Optimal burn-in time under cumulative free replacement warranty

In this paper, optimal burn-in time to minimize the total mean cost, which is the sum of manufacturing cost with burn-in and cumulative warranty-related cost, is studied. When the products with cumulative warranty have high failure rate in the early period (infant mortality period), burn-in procedure is considered to eliminate the early product failures. After burn-in, the posterior product life distribution and the cumulative warranty-related cost are dependent on burn-in time; long burn-in period decreases the warranty-related cost, but it increases the manufacturing cost. The paper provides a methodology to obtain the total mean cost under burn-in and cumulative warranty. Properties of the optimal burn-in time are analyzed here. Numerical examples and sensitivity analysis are used to demonstrate the applicability of the methodology derived in the paper.     

A two-dimensional preventive maintenance strategy for items sold with warranty

Conventional preventive maintenance (PM) strategies under two-dimensional (2D) warranties are usually age-based or usage-based, which means that the implementation of PM activities is based solely on item age or usage. In this paper, a new PM strategy, called 2D PM strategy, is proposed for items sold with a 2D warranty. Under this strategy, the item is preventively maintained every K units of age or L units of usage, whichever occurs first. The marginal approach is used to describe the effect of age and usage on item reliability by treating usage as a random function of age. Besides, the effect of PM is characterised by the reduction of virtual age. The objective of this study is to identify the optimal 2D PM strategy under fixed warranty terms so as to minimise the total expected warranty servicing cost from the manufacturer’s perspective. A numerical example is provided to demonstrate the effectiveness of the proposed PM strategy. It is shown that the 2D PM strategy contains the age-based and usage-based strategies as special cases, and outperforms them in terms of warranty servicing cost. Finally, how to implement the proposed PM strategy in practice is discussed with an illustrative case.     

Investigating reliability improvement of second-hand production equipment considering warranty and preventive maintenance strategies

A cost model for optimal reliability improvement of warranted second-hand production equipment is developed. The second-hand production equipment of age x is subjected to an upgrade action of a certain level u before it is sold with a Free Repair Warranty. We look at determining the optimal upgrade level when not performing and when performing periodic preventive maintenance (PM) during the warranty period. Two different PM strategies are considered: (a) periodic PM actions having the same efficiency level; (b) periodic multi-phase PM actions with a maintenance efficiency level which varies according to the phase. The proposed model aims at helping the dealer to find the optimal upgrade level to perform before selling the second-hand equipment, and to assess whether performing PM actions during the warranty period, according to a specific maintenance strategy, is worthwhile in terms of cost reduction. Numerical experimentations considering each PM scenario are performed in order to investigate how each PM strategy impacts the improvement level to be performed and the associated total expected cost. The obtained results showed that the expected total cost incurred by the dealer is governed by a sensitive trade-off between the warranty servicing cost and the costs associated with the reliability improvement, and with the PM performed during the warranty period. It is also found that the proposed new periodic multi-phase PM policy with an increasing maintenance efficiency level yields lower upgrade levels, inducing lower costs for the dealer.     

Optimal maintenance policies during the post-warranty period

This paper develops the optimal periodic preventive maintenance policies following the expiration of warranty. We consider two types of warranty policies to discuss such optimum maintenance policies: renewing warranty and non-renewing warranty. From the user's perspective, the product is maintained free of charge or with prorated cost on failure during the warranty period. However, the users will have to repair or replace the failed product at their own expenses during the post-warranty period. Given the cost structure to the user during the cycle of the product, we derive the expressions for the expected maintenance costs for the periodic preventive maintenance following the expiration of warranty when applying two types of warranty policies and obtain the optimal number and the optimal period for such post-warranty maintenance policies by minimizing the expected long-run maintenance cost per unit time. Explicit solutions for the optimal periodic preventive maintenance are presented for illustrative purposes.     

