Free Replacement Warranty Research Articles

Cost analysis for multi-component system with failure interaction under renewing free-replacement warranty

In a multi-component system, the assumption of failure independence among components is seldom valid, especially for those complex systems with complicated failure mechanism. For such systems, warranty cost is subject to all the factors including system configuration, quality of each component and the extent of failure dependence among components. In this paper, a model is developed based on renewing free-replacement warranty by considering failure interaction among components. It is assumed that whenever a component (subsystem) fails, it can induce a failure of one or more of the remaining components (subsystems). Cost models for series and parallel system configurations are presented, followed by numerical examples with sensitivity analysis. The results show that, compared with series systems, warranty cost for parallel systems is more sensitive to failure interaction.

Optimal Overhaul-Replacement Policies for a Repairable Machine Sold with Warranty

This research deals with an overhaul-replacement policy for a repairable machine sold with a free replacement warranty (FRW), which will be used for a finite horizon T and evaluated at fixed interval s. At each evaluation point, the buyer considers three alternative decisions, i.e. (1) keep the machine, (2) overhaul it, or (3) replace it with a new identical one. If the machine fails during the warranty period, this is rectified at no cost to the buyer. Any failure occurring before and after the expiry of the warranty is restored by minimal repair. An overhaul-replacement policy was formulated using a dynamic programming approach. The results show that overhaul rejuvenation may extend the machine life cycle and delay the replacement decision. In contrast, the warranty stimulates early machine replacement and in so doing increases the replacement frequency for a certain range of replacement costs. This implies that in order to minimize the total ownership costs over T, the buyer needs to consider the minimal repair cost reduction due to the rejuvenation effect of an overhaul as well as the warranty benefit due to replacement. Numerical examples are presented for both illustrating the optimal policy and describing the behavior of the optimal solution.

A study on negative binomial inspection for imperfect production systems

Production systems continuously deteriorate with age and usage due to corrosion, fatigue, and cumulative wear in production processes, resulting in an increasing possibility of producing defective products. To prevent selling defective products, inspection is usually carried out to ensure that the performance of a sold product satisfies the customer requirements. Nevertheless, some defective products may still be sold in practice. In such a case, warranties are essential in marketing products and can improve the unfavorable image by applying higher product quality and better customer service. The purpose of this paper is to provide manufacturers with an effective inspection strategy in which the task of quality management is performed under the considerations of related costs for production, sampling, inventory, and warranty. A Weibull power law process is used to describe the imperfection of the production system, and a negative binomial sampling is adopted to learn the operational states of the production process. A free replacement warranty policy is assumed in this paper, and the reworking of defective products before shipment is also discussed. A numerical application is employed to demonstrate the usefulness of the proposed approach, and sensitivity analyses are performed to study the various effects of some influential factors.

Warranty optimisation based on the prediction of costs to the manufacturer using neural network model and Monte Carlo simulation

Warranty is a powerful marketing tool, but it always involves additional costs to the manufacturer. In order to reduce these costs and make use of warranty's marketing potential, the manufacturer needs to master the techniques for warranty cost prediction according to the reliability characteristics of the product. In this paper a combination free replacement and pro rata warranty policy is analysed as warranty model for one type of light bulbs. Since operating conditions have a great impact on product reliability, they need to be considered in such analysis. A neural network model is used to predict light bulb reliability characteristics based on the data from the tests of light bulbs in various operating conditions. Compared with a linear regression model used in the literature for similar tasks, the neural network model proved to be a more accurate method for such prediction. Reliability parameters obtained in this way are later used in Monte Carlo simulation for the prediction of times to failure needed for warranty cost calculation. The results of the analysis make possible for the manufacturer to choose the optimal warranty policy based on expected product operating conditions. In such a way, the manufacturer can lower the costs and increase the profit.

Optimal Unlimited Free-Replacement Warranty Strategy using Reconditioned Products

The long-term sustainability of our resources is dependent on reducing the consumption of virgin resources, and one method of achieving this goal is product remanufacturing. It is already established that the production of remanufactured products costs less than that of creating a new one, however the effects of this on warranty costs are now considered. Due to consumer perceptions of the quality of remanufactured products, it cannot be sold for the same price as a new product. In addition, the warranty costs the manufacturer incurs will also be higher. This paper proposes a mathematical model for the optimal one-dimensional unlimited free-replacement warranty policy with replacements carried out with reconditioned products. Numerical optimization is used to compute the optimal warranty and production parameters which maximize the total profit.

