Warranty Cost Model Research Articles

Joint optimization of two-dimensional warranty period and maintenance strategy considering availability and cost constraints

Abstract Warranty can improve customer satisfaction and increase product sales, but it will bring additional economic burden to manufacturers, so making reasonable warranty decisions is particularly important. The current research focuses more on the interests of manufacturers, while there is less attention paid to indicators that consumers are concerned about, such as system availability. To solve this problem, a joint optimization model of the two-dimensional warranty period and preventive maintenance (PM) strategy considering availability and cost constraints was established. Based on the failure dependence analysis of multi-component systems, the actual failure rate function is constructed by using the failure dependence coefficient matrix. Based on the comprehensive consideration of imperfect PM and minimum maintenance, the two-dimensional warranty cost model and system availability model are established, respectively. Aiming at maximum availability and considering the warranty cost budget constraint, a joint optimization model of the two-dimensional warranty period and PM strategy was built, and a model-solving algorithm combining grid search and binary search was introduced. The effectiveness of the model is verified by the case analysis, and the necessity of the PM strategy and considering failure dependence are reflected in the model comparative analysis and parameter sensitivity analysis. Finally, reasonable suggestions are put forward for manufacturers’ warranty decisions through the result analysis.

Opportunistic Maintenance Strategy for Complex Equipment with a Genetic Algorithm Considering Failure Dependence: A Two-Dimensional Warranty Perspective.

Complex two-dimensional warranty equipment is usually composed of many multi-component systems, which include several key components. During the warranty period, conducting maintenance according to the preventive maintenance plan of each component will increase the warranty costs. Opportunistic maintenance is an effective approach to combine the preventive maintenance of each individual component, which can reduce the warranty cost and improve the system availability. This study explored the optimal opportunistic maintenance scheme of multi-component systems. Firstly, the failure rate model and reliability evaluation model of the multi-component system considering failure dependence were established. Secondly, the preventive maintenance plan of each individual component was determined, with the goal of obtaining the lowest warranty cost per unit time in the component life cycle. Thirdly, the preventive maintenance work of each individual component was combined, and the two-dimensional warranty cost model of the multi-component system was established according to the reliability threshold when performing opportunistic maintenance. In the experimental verification and result analysis, the genetic algorithm was used to find the optimal opportunistic maintenance scheme for the power transmission device. The comparative analysis results show that the opportunistic maintenance scheme reduced the warranty cost by 5.5% and improved the availability by 10%, which fully verified the effectiveness of the opportunistic maintenance strategy.

Optimal warranty policy for repairable products with a three-dimensional renewable combination warranty

Nowadays, the post-sale warranty has become a crucial marketing strategy, and how to design and determine the optimal warranty policy has become one of the important issues for manufacturers. In the existing literature, warranty design and optimization mainly focus on one-dimensional and two-dimensional policies. However, as competition intensifies and customer requirements increase, product warranty terms usually involve three or more factors. In this paper, we propose a three-dimensional warranty policy for repairable products, in which limitations on failure time, repair time, and repair number are integrated. Considering the conflict between manufacturers and consumers, a novel renewable combination replacement warranty is further designed. By developing the corresponding sale price and warranty cost models, a profit optimization model is proposed. From the manufacturer’s perspective, the optimal warranty policy is obtained by maximizing the expected profit. A numerical example with sensitivity analysis and comparison studies is conducted to illustrate the proposed model. The results show that the proposed warranty policy can make the manufacturer more profitable and help to reduce the conflict between the manufacturer and the consumer.

Two-Dimensional Extended Warranty Strategy for an Economic Dependence Multi-Component Series System With Grid Search Algorithm

Extended warranty is an optional contract that often provides additional protection for users after the basic warranty expires. Considering the high warranty cost borne by manufacturers and the lack of system availability guarantee, the present study proposes a two-dimensional extended warranty approach for a multi-component series system considering economic dependence. Based on the imperfect preventive maintenance model and the combination of free warranty and pro-rata warranty policies, the manufacturer’s and user’s warranty cost model and availability model for a single component are established. Considering the economic dependence between multi-components, the preventive maintenance of each component is combined using the grouping maintenance approach. In the case study, we consider the reconnaissance equipment as the research object and use the grid search method to obtain the two-dimensional extended warranty scheme of reconnaissance equipment considering economic dependence. Comparative and sensitivity analyses verify that the approach can effectively reduce the extended warranty cost of the manufacturer and improve the availability of the multi-component system. Additionally, the approach can provide support for warranty cost calculation and system availability estimation under different extended warranty periods.