Optimal reliability, warranty and price for new products

The success of a new product depends on both engineering decisions (product reliability) and marketing decisions (price, warranty). A higher reliability results in a higher manufacturing cost and higher sale price. Consumers are willing to pay a higher price only if they can be assured about product reliability. Product warranty is one such tool to signal reliability with a longer warranty period indicating better reliability. Better warranty terms result in increased sales and also higher expected warranty servicing costs. Warranty costs are reduced by improvements in product reliability. Learning effects result in the unit manufacturing cost decreasing with total sales volume and this in turn impacts on the sale price. As such, reliability, price and warranty decisions need to be considered jointly. The paper develops a model to determine the optimal product reliability, price and warranty strategy that achieve the biggest total integrated profit for a general repairable product sold under a free replacement-repair warranty strategy in a market and looks at two scenarios for the pricing and warranty of the product. The model assumes that the sale rate increases as the warranty period increases and decreases as the price increases. The maximum principle method is used to obtain optimal solutions for dynamic price and warranty situations. Finally, numerical examples are given to illustrate the proposed model.     

Optimal Burn-in Time to Minimize Cost for Products Sold Under Warranty

For products with an initially high failure rate, burn-in can be used to reduce the warranty cost. This paper examines the optimal burn-in time to achieve a trade-off between the reduction in the warranty cost and the increase in the manufacturing cost (as burn-in can be viewed as a part of the manufacturing process). Conditions for burn-in to be beneficial are derived for various warranty policies. A numerical example is presented.     

Optimal economic production quantity policy for a parallel system with repair,rework, free-repair warranty and maintenance

Hot standby redundancy maintains the working order of a system, repairs offer restoration in case of failure, and preventive maintenance (PM) prevents trouble. Warranties provide assurance to customers, and a superior warranty signifies higher product quality. The running costs of redundancy, maintenance and warranties influence decisions during product manufacture. Therefore, this paper presents an economic production quantity (EPQ) model for a parallel system with maintenance, production, and free-repair warranty (FRW) programmes. The production system begins with a basic unit and produces conforming items. PM is performed after the production run period and is classified as imperfect or perfect. If the basic unit fails, it is repaired and returned to operation after perfect PM; the spare unit is online only during the repair time of the basic unit. The spare will produce some number of defective goods, which are reworked in the same inventory cycle. The hot spare is minimally repaired if it fails in its standby or online mode. In this study, an inferior item is defined as one that satisfies specifications on inspection and is usable but is likely to incur postsale servicing costs when sold under an FRW. The total cost of this EPQ model includes setup, holding, PM, restoration, minimal repair, and warranty costs. The optimal production runtime is determined by minimising the total cost. Several cases are discussed in this paper, and the proposed model is illustrated using a numerical example and sensitivity.     

Optimal preventive maintenance strategy for leased equipment under successive usage-based contracts

In the context of equipment leasing, maintenance service is usually bundled with the leased equipment and offered by the lessor as an integrated package under a lease contract. The lessor is then responsible to prescribe an effective maintenance policy to keep the equipment operational in an economical way. This paper investigates upgrade and preventive maintenance (PM) strategies for industrial equipment during successive usage-based lease contracts with consideration of a warranty period, from the lessor's perspective. The accelerated failure time model and age reduction model are adopted to capture the effect of usage rate and imperfect PM/upgrade on the equipment reliability, respectively. More importantly, since equipment usage rates may vary across different lease contracts, this study develops an age correspondence framework to characterise usage rate shifts between successive lease periods. The optimal upgrade degree and the optimal number and level of PM actions are progressively updated for each upcoming lease period to minimise the total expected lease servicing cost, by considering the usage rate and maintenance implementation history. Numerical studies show that under given cost structures, periodical PM activities within each lease period tends to outperform the pre-leasing upgrade actions, though both of them can reduce the lease servicing cost.     