The Effects of a Renewing Free-Replacement Warranty on the Discrete Age Replacement Policy

This paper presents the effects of a renewing free-replacement warranty (RFRW) on the age-replacement policy in a discrete time process. Consider a product that should be operating over an indefinitely long operation cycle n (n=1,2,...); under the discrete age-replacement policy, a product is replaced at cycle N (N=1,2,...) after its installation, or at failure, whichever occurs first. The cost models from the customer's perspective are developed for both warranted, and non-warranted products. The corresponding optimal replacement age N* (i.e., the optimal number of operation cycles for a preventive replacement) is derived such that the long-run expected cost rate is minimized. Under the assumption of the discrete time increasing failure rate, the existence and uniqueness of the optimal N* are shown, and the impacts of a RFRW on the optimal replacement policies are investigated analytically. The optimal N* for a warranted product is closer to the end of the warranty period than for a non-warranted product. Finally, a numerical example is demonstrated for the optimal policy illustration and verification. The observations from the technical analysis and numerical results provide valuable information for a buyer (user) to adjust the optimal age-replacement policy if a product is operating in discrete time under a RFRW.

A profit assessment model for equipment inspection and replacement under renewing free replacement warranty policy

Abstract For many types of equipment whose maintenance requires skilled labor or whose random failure may have serious consequences, such as aircraft engines, medical equipment and others, customers generally prefer to entrust maintenance activities to the manufacturer or any of its representatives. The latter must, in turn, provide the customer with a maintenance program that is economically viable for both parties. In this study, the customer and the manufacturer agree on what follows regarding a non-self-announcing failure equipment whose state is only known through inspection: during the warranty period, the manufacturer inspects the equipment according to a specified schedule which he establishes taking into account that the costs incurred for inspections and replacements are supported by him during the warranty period. After the expiration of the warranty, inspections and replacements are performed by the manufacturer and billed to the customer. Moreover, penalties related to inactivity periods between failures and their detection are always supported by the manufacturer. The warranty is applicable to any equipment replaced during the validity period of the service contract. This type of contract generates a profit for the manufacturer. In this paper, an analytical model taking into account the commitments of both parties has been developed. The model allows generating the instants (x1, x2,…, xn) at which the inspections must be performed and the corresponding expected profit for the manufacturer while considering the warranty period offered on the market for similar equipment. An algorithm has also been developed to generate the inspection instants given the costs structure and the lifetime probability distribution of the equipment. In a context where business models argue for a greater implication of suppliers towards their customers, the proposed decision model may be relevant and very useful.

Warranty servicing for discretely degrading items with non-zero repair time under renewing warranty

This paper considers a repair-replacement strategy for a special class of discretely degrading and repairable products under renewing free replacement warranty. Each product may experience N different working states with different exponential hazard functions, before the warranty contract expires. Once the item enters working state i (i=1,2,…,N), it can either fail or move to any of the subsequent working states with different probabilities, given that a transition has been made. In the former case, the best rectification action, replacement or minimal repair, regarding the failure status, i.e., the product degradation level at the failure time and the remaining warranty time, should be conducted to put the item into operation. It is assumed that replacement of the faulty item occurs instantly and the product warranty is renewed, but non-zero repair time has been included in the model. We derive the optimal replacement-repair policy to minimize the manufacturer’s expected warranty servicing cost per item sold. The Adomian decomposition method is used to find an analytic approximate solution for a special case with two working states. For N>2, a simulation based optimization method has been developed to analyze the expected warranty cost. Some numerical examples in each section are given to clearly demonstrate the application of this model.

Modeling Total Expenditure on Warranty Claims

We approximate the distribution of total expenditure of a retail company over warranty claims incurred in a fixed period [0, T], say the following quarter. We consider two kinds of warranty policies, namely, the non-renewing free replacement warranty policy and the non-renewing pro-rata warranty policy. Our approximation holds under modest assumptions on the distribution of the sales process of the warranted item and the nature of arrivals of warranty claims. We propose a method of using historical data to statistically estimate the parameters of the approximate distribution. Our methodology is applied to the warranty claims data from a large car manufacturer for a single car model and model year.

