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.     

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 buffer inventory and preventive maintenance for an imperfect production process

In this paper we present a model to determine the optimal length of continuous production periods between maintenance actions and the optimal buffer inventory to satisfy demand during preventive maintenance or repair of a manufacturing facility. We include in the model the possibility of imperfect production. We consider that the duration and cost of the maintenance action depend on the state of the production facility.     

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.     

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.     

Optimal replacement and overhaul decisions with imperfect maintenance and warranty contracts

In this article, we develop a model to help a maintenance decision making situation of a given equipment. We propose a novel model to determine optimal life-cycle duration and intervals between overhauls by minimizing global maintenance costs. We consider a situation where the costumer, which owns the equipment, may negotiate a better warranty contract by offering an improved preventive maintenance program for the equipment. The equipment receives three kind of actions: repairs, overhauls, and replacement. An overhaul represents an imperfect maintenance action, that is, the failure rate is improved but not a point that the equipment is as good as new. Corrective maintenance actions are minimal, in the sense that the failure rate after each repair is the same as before the failure. The proposed strategy surpasses others seen in the literature since it considers at the same time the warranty negotiation situation and the optimal life-cycle duration under imperfect preventive actions. We also propose a simplified approach that facilitates the task of implementing the method in standard solvers.     

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 decision of an economic production quantity model for imperfect manufacturing under hybrid maintenance policy with shortages and partial backlogging

Considering the characteristics of the stochastic shift of the machine state and the uncertainty of the product quality of production, in this paper, we develop an optimisation decision of economic production quantity model for an imperfect manufacturing system under hybrid maintenance policy with shortages and partial backlogging. We assume that the production process is imperfect stemming from the machine reliability and the probability of out-of-control, a hybrid maintenance policy combined of emergency maintenance and preventive maintenance is executed during each production run. Three decision models based on the scenarios of machine breakdown and repair time are developed. The optimal production quantity and maintenance inspection number during each production run are solved with minimising the expected average cost of the system. Numerical examples are used to demonstrate the effectiveness and feasibility of the model. Sensitivity analysis is conducted to analyse the impacts of key parameters on the optimal decision. Some implications related to the effective and economical execution of maintenance policy for practitioners are derived.     

A modeling framework for assessing the impact of new time/mileage warranty limits on the number and cost of automotive warranty claims

An automobile with over 7000 parts is a highly complex product. In spite of employing the best quality and reliability practices during product development, manufacturing, and assembly, unexpected failures during warranty period do occur and cost automobile companies billions of dollars annually in warranty alone. Warranty coverage for an automobile is generally stated in terms of mileage (in miles) and time (in months or years). The coverage expires when any of the two limits is crossed. Any change in warranty coverage too, influences warranty cost significantly. However, changes made to warranty coverage are often market driven. In either case, a company needs to plan for maintaining a large cash reserve to pay for the warranty services on their products.In this paper, we present a simple method to assess the impact of new time/mileage warranty limits on the number and cost of warranty claims for components/sub-systems of a new product. We highlight the use of mileage accumulation rates of a population of vehicles to arrive at claims per thousand vehicles, sold with new time/mileage warranty limits. We also discuss the bias in warranty cost estimates that may result in using cumulative cost per repair information. We recommend the use of incremental cost per repair especially when populations with different mileage accumulation rates are under consideration. Application examples are included to illustrate the use of the proposed methodology.     

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.     

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。     

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.     

A General Model for Estimating Warranty Costs for Repairable Products

For a product sold with a warranty period T, the manufacturer must pay all repair costs for failures in [O, T]. This paper presents a model to estimate warranty liability associated with this type of warranty policy. The quantities estimated are: (i) the expected total warranty cost and prediction interval for a fixed lot size of sales, and (ii) the expected number of units returned for repair and the expected warranty costs incurred in any time interval during the product life cycle, when sales occur continuously. The results are applicable for any failure time distribution and for various types of repair. A numerical example is given to illustrate the application of the model.     

考虑缓冲区库存分配的并联系统预防维护策略研究

为提高并联系统生产过程的连续性,提出了考虑缓冲区库存分配的并联系统(3M1B)预防维护模型。首先,考虑并联系统每台设备的故障率与维护率,在并联系统中上下游设备之间建立缓冲区,构建3M1B系统。其次,考虑设备不完美生产的可能性,以缓冲区库存量与设备运行周期为决策变量,以设备最小生产成本率为目标函数建立预防维护模型,求解最佳的预防维护策略与缓冲区库存分配策略。针对此维护模型,采用离散迭代算法与遗传算法进行求解,并比较了2种算法的优劣,结果表明,对于此模型,离散迭代算法优于遗传算法。最后,通过算例验证模型的可行性和有效性。     

Preventive maintenance policy of single‐unit systems based on shot‐noise process

This paper develops reliability and maintenance models for a single‐unit system subject to hard failures under random environment of external shocks. Motivated by the observations of shot‐noise process in practice, the impact of shock damage on system failure behavior is characterized by random hazard rate increments. To remove such negative impact, imperfect preventive repair is performed periodically, and preventive replacement is performed after several repairs. Considering the joint effects of both random shocks and imperfect repair on the system hazard rate, we derive recursive equations for the system reliability function. Furthermore, we investigate the optimal maintenance policy that minimizes the expected cost per unit time of the system. The applicability of the reliability and maintenance model is validated by a case study on a wind turbine system.     

Optimum Maintenance and Availability of Series Systems Subject to Imperfect Repair

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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.     

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.     

Optimization of cost and downtime for replacement model following the expiration of warranty

This paper deals with the optimal replacement policies following the expiration of warranty: renewing warranty and non-renewing warranty. If the system fails during its warranty period, it is replaced with a new one and if the system fails after the warranty period is expired, then it is minimally repaired at each failure. The criterion used to determine the optimality of the replacement period is the overall value function, which is established based on the expected downtime and the expected cost rate combined. Firstly, we develop the expected downtime per unit time and the expected cost rate per unit time for our replacement model when the cost and downtime structures of maintaining the system are given. The overall value function suggested by Jiang and Ji [Age replacement policy: a multi-attribute value model. Reliab Eng Syst Saf 2002;76:311–8] is then utilized to determine the optimal maintenance period based on the expected downtime and the expected cost rate. Numerical examples are presented for illustrative purpose.     

Optimal preventive maintenance strategy using two repair crews having different efficiencies: a quasi renewal process based modelling approach

This paper considers randomly failing, single-unit equipment subject to a periodic preventive maintenance (PM) policy. In case of failure between successive perfect PM actions (renewals), imperfect repairs are performed following a decreasing quasi-renewal process. One of two different maintenance crews can perform the repairs. One team is more experienced, and consequently more efficient than the other, but more costly. A mathematical model is developed in order to determine the PM period, T, and the kth repair, during a PM period, after which the repair team should be changed, minimising the average total cost per time unit over an infinite time span. It is also proved that an optimal solution in terms of the PM period always exists for any given system lifetime distribution and any set of maintenance costs. Numerical examples are presented and the obtained results are discussed.