基于最小与缺陷维修的二维产品保证策略研究

通过对相关文献的研究,提出采用使用时间和使用程度二维变量把产品保证区域划分成三个子区域,对第二个子区域里发生的第一次故障采用缺陷维修策略,对在第一、第三个保证子区域里发生的故障和在第二个保证子区域内第一次故障后的所有故障都采用最小维修策略;通过建立该产品保证策略下产品保证成本模型并获得优化处理的结果,又与相关文献所提供数例处理结果比较后发现:当故障产品最小维修费用相对于更换维修费用较小时,本文提供的产品保证策略方案更优.     

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.     

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.     

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.     

Optimal burn-in strategy for two-dimensional warranted products considering preventive maintenance

Burn-in and preventive maintenance (PM) are effective approaches to reduce the number of warranty claims and warranty cost during post-sale support. With harsher burn-in settings, early product defects can be removed, but at the same time product degradation is accelerated and more wear-out failures may be introduced. PM actions within warranty alleviate these negative effects. This paper proposes an optimal burn-in strategy for repairable products sold with a two-dimensional base warranty (BW) and an optional extended warranty (EW). Both performance-based and cost-based models incorporating PMs are developed to obtain optimal burn-in settings, including the burn-in duration and the burn-in usage rate, so as to minimise the expected number of warranty claims and total cost respectively. The impacts of different accelerated coefficients and PM degrees on the optimal burn-in strategy are analysed. In view of the performance and cost structures, we conduct numerical examples to illustrate the applicability of the proposed models. Practical implications from a sensitivity analysis for key parameters are also elaborated.     

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.     

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.     

Maintenance policies with two-dimensional warranty

A new maintenance policy which minimizes the total expected servicing cost for an item with two-dimensional warranty is proposed. An iterative procedure to estimate the item's failure rate function from historical observations and an optimization algorithm based on Monte Carlo simulation are applied to obtain the best maintenance policy. Numerical examples and sensitivity analysis are presented.     

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。     

Two-dimensional base warranty design based on a new demand function considering heterogeneous usage rate

Warranties are prevalent in the market. The manufacturer of products sold with warranties often faces a problem of balancing a trade-off between warranty cost and boosted demand by warranties when designing the warranties. For a two-dimensional base warranty with both age limit and usage limit, the heterogeneous usage rate of customers not only has an effect on warranty cost but also differentiates customers’ perceptions on warranty period. For example, the high-usage customers are more concerned about the usage limit of the warranty period, while the low-usage customers are more preferred to a longer age limit. This paper defines an attractiveness index based on the available warranty region to describe the extent of attractiveness of a two-dimensional warranty period to customers with heterogeneous usage rate. Moreover, a demand function based on the attractiveness index is proposed to describe the boosted demand of extending the warranty period. From the perspective of the manufacturer, the optimal two-dimensional base warranty period is designed by maximising the expected profit considering the trade-off. Both numerical examples and a case study are presented to illustrate the application of the proposed method.     

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.     

On optimal upgrade strategy for second-hand multi-component systems sold with warranty

Reliability improvement strategies such as upgrade, reconditioning and remanufacturing have been extensively adopted by dealers of second-hand systems to improve the system reliability and reduce the warranty servicing cost. However, most existing studies on this topic do not consider the multi-component structures of complex second-hand systems, and either treat them as black-box systems by ignoring their internal structures or simply deal with individual components. In this paper, a new upgrade model is developed for complex second-hand systems sold with a non-renewing free repair/replacement warranty, by explicitly considering their multi-component configurations. Two types of components, i.e. repairable and non-repairable components, are taken into account. During the upgrade process, non-repairable components can be upgraded only by replacement (if necessary), while repairable ones may be imperfectly upgraded with various degrees. The main objective of the dealer is to determine which components to upgrade and the corresponding upgrade degrees, to minimise the total expected servicing cost. In view of the problem structure, a marginal analysis based algorithm is presented. It is shown that the proposed upgrade strategy contains the ‘no upgrade’ strategy and the ‘component-level perfect upgrade/replacement’ strategy as special cases, and outperforms them. Finally, several extensions of the proposed upgrade model are discussed.     

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.     

