Total Warranty Cost Research Articles

A study on two‐dimensional warranty with a preventive maintenance policy under burn‐in or run‐in

AbstractProducts are often offered with warranties, which have become a common marketing strategy intended to indicate that product quality is guaranteed by the firm. Warranties can attract consumer purchases, but they also incur warranty costs, especially when firms falsely claim that their products are high quality; therefore, the determination of an appropriate warranty policy is of particular importance. This study considers a two‐dimensional warranty for complex repairable products, such as a vehicle, a lathe, or industrial machinery, with consideration of (1) burn‐in (run‐in), which is a supervised accelerating testing process performed before product launch to prevent defective products from being sold on the market, and (2) periodic preventive maintenance, which is performed during the usage period to prevent the occurrence of unexpected failures under normal usage conditions. The optimal burn‐in (run‐in) time and preventive maintenance intervals are determined with the aim of minimizing warranty costs for firms. The results of the study show that given a higher repair cost and a greater infant mortality failure rate, more frequent preventive maintenance is preferable, and the repair cost has the largest effect on the total warranty cost for the firm.

Non-renewable warranty cost analysis for dependent series configuration with distinct warranty periods

A warranty product often has an interval structure, resulting in different warranty periods for each component due to their distinct degradation paths. From the manufacturer’s perspective, it is reasonable to establish appropriate warranty periods for each part to achieve cost savings. This paper introduces a dependent series configuration consisting of a main component and an auxiliary component. The failure of the main component leads to system failure, while the failure of the auxiliary component only causes a random damage to the main component. These two components follow different Wiener degradation paths, and then their first passage times (FPTs) follow disparate inverse Gaussian distributions. Assuming a pre-deterministic warranty period, W, for the main component, and ηW,0<η<1, for the auxiliary component, the warranty period can be divided into two stages: [0,ηW] and [ηW,W]. In this context, the paper proposes warranty claim policies for replacement, objective-oriented imperfect repair (OOIR), and refund. The corresponding warranty costs sustained by manufacturer and consumer within these two stages are considered. Finally, a numerical example is presented to illustrate the warranty costs sustained by manufacturer and consumer under different scenarios, as well as the total warranty costs.

Optimization of two‐dimensional warranty policy for repairable products based on age and usage, applicable to lemon law conditions

AbstractThis paper proposes a new two‐dimensional warranty policy based on two factors—age and usage—that simultaneously incorporates both the warranty period and the refund period for a repairable product with an increasing failure rate. In this policy, the product is warranted by taking into account both its age and usage, and the warranty expires when the product reaches a specified age or a specified usage, whichever comes first. One unique framework of the policy presented in this work is that, under a specific type of lemon law, it defines a refund period during which the manufacturer must either replace the purchased product or offer a full or partial refund to the buyer if the product fails in such a way that meets certain conditions involving either the number of failures or the length of each repair time. The refund period is generally assumed to be shorter than the warranty period, and each failure that occurs after the refund period is only minimally repaired until the termination of the warranty. In this article, we consider both age and usage in warranting a product and we define an age‐based univariate warranty period based on the usage rate. Under a specified cost structure, we evaluate the expected total warranty cost during the age‐based warranty period and determine an optimal age‐based warranty period from the manufacturer's perspective. We also suggest a heuristic method that can be used to obtain an optimal warranty premium for the two‐dimensional warranty policy considered in this study. Finally, relevant numerical examples are provided to analyze the proposed warranty policy.

Cost Analysis of the Extended Two-Phase Warranty Model

Jung, Park, Park(2015)은 수리가 가능한 시스템(repairable system)에 대하여 이단계 보증(two-phase warranty)을 고려하였는데, 이는 교체보증(replacement warranty)과 최소수리보증(minimal repair warranty)으로 구성되는 일반적인 형태의 기본보증(original warranty) 모형이다. 즉, 시스템에 주어진 이단계 보증 하에서는 보증기간이 두 구간으로 구분되는데, 보증기간의 첫 번째 구간에서는 재생교체보증이 주어지고, 두 번째 구간에서는 최소수리보증이 주어진다. 한편, 최근에는 기본보증이 종료된 이후에 주어지는 연장된 보증(extended warranty)에 대하여 사용자와 생산자의 관심이 커지고 있다. 이러한 측면에서 본 논문에서는 이단계 보증 하에서의 네 종류의 연장된 보증모형을 고려하였다. 수리가 가능한 시스템에 대하여 주어지는 연장된 이단계 보증(extended two-phase warranty) 하에서 보증기간 동안에 발생되는 생산자 측면의 총기대보증비용(expected total warranty cost)을 유도하였다. 그리고 시스템의 수명분포(life distribution), 기본보증, 연장된 보증, 교체비용 (replacement cost), 최소수리비용(minimal repair cost)이 주어져 있을 때 총기대보증비용을 구하고 이를 비교하였다.

