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.     

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 .     

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.     

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.     

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 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.     

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.     

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。     

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.     

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.     

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.     

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.     

Optimal lot size and inspection policy for products sold with warranty

This paper develops a mathematical model to jointly determine the optimal lot size and product inspection policy for a deteriorating production system, when products are sold with free minimal repair warranty. Due to system deterioration, a last-K product inspection scheme is proposed, under which the last K products in a production lot are inspected and nonconforming products found are reworked. Based on the model, we show that there exist a unique optimal lot size and a corresponding inspection policy such that the expected total cost per unit time is minimized. Since there is no closed-form expression for the optimal lot size, an upper bound and approximate solutions are obtained to facilitate the search process. Furthermore, an algorithm is provided to efficiently search for the optimal policy and the performance of the optimal policy is evaluated through numerical examples.     

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.     

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。     

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。     

On a conjecture of optimal repair-replacement strategies for warranted products

Under a free replacement warranty policy, the manufacturer has the option of rectifying a failure by either repairing the failed item or replacing it with a new one. In [N. Jack, F. Van der Duyn Schouten, Optimal repair-replacement strategies for a warranted product, Int. J. Prod. Econ. 67 (2000) 95–100] a conjecture is made on the optimality of an age-limit policy: there exists a control limit , such that a minimal repair is performed on failure with t time units remaining in the warranty period if the age of the failing unit is less than or equal to . In this paper, we prove that this conjecture is indeed correct. Moreover, we show that for a more general model where the repair cost is random, a generalized repair-cost-limit policy is optimal, and the age-limit policy becomes its degenerated form. Numerical examples are provided to illustrate the computational algorithm and to compare the performance of these policies.     

An extended replacement policy for a deteriorating system with multi-failure modes

In this paper, the maintenance problem for a deteriorating system with k + 1 failure modes, including an unrepairable failure (catastrophic failure) mode and k repairable failure (non-catastrophic failure) modes, is studied. Assume that the system after repair is not “as good as new” and its deterioration is stochastic. Under these assumptions, an extended replacement policy N is considered: the system will be replaced whenever the number of repairable failures reaches N or the unrepairable failure occurs, whichever occurs first. Our purpose is to determine an optimal extended policy N^∗ such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit expression of the average cost rate is derived, and the corresponding optimal extended policy N^∗ can be determined analytically or numerically. Finally, a numerical example is given to illustrate some theoretical results of the repair model proposed in this paper.     

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 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.