Optimal imperfect preventive maintenance policy for equipment leased during successive periods

In this paper, we consider randomly failing equipment leased several times during their life cycle with a given warranty period. A mathematical model is developed to determine the optimal efficiency levels of preventive maintenance (PM) to be performed on the equipment between successive lease periods, maximising the expected total profit of the lessor over the equipment life cycle. The model considers the expected leasing revenue as well as the equipment acquisition cost and the average PM and repair costs. PM actions allow reducing the age of the equipment to a certain extent with a corresponding cost depending on the PM level adopted. The efficiency of the PM is determinant of the expected revenue during the next lease period. Given a set of K possible PM levels and the number of lease periods n over the equipment life cycle, K^{n?1 PM} strategies are possible. A genetic algorithm is proposed in order to obtain nearly optimal policies in situations where the number of possibilities K^n?1 is very high. Obtained numerical results are discussed. Small- and big-size instances of the problem are considered in the case of a service company in the oil and gas industry specialised in leasing specific equipment such as separators, to oil companies for production activities with a limited duration of several months like well testing or short production tests.     

A flexible two-dimensional basic warranty policy with two continuous warranty regions

Flexible warranty policies can satisfy customers by allowing them to select the warranty regions according to their usage rates. However, customers are usually unaware of their future usage rates when they purchase a product, which makes it difficult to make sound decisions. To address the problem, this paper proposes a flexible two-dimensional basic warranty policy with two continuous rectangular regions. Customers can gain experience of their usage rates through the first region, and thus make the second region more cost-effective. The total price of the two subregions is equal to the basic warranty price, which is prespecified by the manufacturer. The objective is to determine the optimal boundary between the two regions from the perspective of customers. First, the learning effect is used to depict the process of gaining experience from the first region. A warranty pricing model is then developed based on the polynomial failure intensity model. On that basis, the customer's expected repair cost over the warranty period is analyzed, and a numerical method is proposed for the optimization problem. A numerical example is presented to demonstrate the effectiveness of the proposed policy. The results show that customers can benefit more from the proposed policy than from the iso-cost warranty policy.     

A consumer incentive warranty policy and servicing strategy for products with uncertain quality

Owing to quality uncertainty in manufacturing, some of the items produced can be non-conforming. When items are sold with warranty, the warranty servicing cost for non-conforming items can be high. Life testing can be used to weed out such items and reduce the warranty cost. Such testing is expensive in terms of time and money. Releasing items with no testing can result in an increased number of early failures which in turn leads to consumer dissatisfaction and affects future profits, due to a loss of consumers. We propose a new policy which involves no testing and incorporates an incentive feature to reduce consumer dissatisfaction.     

二维保证下汽车维修备件动态库存控制策略

以汽车产品为例,针对失效率以时间或里程为计量单位的单位价值高、需求率低的不可修零部件,以未来销售预测为起点,依据二维保证政策的特点确定某时点处于保证时效内的汽车数量,基于产品可靠性对保证备件的需求进行预测,针对保证备件需求的特点,提出动态分段(Q,r)库存控制策略,通过案例验证了该库存策略可有效降低库存成本支出。     

Designing and pricing of two-dimensional extended warranty contracts based on usage rate

For vehicles sold under a two-dimensional warranty, which consists of two-dimensional region of age and usage, automobile manufacturers or third-party after-sales departments offer free warranty service under the base warranty. Consumers require a longer and better developed warranty service because of the rapidly developing production technology and other reasons. In the topic of two-dimensional warranty, previous research has extended the coverage of the base warranty, which satisfies consumers’ requirements but places significant pressure on automobile manufacturers. This study proposes a designing and pricing model of two-dimensional extended warranty contracts. The mathematical model is divided into two categories: the purchase of two-dimensional extended warranty service at the point of sale and the expiration of the base warranty. Based on the maintenance strategy used during the extended warranty, we classify this study under the minimal repair and combined maintenance strategy models. With the use of the failure and usage rate distribution functions, the mathematical pricing models of each sub-case are presented. A numerical example of a vehicle made in China is given to illustrate the procedure of the models. The results of this study provide automobile manufacturers with guidelines on designing and pricing two-dimensional extended warranty contracts.     

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.