한국의 레몬법 하에서 2차원 보증비용의 추정

This paper deals with estimating the warranty cost of a product sold under Korean Lemon Law. Based on age and usage under Korean Lemon Law, a two dimensional warranty policy is applied and we consider repair (minimal repair) service and refund based on usage rate. We estimate the expected total warranty cost of a product for the two dimensional warranty. Numerical examples are also studied to investigate the effects of the model parameters on the expected total warranty cost using simulation approach.

Analysis of a two-dimensional stair-case warranty policy with preventive maintenance

Abstract We develop a mathematical model to study optimal preventive maintenance (PM) strategy under a two-dimensional stair-case warranty policy considering both age and usage of a product. During the warranty term, sellers implement preventive maintenance within the stair-case region of the warranty policy and upon failure a product is repaired minimally and immediately. Our objective is to find the optimal PM strategy that minimizes the seller’s cost of warranty while jointly considering the age and usage intervals of the PM policy and the level of PM executed. We also discuss how our results compare to those in a two-dimensional warranty policy with a rectangular region, and we find that the stair-case policy is preferable for sellers. An algorithm is provided to find the optimal solution and a numerical example is presented to illustrate how to find an optimal strategy with our proposed method. We show numerically that the expected total warranty cost is convex both in the age and the usage of the product under certain conditions.

An unpunctual preventive maintenance policy under two-dimensional warranty

In the business-to-consumer context, e.g., the automobile industry, preventive maintenance (PM) of warranted items usually relies upon customers to return their items to authorized maintenance centers according to prescribed schedules. However, item owners may be unpunctual, causing actual maintenance instants deviating from scheduled instants. This paper studies the impact of customer unpunctuality on the optimization of PM policy and the resultant warranty expenses. An unpunctual imperfect PM policy, which allows customers to advance or postpone scheduled PM activities in a tolerated range, is proposed for repairable items sold with a two-dimensional warranty. The expected total warranty costs of the unpunctual (and punctual) PM policies are derived under the assumption that customer unpunctuality is governed by a specific probability distribution. The optimization and comparison of the two policies are investigated in different scenarios regarding the product’s failure rate function. The results for two possible unpunctuality distributions—uniform and triangular—are discussed and compared. Numerical studies show that the expected total warranty cost of the unpunctual policy could be either higher or lower than that of the punctual policy, depending on customer behaviors and the shape of failure rate function. Accordingly, manufacturers could induce customers to adjust their unpunctuality behaviors by modifying PM policies or introducing penalty/bonus mechanisms.

Design of a flexible preventive maintenance strategy for two-dimensional warranted products

Offering appropriate preventive maintenance strategy has an effective impact on achieving higher customer satisfaction. This article presents a flexible preventive maintenance strategy, where customers are grouped into two groups according to their usage rates, and then different preventive maintenance programs are applied to different types of customers. The product follows a two-dimensional failure process and the preventive maintenance cost is shared between the manufacturer and customer on a pro rata basis. The manufacturer’s warranty cost is minimized by jointly optimizing the pro rata proportion of the preventive maintenance cost, the preventive maintenance number and the corresponding preventive maintenance levels. Numerical experiments are presented to illustrate the effectiveness of the proposed approach. Results prove that the flexible preventive maintenance strategy outperforms the conventional unified preventive maintenance strategy in terms of total warranty cost. Besides, some managerial suggestions are also given to provide guidance of implementing the proposed preventive maintenance strategy.

Optimal maintenance level for second‐hand product with periodic inspection schedule

This paper formulates a periodic inspection/upgrade model under free non‐renewable warranty policy with a fixed length of warranty period for the second‐hand product and derives an optimal number of inspections required and an optimal improvement level to minimize the expected total warranty cost from the perspective of the dealer during the warranty period. At each inspection, the product is taken an upgrade action in order to reduce its failure rate, which is characterized by an improvement level. It is true in general that the higher improvement level and more frequent inspections increase the warranty cost but lower the chance of product failures. In this paper, we propose an optimal strategy with respect to the inspection/upgrade action for the dealer to lower the total warranty cost. Firstly, we define an inspection/upgrade action, which reduces the product's failure rate proportionally to the improvement level at each inspection and then evaluate the expected total warranty cost. Secondly, the optimal solutions for the decision variables and its uniqueness are discussed in general. Numerical results are presented when the failure distribution follows a Weibull distribution under the proposed model. Copyright © 2014 John Wiley &amp; Sons, Ltd.

