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.     

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.     

Optimal warranty policies for systems with imperfect repair

We investigate a system whose basic warranty coverage is minimal repair up to a specified warranty length. An additional service is offered whereby first failure is restored up to the consumers’ chosen level of repair. The problem is studied under two system replacement strategies: periodic maintenance before and after warranty. It turns out that our model generalizes the model of Rinsaka and Sandoh [K. Rinsaka, H. Sandoh, A stochastic model with an additional warranty contract, Computers and Mathematics with Applications 51 (2006) 179–188] and the model of Yeh et al. [R.H. Yeh, M.Y. Chen, C.Y. Lin, Optimal periodic replacement policy for repairable products under free-repair warranty, European Journal of Operational Research 176 (2007) 1678–1686]. We derive the optimal maintenance period and optimal level of repair based on the structures of the cost function and failure rate function. We show that under certain assumptions, the optimal repair level for additional service is an increasing function of the replacement time. We provide numerical studies to verify some of our results.     

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.     

Dynamic pricing and warranty policies for products with fixed lifetime

We consider a repairable product with known market entry and departure times. A warranty policy is offered with product purchase, under which a customer can have a failed item repaired free of charge in the warranty period. It is assumed that customers are heterogeneous in their risk attitudes toward uncertain repair costs incurred after the warranty expires. The objective is to determine a joint dynamic pricing and warranty policy for the lifetime of the product, which maximizes the manufacturer’s expected profit. In the first part of the analysis, we consider a linearly decreasing price function and a constant warranty length. We first study customers’ purchase patterns under several different pricing strategies by the manufacturer and then discuss the optimal pricing and warranty strategy. In the second part, we assume that the warranty length can be altered once during the product lifetime in developing a joint pricing and warranty policy. Numerical studies show that a dynamic warranty policy can significantly outperform a fixed-length warranty policy.     

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.     

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.     

An extended warranty policy with options open to consumers

An extended warranty model that includes a free repair period and an extended warranty period will be discussed. Consumers have choices to renew or not to renew at the end of free repair period. Different choices will have different cost implications for consumers and manufacturers. The exact expressions of the total expected discounted cost, and the long-run average cost per unit time for a consumer and the manufacturer are derived. Then the optimal policies for the consumers are obtained. Under the assumption that a consumer has applied his/her optimal policy, an optimal policy or an ε-optimal policy for the manufacturer is then determined analytically.     

Optimal maintenance strategy for non‐renewing replacement–repair warranty

In this paper, we study the maintenance policy following the expiration of the non‐renewing replacement–repair warranty (NRRW). For such purposes, we first define the non‐renewing free replacement–repair warranty and the non‐renewing pro rata replacement–repair warranty. Then the maintenance model following the expiration of the NRRW is discussed from the user's point of view. As the criterion to determine the optimal maintenance strategy, we formulate the expected cost rate per unit time from the user's perspective. All system maintenance costs incurred after the warranty is expired are paid by the user. Given the cost structures during the life cycle of the system, we determine the optimal maintenance period following the expiration of the NRRW. Finally, a few numerical examples are given for illustrative purposes. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

考虑维修时间的总质保需求预测模型

激烈的市场竞争迫使制造商们逐渐向以顾客需求为中心的公司转变。在近 20 年内,作为影响顾客满意度的主要因素,产品的质保服务管理的相关研究开始成为学术界的焦点。良好的质保服务会给企业节省较多的运营成本,故对于刚投入市场的新产品而言,准确地预测质保需求对制造商合理分配资金等具有重要意义。以往对质保需求的预测模型都局限于分析长期意义上一个产品的总质保成本,忽略了产品的维修时间和动态销售过程对准确预测产品的总质保需求及成本的影响。为此,以销售期内的产品所产生的维修需求为主要的研究对象,深入探讨维修时间对预测质保需求的影响。模型中,利用非齐次泊松过程模拟产品的动态销售过程,并利用复合随机过程中的交错更新理论来刻画维修时间对总质保需求的影响。最后的参数分析,为企业更好地管理质保服务提供了重要的现实依据。     

Optimal system design considering warranty,periodic preventive maintenance,and minimal repair

This paper presents a cost minimisation model for an optimal design of a mixed series-parallel system with deteriorating components. The model incorporates warranty, periodic preventive maintenance, and minimal repair in the design of system configuration. Imperfect repair is adopted to model the effect of preventive maintenance. Both free and pro-rata warranty policies are considered. A numerical example is given to demonstrate the application of this model.     

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.     

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.     

考虑更新延长两阶段保修的二手产品维修策略优化

针对二手产品的维修问题,给出了二手产品生命周期的定义,提出了考虑更新延长两阶段保修的维修策略模型。该策略综合考虑了产品的年龄变化、延保折扣、小修和生产损失费用等因素,从顾客的角度出发,建立以顾客期望总费用率最小化为目标的免费更换保修和按比例更换保修两种策略模型,并给出模型最优化的相关理论证明。算例研究验证了模型的有效性,并对参数的灵敏度进行了分析,文中结论可为顾客进行产品维修计划提供决策依据。     

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.     

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.     

基于促销和延保的渠道入侵与订货时序策略

针对单个制造商和单个零售商组成的二级供应链,制造商一方面考虑是否开拓电子商务市场而建立直销渠道与零售商展开渠道竞争,另一方面为刺激市场需求开展促销活动并对所有消费者提供有偿延保服务。分别针对先后订货和同时订货两种情形,刻画了不同入侵成本下制造商的最优入侵、促销、定价以及销售策略,并分析了制造商渠道入侵策略对零售商订货决策和盈利能力的影响。研究表明：满足入侵成本阈值条件时,渠道入侵有利于改善制造商利润;同时订货会降低制造商的入侵动机和零售商利润;在延保服务价格敏感系数和促销成本系数满足相关约束时,零售商能够从制造商渠道入侵中攫取更多利润,实现供应链节点企业的互利共赢;无论订货时序如何,渠道入侵总会提高促销努力水平和延保服务价格。     

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.     

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.