Random periodic replacement models after the expiry of 2D-warranty

The rapid development of advanced sensor technologies makes it possible to monitor the working cycle of products, which enables manufacturers to design warranty policies by monitoring working cycle during the warranty period and facilitates consumers to carry out post-warranty maintenance by tracking the post-warranty working cycle. The optimal warranty and maintenance policies considering random working cycles is rarely studied in existing literature. In this article, we make contribution by incorporating the limited number of random working cycle into a warranty term and proposing two types of two-dimensional warranty, which guarantees the product reliability performance by monitoring working cycle during the warranty period. Based on the proposed warranty policy, we further investigate the optimal post-warranty random maintenance policies from consumers’ perspective, including the random periodic replacement first and replacement last policies, which enhances the post-warranty reliability by monitoring the post-warranty working cycle. The warranty cost model is established under each proposed warranty policy, and the cost rate is evaluated under each post-warranty random maintenance policy. Some special cases of the established models are provided and discussed. By numerical experiments, we conduct sensitivity analysis of the proposed warranty and post-warranty random maintenance polices.

Dynamic pricing of two-dimensional extended warranty considering the impacts of product price fluctuations and repair learning

Product prices fluctuate dynamically with changes in market supply and demand. This poses a dilemma for dealers, that is, dealers need to establish a dynamic extended warranty (EW) pricing strategy based on the fluctuations in product prices to attract consumers. To address this challenging issue, we establish a dynamic integration model to derive optimal product prices and two-dimensional (2D) EW prices in a multistage dynamic market environment to maximize the dealer’s expected discounted profit during the product life cycle. In order to explore the dynamic influence mechanism between reliability engineering factors and market elements, this model combines the warranty cost model influenced by reliability related repair learning characteristics and the 2D EW demand model influenced by product price fluctuations. The model allows dealers to identify the relationships among various factors, including repair learning characteristic, production scale effect, product cost, EW cost in product reliability level, and fluctuating product demand and EW demand in market demand level, and more important, their effects, on the dealers’ profit. The necessary optimality conditions and case study are conducted for static and dynamic markets.

Two-stage renewing warranty policy with the threshold of maintenance times

Compared with non-renewing warranty, renewing warranty is more attractive to the customers. To reduce the possible cost pressure of the manufacturers, this study proposes a novel two-stage renewing warranty model with a threshold of maintenance times. Based on a preset allocation ratio, the warranty period is divided into two stages, i.e. the renewing warranty stage and the minimal repair warranty stage. In the first stage, when the number of maintenance actions exceeds the given threshold, the failed item will be replaced with a new one and attached with a new warranty period; otherwise, the product will enter the second stage when its operating time exceeds the time span of the renewing warranty stage. When the product fails in the second stage, only minimal repair is performed. On this basis, four types of maintenance schemes are proposed, and the corresponding warranty cost and profit models are developed to optimise the warranty policy. A numerical example is provided to illustrate the effectiveness of the proposed model, and sensitivity analysis is conducted. The results show that by considering the threshold of maintenance times, the warranty cost can be reduced and the manufacturer's expected profit can be improved simultaneously.

Design of customized two-dimensional extended warranties considering use rate and heterogeneity

Extended warranties have become a rich source of profits for manufacturers. In the current marketplace, two-dimensional extended warranties are often sold to all customers with a fixed coverage region and the same price. However, customers are heterogeneous, as they have different use rates and failure history, which significantly affects the cost of the extended warranty. In this study, we first propose a customized extended warranty strategy that takes into account the use rate of the customer. Under the strategy, we develop a warranty cost model to compute the expected repair cost and the expected profit of the manufacturer, based on which the optimal price for the customized extended warranty can be determined. Building upon this model, we further propose a policy that makes use of both the customer’s use rate and the product’s failure history. We conduct a comprehensive numerical study to compare the two proposed policies with the prevailing fixed-region strategy. The results reveal that the customized policies are better than the prevailing policy in terms of fairness, flexibility, and profitability.

