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.     

Warranty cost analysis for second-hand products

For second-hand products sold with warranty, the expected warranty cost for an item to the manufacturer, depends on

• 1.(i) the age and/or usage as well as the maintenance history for the item
• 2.(ii) the terms of the warranty policy.

The paper develops probabilistic models to compute the expected warranty cost to the manufacturer when the items are sold with free replacement or pro rata warranties.     

The effect of lifetime buys on warranty repair operations

Lifetime buys are a common practice in the electronics and telecommunication industries. Under this practice, manufacturers procure their repair parts inventory in one order to support the spare part needs of a product for the duration of its warranty repair period. In this paper, we consider a repair operation in which defective items under warranty are returned to a manufacturer who either repairs these items using its spare parts inventory or replaces each defective unit with a new product. We show how fixed repair capability costs, variable repair costs, inventory holding costs, and replacement costs affect a firm's optimal repair and replacement decisions. The model is used to gain insights for products from a major mobile device manufacturer in the United States.     

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.     

Last time buy decisions for products sold under warranty

Manufacturers supplying products under warranty need a strategy to deal with failures during the warranty period: repair the product or replace it by a new one, depending on e.g. age and/or usage of the failed product. An (implicit) assumption in virtually all models is that new products to replace the failed ones are immediately available at given replacement costs. Because of the short life cycles of many products, manufacturing may be discontinued before the end of the warranty period. At that point in time, the supplier has to decide how many products to put on the shelf to replace failed products under warranty that will be returned from the field (the last time buy decision). This is a trade-off between product availability for replacement and costs of product obsolescence. In this paper, we consider the joint optimization of repair-replacement decisions and the last time buy quantity for products sold under warranty. We develop approximations to estimate the total relevant costs and service levels for this problem, and show that we can easily find near-optimal last time buy quantities using a numerical search. Comparison to discrete event simulation results shows an excellent performance of our methods.     

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.     

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.     

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.     

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.     

Evaluation of the warranty cost of a product with type III stochastic dependence between components

This paper analyses respectively the expected warranty costs from the perspectives of the manufacturer and the consumer. For a two-component series system with stochastic dependence between components, both the non-renewing free replacement policy and the renewing replacement policy are examined. It is assumed that whenever component 1 fails, a random damage to component 2 is occurred while a component 2 failure causes the system failure. Component 2 fails when its total accumulative damage exceeds a pre-determined level L. By considering the consumer’s behavior and the product service time, the warranty costs allocations between the manufacturer and the consumer are presented. Numerical examples are given to demonstrate the applicability of the methodology. It is proved that, independent of the type of the warranty policy, the failure interaction between components impacts the manufacturer profits and the consumer costs. The initial warranty length has also an impact on the product quality preferences to both the consumer and the 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.     

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.     

Optimal production run length for products sold with warranty

This article studies the optimal production run length for a deteriorating production system in which the products are sold with free minimal repair warranty. The deterioration process of the system is characterized by a two-state continuous-time Markov chain. For products sold with free minimal repair warranty, we show that there exists a unique optimal production run length such that the expected total cost per item is minimized. Since there is no closed form expression for the optimal production run length, an approximate solution is derived. In addition, three special cases which provide bounds for searching the optimal production run length are investigated and some sensitivity analysis is carried out to study the effects of the model parameters on the optimal production run length. Finally, a numerical example is given to evaluate the performance of the optimal production run length.     

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.     

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.     

保修策略下的系统最优更换模型

本文研究了单部件组成系统的保修策略 ,提出了一种新的按比例保修和免费保修策略 .在假定故障部件不能“修复如新”的条件下 ,利用几何过程分别考察了顾客和商家关于产品的长期运行平均费用 ,求出了它们的明显表达式 ,并且可以通过数值法或分析法求出其最优保修期 .     

Three-level warranty service contract among manufacturer,agent and customer: A game-theoretical approach

A warranty is a service contract between a manufacturer and a customer which plays a vital role in many businesses and legal transactions. In this paper, various three-level service contracts will be presented among the following three participants; a manufacturer, an agent, and a customer. In order to obtain a better result, the interaction between the aforementioned participants will be modeled using the game theory approach. Under non-cooperative and semi-cooperative games, the optimal sale price, warranty period and warranty price for the manufacturer and the optimal maintenance cost or repair cost for the agent are obtained by maximizing their profits. The satisfaction of the customer is also maximized by being able to choose one of the suggested options from the manufacturer and the agent, based on the risk parameter. Several numerical examples and managerial insights are presented and used to illustrate the models presented in this paper.     

A static allocation model for the outsourcing of warranty repairs

There has been a strong recent trend among original equipment manufacturers toward the outsourcing of work relating to the repair of items under warranty. In the typical cases where a large manufacturer uses several vendors to perform such work, we develop and analyse models to support decisions concerning how the work should be distributed among them. We depart from previous work in arguing the importance of an approach to the modelling of goodwill costs which takes explicit account of the delays experienced by customers. Theoretical considerations and numerical work both lend strong support to the contention that simple greedy approaches to workload allocation work well.     

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 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.