Repairable Products Research Articles

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.

Extended warranty pricing considering the time of money

Warranty usually plays an important role in providing customers with product assurance. Although the customers have to pay extra money to buy an extended warranty, they can obtain more protections from the company. Our study focuses on the extended warranty; the successive failure times of the repairable product are assumed to be drawn from a non-stationary Poisson process, taking into the consideration of time value of money, to figure out a more precise model of warranty cost.Anumerical example is given to illustrate the model.

Warranty costs for repairable products with a two-attribute policy: impact of warranty execution

A warranty policy involving two attributes, for example time and usage, is considered. Usage is assumed to be related to time through the usage rate, considered to be a random variable satisfying a specified probability distribution. The paper analyses a policy where the product is repaired on failure within the specified parameters but warranty is not renewed. The failure distribution of the repaired items is assumed to be different from the failure distribution of new items. Furthermore, the situation that warranty may not be executed all the time is incorporated. Consumer behaviour is modelled through a warranty execution function.

Lot sizing, preventive maintenance, and warranty decisions for imperfect production systems

PurposeSets out to develop an integrated model that considers simultaneously inventory production decisions, PM schedule, and warranty policy for a deteriorating system that experiences shifts to an out of control state. The time to shift follows a general probability distribution with increasing hazard rate, so that time‐based PM is effective in improving the system reliability.Design/methodology/approachA profit function is used to model the production system. Optimization techniques are used to generate optimal solutions for the problem. Although global optimality cannot be guaranteed, empirical results show that global optimal solutions are obtained.FindingsThe integrated model provides decisions on inventory levels, production run length, and PM schedule simultaneously. It is illustrated through numerical examples that investment in PM can lead to savings in warranty claims for repairable products. As a result, the overall profit per unit, in certain cases, is higher with PM than without PM.Research limitations/implicationsThe production system is taken, numerical examples are presented and a sensitivity analysis is conducted to gain more insight into the developed model. In particular, the numerical analysis shows that a better PM program reduces warranty claims.Practical implicationsIn addition to the joint optimization of production/inventory decisions and PM schedule, such models can be very useful in making resource allocation decisions between warranty and PM programs. It is clear from the numerical analysis that a better PM program reduces warranty claims.Originality/valueThe paper provides a joint optimization of production inventory decisions and the PM schedule for a system subject to a time to shift that follows a general probability distribution. Previous research considered only an exponential distribution and did not consider PM.

A study of the optimal use period and number of minimal repairs of a repairable product after the warranty expires

The two-phase warranty models for repairable products are considered. We define the time interval [0, W] as the first phase and the time interval (W, T + W] as the second phase. The products have two types of failures: type I failures (minor failures) and type II failures (catastrophic failures). In the model, type I failures are removed by minimal repairs in the first and the second phases, and type II failures are removed by the replacements in the first phase. If type II failures take place in the second phase, because the type II failures (catastrophic failures) occur in the second phase, catastrophic failures will incur a very large repair cost for the buyer. So, we suppose that the life of products will be ended, that is the buyer will buy another new product. The process of buying a new product is conducted at time T + W, upon type II failures, or the nth of type I failures, whichever occurs first. Whenever each replacement takes place, the spare is ordered, and then delivered. Therefore, the lead time is considered. In this paper, we consider three warranty and maintenance models for seller, buyer and the society. Our objective here is to obtain the optimal minimal repairs n* and use time limit T* when the long-run average cost of society is the smallest. A numerical example is provided.

OPTIMAL WARRANTY PERIOD AND OPTIMAL REPLACEMENT AGE OUT-OF-WARRANTY

This paper considers a general repairable product sold under a failure-free renewing warranty agreement. In the case of a general repairable model, there can be two types of failure: type Ⅰ failure (a minor failure), which can be rectified by minimal repairs; and type Ⅱ failure (a catastrophic failure), which can be removed only by replacement. After a minimal repair, the product is operational but the failure rate of the product remains unchanged. The aim of this paper is to determine the optimal warranty period and the optimal out-of-warranty replacement age, from the perspective of the seller (manufacturer) and the buyer (consumer), respectively, while minimizing the corresponding cost functions. And we can prove under some mild conditions, the optimal solution that minimizing the cost function is uniquely exists and finite. Finally, a numerical example is presented.