A new replacement warranty policy indexed by the product’s correlated failure and usage time

We study a new warranty policy for non-repairable products which is indexed by two correlated random variables, age and usage and covers all failures in (0,t]. Two different warranty costs for the replacement of the failed product are considered, according to its usage being greater or less than a pre-specified level s>0. A bivariate probability distribution function is applied to incorporate the correlation effect of the two variables. Analytical expressions of the probability density function of the total warranty cost and its expected value, the probability distribution functions of the number of the failed products with usage greater or less than s and their corresponding expected values and costs are derived. Limit results are also obtained. The results obtained are useful measures in establishing the compensation policy and the evaluation of its performance under the proposed warranty. Illustrative numerical examples of the expected cost for Paulson, Pareto and Beta Stacy bivariate distributions are presented and discussed. In particular for Paulson’s bivariate probability distribution, closed form expressions for the expected costs are obtained.

주기적인 유지보수 계획에 따른 중고제품에 대한 최적 향상수준

Due to a growing demand for the second-hand product, especially for the expensive one, the warranty and maintenance policies for such products have been studied to improve the product reliability of late. In this paper we study a periodic maintenance model for the second-hand product which is purchased by the customer at the age of . When purchased, the dealer provides a warranty of a fixed length during which the product is maintained periodically to reduce the failure rate of the product and thus, to improve the reliability after each maintenance is served. If a failure occurs between two successive maintenances, only minimal repair is conducted. As for the warranty policy, we adopt free non-renewing repair action on each failure, in addition to the periodic maintenance service during the warranty period. Thus, under the given warranty policy, all the maintenance and repair costs incurred during the warranty period are charged to the dealer. For the proposed periodic maintenance scheme, we formulate a cost model to evaluate the expected total cost charged to the dealer during the warranty period and derive an optimal upgrade level of the failure rate at each maintenance to minimize the expected total warranty cost from the perspective of the dealer. We also present numerical results for an optimal upgrade level based on the proposed methods.

Competitive and Collaborative Quality and Warranty Management in Supply Chains

Product quality and product warranty coverage are two important and closely related operational decisions. A longer warranty protection period can boost sales, but it may also result in dramatically increased warranty cost, if product quality is poor. To investigate how these two decisions interact with each other and influence supply chain performance, we develop a single‐period model with a supplier that provides a product to an original equipment manufacturer, which in turn sells it to customers. Customer demand is random and affected by the length of the product warranty period. Warranty costs are incurred by both the supplier and the manufacturer. We analyze two different scenarios based on which party sets the warranty period: manufacturer warranty and supplier warranty. Product quality is controlled by the supplier, and the manufacturer determines the ordering quantity. We analyze these decentralized systems and provide the structural properties of the equilibrium strategies. We also compare the results of centralized and decentralized systems and identify the conditions under which one system provides a longer warranty and better product quality than the other. Our numerical study further shows that, in decentralized settings, when the warranty period is determined by the firm sharing the larger proportion of total warranty costs, the supply chain can achieve greater system‐wide profit. Both parties can therefore benefit from properly delegating the warranty decision and sharing the resulting additional profit. We further design a supplier‐development and buy‐back contract for coordinating decentralized supply chains. Several extensions are also discussed.

How Does a Retailer's Service Plan Affect a Manufacturer's Warranty?

A service plan is a type of optional warranty beyond manufacturers' base warranties that retailers offer to consumers. In this paper, we examine how a service plan affects the role played by a manufacturer's base warranty. Analysis shows that when consumers can assess product quality (i.e., the probability of product failure), the manufacturer's warranty is negatively affected by the presence of a service plan. In the presence of such a plan, a base warranty is offered only when the manufacturer is very cost-efficient in providing a warranty relative to the retailer. In this case, although the double-marginalization problem is aggravated, offering a (limited) base warranty reduces the total warranty cost in the channel and provokes the retailer into enlarging the service plan coverage. When consumers cannot assess product quality, a high-quality manufacturer is motivated to offer a base warranty to signal its quality. In the presence of a service plan, however, a very cost-efficient manufacturer is discouraged from doing so. This paper was accepted by Preyas Desai, marketing.

Optimisation of warranty reserve policies

Companies typically plan for warranty costs through creation of a reserve fund. Most researchers assume that the warranty reserve is set based on the expected total warranty costs. However, companies rarely keep reserves to cover their liabilities for the whole life of their products, since maintaining excess reserves would cause opportunity cost. We propose an optimal policy rule based on the amount of cash additions/subtractions at the beginning of each period and the amount to contribute to the reserve after each sale. We model the warranty reserve problem as a single period inventory problem. We have shown that when there is no contribution after each sale the optimal policy resembles a ‘base-stock’ policy. When contribution after each sale is permissible, the optimal reserve level decreases as warranty costs can be covered by accruals. However, this kind of ‘pay-as-you-go’ system also increases the uncertainty in net flows from the fund.