On optimal replacement-repair policy for multi-state deteriorating products under renewing free replacement warranty

In this paper a replacement-repair model is developed to study a renewing free replacement warranty (RFRW) for a class of multi-state deteriorating repairable products. After a replacement, the product warranty is renewed. Two parameters affect the manufacturer’s decision to minimally repair or replace a failed item: the product deterioration level at the time of failure and the remaining warranty time. We derive an optimal replacement-repair policy to minimise the expected warranty servicing cost per item sold. In the case of a product with two different working states, we are able to explicitly find the optimal values of the replacement-repair parameters using the Adomian decomposition method. In general, for N > 2 , it is impossible to find the optimal parameter values analytically. Hence, a computational procedure for finding these optimal values is proposed. For more clarification, numerical examples are also presented.

Warranty cost analysis for second-hand products using bivariate approach

This research aims to develop two stochastic models, based on the characterisation of the system failure and to compute the expected warranty cost for a second-hand product, when the products are sold with free replacement and/or pro rata warranties. A two-dimensional warranty, which focuses on both age and usage of the system, has been considered for the above warranty models. Further, a numerical example is provided to demonstrate the methodology of the developed model, using bivariate Weibull and exponential distributions. Also, the sensitivity analysis performed exhibits the effect of the parameters on the cost functions.

An Optimal Age for Preventive Replacement Under Fully Renewing Combination Free Replacement and Pro Rata Warranty

In the present article, an age-replacement policy is considered for non repairable products under the fully renewing combination free replacement and pro-rata warranty (FRW/PRW) policy. For the fully renewing FRW/PRW policy, whenever a product fails within the warranty period, it is replaced by a new one and a new warranty issued. Meanwhile, if the failure occurs during the first time interval (i.e., the free-replacement warranty (FRW) interval), replacement is made at no cost to the buyer; however, if the failure occurs during the second time interval (i.e., the pro-rata warranty (PRW) interval), replacement is made at a pro-rata cost to the buyer. Pre-determining the age for preventive replacement to be in a different certain interval, cost models from the buyer/user perspective are developed, and the corresponding local optimal replacement ages are derived such that the long-run expected cost rate is minimized. Then, the global optimal replacement age (i.e., without any constraint) is determined. Structural properties of these optimal policies are obtained and presented. Special cases of the model are also discussed. Finally, numerical examples are given for illustration, which provides a comprehensive study about the behavior of the optimal solution.

Optimal age for preventive replacement under a combined fully renewable free replacement with a pro-rata warranty

This paper focuses on an age-replacement policy for products under a new warranty strategy, which combines a fully renewable free replacement with a pro-rata warranty policy (called fully renewable FRW/PRW policy). For this combined warranty strategy, whenever a product fails within the warranty period, it is replaced by a new one and a new warranty is issued. Meanwhile, if the failure occurs during the first time interval (i.e., the free-replacement warranty (FRW) interval), replacement is made at no cost to the buyer; however, if the failure occurs during the second time interval (i.e., the pro-rata warranty (PRW) interval), replacement is made at a pro-rata cost to the buyer. Dividing the replacement age into three separate periods: within FRW, during PRW, and post-warranty. Then, given that the replacement age is in a certain interval, the cost model from the user/buyer perspective is developed, and the corresponding local optimal replacement age is derived such that the long run expected cost rate is minimized. Afterward, the global optimal replacement age is determined. Structural properties of these optimal policies are obtained and presented, and special cases of the model are discussed. Finally, a numerical example is given for illustration.

A general age-replacement model with minimal repair under renewing free-replacement warranty

A general age-replacement model in which incorporates minimal repair, planned and unplanned replacement, is considered in this paper for products under a renewing free-replacement warranty policy. For both warranted and non-warranted products, cost models from the user’s perspective are developed, and the corresponding optimal replacement ages are derived such that the long-run expected cost rate is minimized. The impacts of a product warranty on the optimal replacement model are investigated analytically. Furthermore, we show that the optimal replacement age for a warranted product is closer to the end of the warranty period than for a non-warranted product. Finally, numerical examples are given for illustration.

Optimal Age-Replacement Policy Under an Imperfect Renewing Free-Replacement Warranty

This paper investigates the effects of an imperfect renewing free-replacement warranty (RFRW) on the classical age-replacement policy for a product with an increasing failure rate. Under the imperfect RFRW, whenever a product fails during the warranty period, it is replaced by a repaired one from an infinite stock of refurbished items, at no cost to the purchaser, with a new full warranty. We assume that the failure potential of the repaired product is inferior to that of a new product; that is, the repaired product is less reliable than a new one. Long-run expected cost rates for the age-replacement policy are developed for two cases: when the preventive replacement age occurs before, and when it occurs after the warranty expires. The optimal replacement ages that minimize the cost rates are determined, and the impact of an imperfect RFRW on the optimal replacement age is illustrated with a numerical example. We review the literature dealing with warranty and maintenance against this framework, and conclude with some discussions on topics for research in the future. The imperfect RFRW proposed in this paper is practical, and novel; and this study represents a useful extension of Yeh that promises to be of interest to reliability engineers, managers, and theoreticians.