Optimal burn‐in time for general repairable products sold under failure‐free renewing warranty

PurposeTo investigate the optimal burn‐in time from the perspective of minimizing the expected total cost (i.e. manufacturing plus warranty costs) per unit of product sold under a failure‐free renewing warranty policy. The conditions indicating when burn‐in becomes beneficial were also derived.Design/methodology/approachAn age‐dependent general repairable product sold under a failure‐free renewing warranty agreement was considered. In the case of such a general repairable model, there are two ways in which the product can fail: type I failure (minor) can be rectified through minimal repairs; while in type II failure (catastrophic), the product must be replaced. Then optimal burn‐in time is then examined in order to achieve a trade‐off between reducing the warranty cost and increasing the manufacturing cost.FindingsThe optimal burn‐in time depends on the failure/repair characteristics, length of warranty, cost parameters and the probability of failure type II (catastrophic). A burn‐in program is beneficial if the initial failure rate is high or product failures during the warranty period are costly. Moreover, the optimal burn‐in time is always less than the infant mortality period.Originality/valueThe product considered in this paper is an age‐dependent general repairable product: on which no such study has yet been conducted. This is also the first study to apply a failure‐free renewing warranty to a general repairable item. It can be seen that the present model is a generalization of the model considered by Chien and Sheu.

Determining optimal warranty periods from the seller's perspective and optimal out-of-warranty replacement age from the buyer's perspective

This paper considers a general repairable product sold under a failure-free renewing warranty agreement. In the case of a general repair model, there can be two types of failure: Type I failure (a minor failure), which can be rectified by minimal repairs; and type II failure (a catastrophic failure), which can be rectified only by replacement. After a minimal repair, the product is operational but the failure rate of the product remains unchanged. The aim of this paper is to determine the optimal warranty period and the optimal out-of-warranty replacement age, from the perspective of the seller (manufacturer) and the buyer (consumer), respectively, while minimizing the corresponding cost functions. We prove under mild conditions, that the optimal solution of minimizing the cost function exists and is finite. Further, a concise numerical example is demonstrated, and the sensitivity analysis of some of the parameters related to costs is carried out as well. Finally, some practical aspects of renewing the warranty policy for the practitioner and reader are addressed.

The optimal used period of repairable product with leadtime after the warranty expiry

This paper considers the two-phase warranty models for repairable products. It defines the time-interval [0, W] as the first phase (warranty period) and the time interval (W, T + W) as the second phase (buyer survival period). The products have two types of failures: type I failures (minor failures) and type II failures (catastrophic failures). In the model, type I failures are also removed by minimal repairs in the first and the second phases, and type II failures are removed by replacements in the first phase. If type II failures take place in the second phase, then it is supposed the life of products will be ended. To buy a new product is conducted at time T+W or upon the type II failure. Whenever each replacement takes place, the spare unit is ordered and then delivered. Therefore, the lead-time is considered. This thesis considers three warranty and maintenance models for seller, buyer and the society. The objective is to obtain the optimal T *. Finally, a numerical example is provided.

Optimal burn-in time to minimize the cost for general repairable products sold under warranty

Burn-in is used to improve product quality pre-sale. Particularly for products with an initially high failure rate sold under warranty, burn-in can be used to reduce the warranty cost. Since burn-in is usually costly and adds directly to the product manufacturing cost, optimizing the length of the procedure is a major problem. This investigation considers a general repairable product sold under warranty, and examines the optimal burn-in time for achieving a trade-off between reducing the warranty cost and increasing the manufacturing cost (since burn-in can be considered part of the manufacturing process). The expected total cost per unit sold is derived for various warranty policies (failure-free policies with and without renewing, rebate policy). The conditions required for burn-in to be beneficial are derived. Finally, a numerical example is presented.