Optimal Burn-in for Minimizing Total Warranty Cost

Burn-in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, optimal burn-in procedures for a system with two types of failures (i.e., minor and catastrophic failures) are investigated. A new system surviving burn-in time b is put into field operation and the system is used under a warranty policy under which the manufacturer agrees to provide a replacement system for any system that fails to achieve a lifetime of at least w. Upper bounds for optimal burn-in time minimizing the total expected warranty cost are obtained under a more general assumption on the shape of the failure rate function which includes the bathtub shaped failure rate function as a special case.

Burn-in policies for products having dormant states

Many systems might have a long time dormant period, during which the systems are not operated. For example, most building services products are installed while a building is constructed, but they are not operated until the building is commissioned. Warranty terms for such products may cover the time starting from their installation times to the end of their warranty periods. Prior to the commissioning of the building, the building services products are protected by warranty although they are not operating. Developing optimal burn-in policies for such products is important when warranty cost is analysed. This paper considers two burn-in policies, which incur different burn-in costs, and have different burn-in effects on the products. A special case about the relationship between the failure rates of the products at the dormant state and at the operating state is presented. Numerical examples compare the mean total warranty costs of these two burn-in policies.

OPTIMAL PREVENTIVE-MAINTENANCE WARRANTY POLICIES FOR REPAIRABLE PRODUCTS WITH AGE-DEPENDENT MAINTENANCE COSTS

This paper develops a mathematical model to derive the optimal preventive maintenance warranty (PMW) policy for repairable products with age-dependent maintenance costs. Under a PMW, any product failures are rectified by minimal repair, and additional preventive maintenance actions are carried out within the warranty period. When the costs for preventive maintenance and minimal repair are age-dependent, the optimal number of preventive maintenance actions, corresponding maintenance degrees, and the maintenance schedule for designing a PMW policy are derived here such that the expected total warranty cost is minimized. Under some reasonable conditions, we show that there exists a unique optimal PMW policy in which the product is maintained periodically with the same preventive maintenance degree. Using this property, an efficient algorithm is provided to search for the optimal policy. Some related models developed in the literature are discussed and these models are in fact special cases of the model proposed in this paper. Furthermore, when the life-time distribution of a product is Weibull, a closed-form expression of the optimal policy is obtained. Finally, the impact of providing preventive maintenance is evaluated through numerical examples.

OPTIMAL PREVENTIVE WARRANTY POLICY FOR PRODUCTS UNDER MAINTENANCE RESOURCE CONSTRAINTS

ABSTRACT This study investigates preventive-maintenance warranty policies for repairable products under resource constraints. To reduce product failures, preventive maintenance is widely adopted in practice, especially when the product is complex and/or expensive. However, in practice, there usually exist some resource constraints in performing a preventive maintenance action for deteriorating products. Therefore, products cannot be maintained back to a predetermined condition. In this study, a general warranty cost model for repairable products under resource constraints is established. Based on the model, the properties of optimal preventive-maintenance warranty policies are investigated. Using these properties, algorithms are provided to derive the optimal policies such that the expected total warranty cost is minimized. Finally, when the lifetime distribution of a product is Weibull, a closed-form solution of the optimal policy is obtained.

OPTIMAL PREVENTIVE WARRANTY POLICY FOR REPAIRABLE PRODUCTS WITH AGE-DEPENDENT MAINTENANCE COSTS

ABSTRACT This study investigates preventive-maintenance warranty (PMW) policies for repairable products with age-dependent maintenance costs. The primary role of warranty is to offer post-sale remedy for consumers when a product fails to fulfill its intended performance during a warranty period. For repairable products, the most commonly used warranty policy is the minimal repair warranty. To reduce product failures, preventive maintenance is widely adopted in practice, especially when the product is complex and/or expensive. For most PMW policies discussed in the literature, there is a basic assumption that the cost of each maintenance action is constant. However, the cost of a maintenance action is varied as the age of repairable products increases in general. Therefore, a general cost model for repairable products with age-dependent maintenance costs is established in this study to derive the optimal PMW policy such that the expected total warranty cost is minimized.

Optimal preventive-maintenance warranty policy for repairable products

This paper investigates preventive-maintenance warranty (PMW) policies for repairable products. When the length of a warranty period is pre-specified, the optimal number of preventive maintenance actions, corresponding maintenance degrees, and the maintenance schedule are jointly determined. We show that there exists a unique optimal policy such that the expected total warranty cost is minimized. Under some reasonable conditions, structural properties of the optimal policy are obtained. Using these properties, an algorithm is provided to efficiently search for the optimal policy. In the case where the failure density is Weibull, a closed form expression of the optimal policy is derived. Finally, the impact of providing preventive maintenance within a warranty period is illustrated through a numerical example.