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.     

Product warranty and reliability

Product warranty is an important part of new product marketing and sales. Offering warranty implies additional costs in the form of warranty servicing cost. Product reliability has a serious impact on the warranty servicing cost. As such, effective management of product reliability must take into account the link between warranty and reliability. This paper deals with this topic and develops a framework needed for effective management of product reliability. It reviews the relevant literature and defines topics for future research.     

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.     

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。     

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。     

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.     

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.     

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.     

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.     

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.     

基于两类失效的产品保修策略与出保维修优化

基于消费者对保修的需求,设计消费者偏爱的保修策略是制造商巩固市场地位、提升市场竞争力的一种战略决策。与此同时,以较低费用制定较长出保服役时间的出保维修策略也是消费者一直追求的目标。本文以两类失效产品为研究对象,首先从制造商角度将消费者偏爱的更新免费更换保修策略与产品定价相融合,开展了产品保修策略设计。其次,从消费者角度将预防维修与经典周期更换策略相融合,提出了维修—周期更换策略,且将其作为出保维修策略并对相应的性能进行了说明。通过数值实验发现,利润模型可对保修开展设计;与总费用模型作为目标函数相比,费用率模型作为目标函数可降低寿命周期费用;与经典周期更换策略相比,提出的维修—周期更换策略能使出保服役时间更长、费用率更低。     

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.     

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。     

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.     

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.     

Optimal pricing,EOL (end of life) warranty,and spare parts manufacturing strategy amid product transition

We study firm’s strategy to determine its product price and warranty period, and plan the spare parts manufacturing so as to maximize its profit and at the same time to fulfill its commitment to providing the customer with the key part continuously over the relevant decision time horizon, i.e., the product’s life cycle plus its EOL service (warranty) period. To examine the research question, we develop and solve a two-stage optimal control theory model. From the numerical analysis, we infer as follows. It is not always true that the longer the EOL warranty period, the better for the company’s profitability, implying there exists an optimal EOL warranty period that balances all the relevant forces like market demand and cost structures. The relationship between optimal EOL warranty period and failure rate (defect rate) is concave: when the defect rate is moderate, the company has to increase its EOL warranty period as the defect rate increases so as to compensate for the deteriorating quality; but, when the defect rate is beyond a threshold level, the company needs to curtail its EOL warranty commitment as the defect rate increases in order to avoid excessive cost to service the failed parts. By depicting key dynamics in this managerial problem, this paper sheds light on how to make decision for optimal pricing and warranty when the product life cycle is finite and the company is obliged to provide after-sales services to customers for an extended period of time after the current product is no longer produced.     

Joint Determination of Production Cycle and Inspection Intervals in a Deteriorating Production System

This paper considers production-maintenance policy for the deteriorating production system which can go ‘out of control’ while producing items. Once out of control, the production process produces some proportion of defective items. The defective items are reworked at some cost before being shipped, or, if passed to the customer, incur much larger warranty cost. Thus, to operate this system economically, periodic inspection and restoration of the process are needed. A mathematical model representing the expected annual cost is developed to determine the production cycle and process inspection intervals jointly. A case of equally spaced inspection intervals is solved by using an approximation to the cost function.     

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.     

Integrated process for structural–topological configuration design of weight-reduced vehicle components

Due to the speedy development trends of design stages, the material distributions and geometric configurations in view of the weight-reduction design of structures are the details taken into account from the stage of conceptual design with low cost, high performance and quality. In this point, a structural–topological configuration with a feasible design of structure is important. This paper presents the integrated process using three optimization techniques, in which the geometric boundaries and physical dimensions of the structure and material distribution of structure-configured elements are hierarchically optimized in the specifications of the maximum rigidity, plastic strain, residual deformations and lightweight.