Design of differentiated warranty coverage that considers usage rate and service option of consumers under 2D warranty policy

Warranty service providers usually provide homogeneous warranty service to improve consumer satisfaction and market share. Considering the difference of consumers, some scholars have carried out studies on maintenance strategies, service pricing, payment method, claim behaviour and warranty cost analysis in recent years. However, few scholars have focused on the differentiated coverage of warranty service that considers usage rate and service option of consumers. On the basis of previous classification criteria on usage rate, this paper divides consumers into heavy, medium and light usage rate groups with clear boundaries. To avoid discrimination in warranty service, this study divides 2D warranty coverage into disjoint sub-regions and adopts different maintenance modes in each sub-region. By formulating and calculating warranty cost model under warranty cost constraints, we can obtain the maximum warranty coverage under usage rate \begin{document}$ r $\end{document} . Therefore, differentiated warranty scope for consumers in the three groups can be proposed, whilst consumers can choose the most suitable warranty service according to their usage rate. Evidently, the proposed warranty strategy can provide flexible warranty service for consumers, meet the requirements of the warranty cost constraints of warranty service providers and enable enterprises to occupy a favourable position in the market competition.

Two-dimensional extended warranty strategy including maintenance level and purchase time: A win-win perspective

In practice, consumers need to decide whether and when to purchase extended warranty (EW), and there are many factors that influence this decision, such as product reliability and preventive maintenance (PM) conditions, etc. Under the consideration of consumer PM options, purchase time of EW and consumer usage rate diversity, this research first determines the product failure processes based on Generalised Polya Process (GPP) failure mode. Moreover, considering the impact of consumers purchasing decision of EW on warranty costs, we establish warranty cost models based on the product failure processes. Finally, given the warranty cost model, win-win EW price decision models are proposed in the product life cycle. A real case from a leading automobile manufacturer of China is presented to illustrate the application of the proposed model. The isoline of win-win regions and win-win EW intervals are obtained. Also, two management recommendations are given to help manufacturers make relevant decisions.

Warranty Cost Models using Accelerated Life Tests on Dagum Distribution

Warranty one of the main factors which effect on the decision to purchase any product whether it is non repairable or repairable, therefore, in market the manufacturers can compete by using warranty service. The cost of warranty are wanted to predict which are mirrored on the price and profitability of products. To achieve this goal, the research is concerned with predicting the cost of the two common types of warranty models which are free rebate warranty and pro-rata rebate warranty when The lifetime of items is assumed to follow Dagum distribution. The constant stress partially accelerated life tests based on type II censoring is used. Maximum likelihood method is used to estimate the model parameters and acceleration factor of lifetime distribution from the test data. Confidence Interval for the model parameters are constructed using normal approximation and bootstrap method. Finally, Some numerical illustrations are provided.

Two-Dimensional Product Warranty Cost Model under Preventive Maintenance Time Constraints

Two-Dimensional Product Warranty Cost Model under Preventive Maintenance Time Constraints

Minimal repair warranty cost model and optimal periodic replacement policy for repairable products based on generalized exponential distribution

Minimal repair warranty cost model and optimal periodic replacement policy for repairable products based on generalized exponential distribution

A comprehensive analysis of warranty claims and optimal policies

Nowadays many products, such as 3C products (Computer, Communication and Consumer Electronics) and cars, consist of software and hardware. The causes of warranty claims of such products may be attributed to software specific failures, hardware specific failures, software-hardware interaction failures and human errors. Apparently, those causes may be dependent. For example, one may claim warranty due to the malfunction of the embedded software in a product item and then the entire item may be replaced. Nevertheless, the existing research on warranty management studies mainly concentrates on warranty analysis of hardware subsystems, assuming that the warranty claims are statistically independent of those caused by the failures of software subsystems or human factors, that is, the interactions between those causes are neglected.This paper investigates warranty costs incurred due to those three subsystems with a focus on their interactions. It estimates the costs due to different cause, develops integrated warranty cost models and optimises warranty policies considering the above possible combinations. Numerical examples are given to illustrate the proposed models.

Determination of the warranty service method switch time of old generation products after new generation products launched

PurposeThe purpose of this paper is to build a warranty cost model for consumer electronics with short lifecycle and frequently upgraded process in generations. Meanwhile, a new warranty service method of replacing the failed old generation (OG) products by new generation (NG) products is proposed to cease the service capability for the OG products from manufacturers’ viewpoint.Design/methodology/approachA model is built to find an optimal time to switch to the new warranty service method to minimize the warranty cost of the OG products. The inventory cost of spare parts of OG products for warranty, repair cost and manufacturing cost of NG products are taken into account. Meanwhile, a mixed strategy is studied by providing options to customers for replacing their failed OG products with NG products by paying a discounted price of the OG products. Moreover, numerical experiments are conducted to test the effects of different parameters on the optimal solutions.FindingsSolutions to the proposed model are discussed with analytic method and it is proved that the optimal solution exists in the considered situations. The mixed strategy considering the willingness of customers can result in the reduction of the warranty cost.Originality/valueThis paper analyzes the situation that more than one generations of products are in the marketplace simultaneously. Furthermore, this work makes a useful contribution for manufacturers to decrease their warranty cost by changing the service method, and provides the optimal warranty strategy for manufacturers considering the willingness of customers.