Product warranty: modelling with 2D-renewal process

The study of product warranty is of interest to manufacturers for several reasons. Paid claims are a cost of doing business and a liability incurred by the manufacturer at the time of sale. For these reasons, estimating and forecasting warranty expenses is of interest. Also, warranty data provides information about the durability of products in the field and, therefore, is of interest to engineers. Here we emphasise two-dimensional warranties, like automotive warranties, that guarantee free repairs subject to both age and mileage limits. We aim to evaluate the average warranty expenses under a two-dimensional non-renewing free replacement warranty policy using real warranty data. We derive a numerical procedure for the evaluation of the two-dimensional renewal function and use it for the warranty cost analysis. In addition, we test whether the available data can be considered as coming from a two-dimensional renewal process.

Optimal age-replacement policy for renewing warranted products

Preventive replacement is a well-known topic in the literature of operational research and reliability. The effects of a renewing free-replacement warranty (RFRW) on the age replacement policy for a repairable product with a general failure model are discussed. There are two types of failure when the product fails. One is type I failure, which can be removed by a minimal repair, and the other is type II failure, which can be removed only by a replacement. After a minimal repair, the product is operational but the failure rate of the product remains unchanged. For both warranted and non-warranted products, cost models are developed and the corresponding optimal replacement ages are derived based on the minimized long run expected cost rate. The impacts of the RFRW on the optimal replacement age are investigated analytically. Finally, numerical examples are given for the purposes of illustration.

Optimal age-replacement policy for repairable products under renewing free-replacement warranty

This paper investigates the effects of a renewing free-replacement warranty (RFRW) on the age replacement policy for a repairable product with a general failure model. In the general model, there are two types of failure when the product fails. One is type I failure (minor failure), which can be removed by a minimal repair; and the other is type II failure (catastrophic failure), which can be removed only by a replacement. After a minimal repair, the product is operational but the failure rate of the product remains unchanged. For both warranted and nonwarranted products, cost models are developed, and the corresponding optimal replacement ages are derived such that the long-run expected cost rate is minimized. The impacts of the RFRW on the optimal replacement age are investigated analytically. Finally, numerical examples are given for illustration.

On a conjecture of optimal repair-replacement strategies for warranted products

Under a free replacement warranty policy, the manufacturer has the option of rectifying a failure by either repairing the failed item or replacing it with a new one. In [N. Jack, F. Van der Duyn Schouten, Optimal repair-replacement strategies for a warranted product, Int. J. Prod. Econ. 67 (2000) 95–100] a conjecture is made on the optimality of an age-limit policy: there exists a control limit AL ( t ) , such that a minimal repair is performed on failure with t time units remaining in the warranty period if the age of the failing unit is less than or equal to AL ( t ) . In this paper, we prove that this conjecture is indeed correct. Moreover, we show that for a more general model where the repair cost is random, a generalized repair-cost-limit policy is optimal, and the age-limit policy becomes its degenerated form. Numerical examples are provided to illustrate the computational algorithm and to compare the performance of these policies.

Warranty cost analysis: quasi‐renewal inter‐repair times

PurposeTo provide a brief introduction to warranty analysis and a classification of general repairs. To introduce the notion of accelerated probability distribution and use it to model imperfect warranty repairs.Design/methodology/approachThe notion of accelerated probability distribution is discussed and its similarity with quasi‐renewal and geometric processes is observed. An approach to modeling imperfect warranty repairs based on the accelerated probability distributions is presented, and the corresponding expected warranty cost over the warranty period under non‐renewing free replacement warranty policy is evaluated.FindingsIt is observed that quasi‐renewal and the geometric processes are equivalent. Using data from an existing warranty database it is shown that the inter‐repair times form a quasi‐renewal process. The corresponding expected warranty cost over the warranty period under a non‐renewing free replacement warranty policy is evaluated.Research limitations/implicationsThis approach is applicable only if the cost of the warranty repair is an increasing function of the number of repairs.Practical implicationsProvides a useful approach to modeling inter‐repair times incorporating the idea of imperfect repairs in practice.Originality/valueProvides an approach to model imperfect warranty repairs and to evaluate the corresponding expected warranty cost.