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 WARRANTY PERIOD AND OPTIMAL REPLACEMENT AGE OUT-OF-WARRANTY

ABSTRACT This paper considers a general repairable product sold under a failure-free renewing warranty agreement. In the case of a general repairable model, there can be two types of failure: type I failure (a minor failure), which can be rectified by minimal repairs; and type II failure (a catastrophic failure), which can be removed only by replacement. After a minimal repair, the product is operational but the failure rate of the product remains unchanged. The aim of this paper is to determine the optimal warranty period and the optimal out-of-warranty replacement age, from the perspective of the seller (manufacturer) and the buyer (consumer), respectively, while minimizing the corresponding cost functions. And we can prove under some mild conditions, the optimal solution that minimizing the cost function is uniquely exists and finite. Finally, a numerical example is presented.

Warranty costs: An age‐dependent failure/repair model

AbstractAn age‐dependent repair model is proposed. The notion of the “calendar age” of the product and the degree of repair are used to define the virtual age of the product. The virtual failure rate function and the virtual hazard function related to the lifetime of the product are discussed. Under a nonhomogeneous Poisson process scenario the expected warranty costs for repairable products associated with linear pro‐rata, nonrenewing free replacement and renewing free replacement warranties are evaluated. Illustration of the results is given by numerical and graphical examples. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Discounted Warranty Cost of Minimally Repaired Series Systems

Many factors should be considered in modeling DWC (discounted warranty cost) of repairable systems or products including system structure, components' failure processes, methods of discounting as well as the warranty policy itself. In this paper, we present DWC models for repairable series systems. In particular, a free repair warranty policy and a pro-rata warranty policy are studied. The impact of repair actions on components' failure times is assumed to be minimal, hence NHPPs are used to describe the failure processes. Two types of discounting methods are considered in this paper: a continuous discount function and a discrete discount function. Expressions for both the expected value and variance of DWC are derived. The applications of our findings can be seen in warranty design, warranty reserve determination and risk analysis. Our approach incorporates the information of system structure, the value of time and the impact of repair actions, which are of great importance to warranty cost prediction and evaluation, but have not been sufficiently studied in the literature of warranty analysis.

Estimation of future breakdowns to determine optimal warranty policies for products with deterioration

Abstract Warranty has been played an important role not only for safeguarding the rights and interests of consumers but also for promoting the sales and reputation of manufacturers, since a good warranty policy signifies the image of high-quality products and thus becomes a powerful weapon for marketing products in increasingly competitive markets. It is obvious that a more thoughtful warranty policy of a product will attract more customers to consume the specific product, and increase the product's market share accordingly. However, an unlimited warranty for monopolizing the market is absolutely unrealistic, since the cost will significantly increase for maintaining such a warranty policy with better offers. In this paper, a Bayesian decision model for determining the optimal warranty policy for repairable products is proposed. The successive failure times of the repairable product are assumed to be drawn from a nonhomogeneous Poisson process. Both the repair costs for restoring the product to full functionality after each breakdown and the potential sales increases due to the specific warranty policy are also considered. Finally, an application case is utilized to demonstrate the feasibility and validity of the proposed approach.

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.

Statistical analysis of marginal count failure data.

Manufacturers want to assess the quality and reliability of their products. Specifically, they want to know the exact number of failures from the sales transacted during a particular month. Information available today is sometimes incomplete as many companies analyze their failure data simply comparing sales for a total month from a particular department with the total number of claims registered for that given month. This information--called marginal count data--is, thus, incomplete as it does not give the exact number of failures of the specific products that were sold in a particular month. In this paper we discuss nonparametric estimation of the mean numbers of failures for repairable products and the failure probabilities for nonrepairable products. We present a nonhomogeneous Poisson process model for repairable products and a multinomial model and its Poisson approximation for nonrepairable products. A numerical example is given and a simulation is carried out to evaluate the proposed methods of estimating failure probabilities under a number of possible situations.

Optimal repair–replace strategies for a warranted product

When a repairable product is sold with a free replacement warranty, the manufacturer has the option of rectifying a failure by either repairing the failed item or replacing it with a new one. In this paper, repairs are assumed to be minimal in the sense that they leave the product in exactly the same condition it was in prior to failure. We discuss the form of the optimal repair–replace strategy that minimises the expected cost of servicing the warranty over the warranty period.