Hybrid repair warranty cost model for repairable products based on generalized exponential distribution with simulation study

Hybrid repair warranty cost model for repairable products based on generalized exponential distribution with simulation study

Warranty Cost Modeling and Warranty Length Optimization Under Two Types of Failure and Combination Free Replacement and Pro-Rata Warranty

The product warranty has become an indispensable facet of business operations. Burn-in is effective at eliminating infant mortality and improving operational reliability levels for consumers. This paper considers the influence of different failure states and different phases of product reliability and warranty policies on warranty costs from predelivery inspection to the end of the warranty period. We then propose a comprehensive warranty cost model that considers burn-in, free replacement warranty and pro-rata warranty as three phases for repairable products presenting two types of failure (minimal and catastrophic failure) that involve minimal repair and replacement, respectively. Warranty costs are the result of a combination of the three phases, where two types of failure occur individually or simultaneously. Moreover, we developed a framework for the modeling process of warranty costs, and the effects of various parameters, such as the burn-in time, warranty period, and distribution function on warranty costs, were analyzed. Finally, a practical case was examined by using a warranty cost model, and through an after-sales service data analysis, we obtained the failure rate distribution and optimal warranty length by minimizing the average warranty cost, which can serve as a reference for manufacturers when developing warranty policies.

A Generalized Age Replacement Policy for Systems Under Renewing Repair-Replacement Warranty

This paper presents a warranty cost model for repairable products when an age replacement policy is adopted in conjunction with the renewal of a minimal repair-replacement warranty. A study of the optimal choice of the preventive replacement age is also presented. When renewing a minimal repair-replacement warranty, either minimal repair is carried out or the product is replaced, depending on the length of repair time when the product failures occur during the warranty period. In this study, we develop mathematical formulas to evaluate the long-run expected cost rates during the life cycle of the product under the proposed cost models and determine the optimal preventive replacement ages by minimizing the objective functions. Furthermore, the effects of the renewing warranty on the optimal preventive replacement age and its corresponding expected cost rate are investigated for various situations regarding the warranty policy. This study extends the existing results on the age replacement policy by considering situations that are more practical, where both minimal repair and replacement are considered simultaneously upon product failure. Assuming that the product deteriorates with age, we illustrate our proposed cost model and its optimization using numerical examples and observe the impact of relevant parameters on the optimal solutions regarding the preventive replacement age.

Optimal Two Dimensional Preventive Maintenance Policy Based on Asymmetric Copula Function

For some kinds of products, the consumers have strict requirements to the reliability of these products in the based warranty period. Then the manufacturer is inclined to provide the two-dimensional preventive maintenance policy to take the usage degree of the product into account. As a result, two-dimensional preventive maintenance policy in the warranty period has recently obtained increasing attention from manufacturers and consumers. In this paper, we focused on the optimization of based warranty cost and proposed a new expected based warranty cost model considering the two-dimensional imperfect preventive maintenance policy from the perspective of the manufacture. Asymmetric copula function was applied to modeling the failure function of the product. And the optimal two-dimensional preventive maintenance period was obtained by minimizing based warranty cost. At last, numerical examples are given to illustrate the proposed models, of which the results prove the model effective and validate.

An attractiveness index based approach for warranty optimization

Purpose – The purpose of this paper is to develop an attractiveness index-based warranty cost model considering decision variables as design alternatives, warranty duration and support level. Design/methodology/approach – A warranty optimization approach is illustrated using a real life example of an automobile engine with Mean Time Between Failures and Warranty Attractiveness Index as constraints. Findings – It will help to improve the customer satisfaction by giving a more attractive warranty compared to that being offered by the competitors. Practical implications – Approaches that consider the effect of decision variables on attractiveness of a warranty policy in a quantitative manner have received relatively less attention. The paper attempts to capture the attractiveness of warranty from the manufacturer as well as customer point of view. Originality/value – The proposed approach will help manufacturers to take appropriate decisions related to warranty parameters and component selection at the design stage.