Optimal pricing and two-dimensional warranty policies for a new product

For commercial products, pricing and warranty are two crucial marketing strategies, which are used to promote the potential market share. The warranty policy adopted by most of the capital-intensive products, such as machines and automobiles, usually has two dimensions, i.e. warranty age and warranty usage. In this paper, we propose to investigate the profit-maximisation problem, in which the revenue and costs will be affected by the product price and the area of warranty region, for a new product sold under two-dimensional warranty. We assume that the product sales can be captured by a stochastic Bass model based on the nonhomogeneous Poisson process. The product follows a two-dimensional failure process and is covered by a non-renewable free minimal-repair warranty, with age and usage limits. We focus on three revenue/cost components, i.e. sales revenue, warranty cost and production cost, that will significantly affect a firm’s total profit. The profit is maximised by jointly optimising three decision variables, i.e. product price, warranty age limit and warranty usage limit. Numerical experiments are conducted to illustrate the effects of some key parameters, including product reliability, price elasticity, warranty elasticity and learning effect factor, on the optimal settings of the price and warranty region.     

基于成本/效益分析的产品保证策略

从成本／效益角度对产品售后保证策略问题进行研究,对产品保证的特征和保证策略类型进行论述,探讨了产品保证策略的形成过程,最后运用产品保证策略成本模型对我国彩电产品保证策略优化处理。     

考虑顾客不同使用强度的产品质保期和价格最优设计

站在制造商的角度进行一维质保期及产品价格策略的最优设计。考虑顾客不同使用强度对现场可靠性的影响,分别构建产品的失效率模型及最小维修策略时的质保成本模型。以期望利润最大化为目标,对最优的一维质保期和价格策略进行设计。最后,以某中央空调制造商作为算例,对中央空调的最优一维质保期和产品售价进行优化,并对主要参数进行敏感性分析。研究发现,特别是针对具有顾客不同使用强度的大型装置或系统,通过最优的质保期和价格策略设计可以有效地提升产品的利润期望值。     

Warranty Data Analysis: A Review

Warranty claims and supplementary data contain useful information about product quality and reliability. Analysing such data can therefore be of benefit to manufacturers in identifying early warnings of abnormalities in their products, providing useful information about failure modes to aid design modification, estimating product reliability for deciding on warranty policy and forecasting future warranty claims needed for preparing fiscal plans. In the last two decades, considerable research has been conducted in warranty data analysis (WDA) from several different perspectives. This article attempts to summarise and review the research and developments in WDA with emphasis on models, methods and applications. It concludes with a brief discussion on current practices and possible future trends in WDA. Copyright © 2012 John Wiley & Sons, Ltd.     

基于故障树映射的产品族保证成本分析

针对当前制造企业的产品通常以产品族而不是单一产品的形式存在的现实,对现有的基于单一产品的保证成本计算模型进行了改进,并指出产品族保证成本计算取决于配置产品的元件的可靠性。通过逆向搜索的方法,元件可靠性可以根据故障树模型向BOM模型映射得到。作者通过一个笔记本电脑的案例说明文中方法的操作过程,并比较了企业采用FRW和PRW两种策略时保证成本的差异。     

保证成本的统计估计

研究了保证及保证成本，并分别用极大似然法和非参数估计，估计出产品寿命分布参数和更新函数。在此基础上，建立了可修产品和不可修产品在不可更新免费更换保证下的成本模型。最后，通过算例对模型的应用进行了说明。     

Failure modeling and optimizing preventive maintenance strategy during two-dimensional extended warranty contracts

Offering extended warranty (EW) contracts for products such as automobiles is a good source of revenue for manufactures, insurers and third party companies. However, difficulties in the modeling of product’s failure process and assessing corrective and preventive maintenance actions’ effects on the reliability of product enforce the service providers to propose limited EW contracts with simple “minimal repair at failures” servicing strategy. In this paper for a product sold with a two-dimensional warranty, we model the failure process of product, the effect of imperfect preventive maintenance (PM) and corresponding servicing cost in terms of product’s age and usage. Then, we propose a mathematical optimization model to derive optimal number and degrees of preventive repairs to minimize the EW provider’s servicing cost. We also provide some guidelines to help the EW provider to design flexible EW contracts and determine their corresponding optimal maintenance strategies. To reproduce an illustrative numerical example, we use the failure history of a commercial vehicle produced in a plant in Iran. The provided results reveal that considering proper preventive maintenance strategy during the EW period may effectively reduces the cost of EW servicing.     

