general constraints on the firm's decision variables. Warranty serves as a signal of product reliability, which is not observable by consumers. We present a game-theoretic model of warranty-reliability-price competition in such a market and examine Nash equilibria for this game. We show that under fairly general assumptions each firm can optimally set its warranty and reliability independently of price and competitors' actions. In addition, we show that optimal warranties and reliabilities are complementary, and we explore the impact of different market factors on the optimal warranty and reliability. Finally, we show that optimal warranties are longer and products more reliable when consumers are risk averse.