A maintenance strategy for two-dimensional extended warranty based on dynamic usage rate

Maintenance strategies are commonly used for repairable products or items to reduce the warranty cost in the warranty coverage. This study proposes a new warranty maintenance strategy for two-dimensional extended warranty (EW) based on dynamic usage rate. Unlike previous studies that assumed a constant usage rate, the present study regards the consumer usage rate as dynamic in the two-dimensional EW coverage. A maintenance model is constructed to determine the optimal maintenance degree of warranty claim points and help service providers accurately estimate and reduce warranty cost. A numerical example of an automobile made in China is discussed to demonstrate the effectiveness of the proposed model. The formulated model can effectively reflect the changes in the consumer usage rate and thus helps service providers develop an accurate maintenance strategy. Meanwhile, the developed model can better reduce warranty cost compared with maintenance strategies with minimal repair.     

Bayesian calculation of cost optimal burn-in test durations for mixed exponential populations

The burn-in process is a part of the production process whereby manufactured products are operated for a short period of time before release. In this paper, a Bayesian method is developed for calculating the optimal burn-in duration for a batch of products whose life distribution is modeled as a mixture of two (denoted ‘strong’ and ‘weak’) exponential sub-populations. The criteria used is the minimization of a total expected cost function reflecting costs related to the burn-in process and to product failures throughout a warranty period. The expectation is taken with respect to the mixed exponential failure model and its parameters. The prior distribution for the parameters is constructed using a beta density for the mixture parameter and independent gamma densities for the failure rate parameters of the sub-populations. It is assumed that the optimal burn-in time is selected in advance and remains fixed throughout the burn-in process. When additional failure information is available prior to the burn-in process, the minimization of posterior total cost is used as the criteria for selecting the optimal burn-in time. Expressions for the joint posterior distribution and cost are provided for the case of both complete and truncated data. The method is illustrated with an example.     

基于寿命周期成本分析的产品延伸保修决策优化模型

随着用户对产品寿命周期成本的日益重视,延伸保修已成为生产商新的关注点。延伸保修对产品维修使用费用以及市场竞争力有很大影响,为得到产品延伸保修决策优化方案以降低寿命周期成本,在考虑预防性维修策略的基础上,分析了生产商延伸保修定价策略,构建出一种以用户在产品使用寿命期内单位时间总维修成本最小为目标的延伸保修决策优化模型,并提出了求解模型的网格搜索(grid search)算法。通过引入算例,借助Matlab仿真软件实现网格搜索算法,在保证生产商利益的基础上,有效的降低了产品单位时间总维修成本,延长了产品使用寿命周期长度,由此得到了用户最优延伸保修决策方案,验证了模型和算法的合理性和有效性。     

A repair-replace strategy based on usage rate for items sold with a two-dimensional warranty

When a repairable item fails under warranty, the manufacturer has the option of either repairing the failed item or replacing it with a new one. In this paper, a repair-replace strategy is discussed for the manufacturer of a product sold with a two-dimensional warranty. The strategy is based on a specified region of the warranty defined in terms of age and usage with the first failure in the region rectified by replacement and all other failures being minimally repaired. An accelerated failure time (AFT) model is used to allow for the effect of usage rate on item degradation.     

保修计划中的成本与最优保修期研究

首先讨论了保修策略的各种类型,在此基础上建立了一种保修成本模型,最后,对保修策略中最优保修期问题进行了分析,给出了在不同产品故障分布情况下最优保修期的计算方法。