Warranty Model Research Articles

Customizing Random Replacement Model and Flexible Warranty Model from the Perspective of Screening Reliability

In the present academic and engineering fields, every measure function of product reliability is modeled and estimated from the statistical perspective. These indicate that there universally exist differences in the reliabilities of new identical products that survive the burn-in test. On the basis of the differences in the reliabilities of new identical products, designing through-life maintenance models for managing the different reliabilities is a very practical topic for engineering fields. In this study, a random warranty model and a random maintenance model are designed by screening product reliabilities to manage the through-life reliabilities of products. In the random warranty model, the coverage areas of the warranty are set as the different areas for applying flexibility to them to control the warranty costs of new identical products with different reliabilities, and thus this warranty is called a flexible random free repair warranty (FRFRW) model. In the random maintenance model, two random replacement actions are customized by setting different replacement ranges for controlling maintenance costs and lengthening service life. This random maintenance model is called a customized random replacement (CRR), which is used to manage product reliabilities after the FRFRW expiration. These two random models are characterized from the mathematical perspective, and some derivatives of both are provided to model other maintenance problems. The characteristics of every model and the performance of the CRR are explored and illustrated through numerical experiments. The results show that the CRR is superior to random age replacement.

Study of a Random Warranty Model Maintaining Fairness and a Random Replacement Next Model Sustaining Post-Warranty Reliability

With the help of advanced digital technologies, product managers can use monitored mission cycles to sustain product reliability. In this study, a random warranty model and a random replacement next (RRN) model are designed to sustain the through-life reliability of the product with monitored mission cycles. The designed random warranty, called a two-stage two-dimensional free repair warranty (2DFRW), can be carried out to sustain the reliability of the product during the warranty stage. In this warranty, ‘whichever occurs first and last’ is used to distinguish the coverage ranges of the latter stage warranties, which is to maintain the warranty fairness by removing the inequity of the former stage warranty. The RRN can be performed to sustain post-warranty reliability, which defines that if the limited number of mission cycles is completed before a working time, then the product will be replaced at next mission cycle completion to extend remaining service life; otherwise, the product will be replaced at a working time. Under the case of the two-stage 2DFRW, the cost rate of the RRN is constructed based on the renewable reward theorem. By simplifying the parameters, some derivative models of the cost rate are presented. Numerical analysis is performed to explore characteristics.

Joint optimization of two-dimensional preventive maintenance parameters, technology level and product price under continuous usage rate and agent warranty services

ABSTRACT An efficient two-dimensional warranty model with the possibility of extending after-sale services to the end of the product life is developed in which services in the extended warranty period are assigned to an agent as a transaction side. To control product failures, two factors are taken into account in the proposed model: (1) the manufacturing technology level which results in a different reliability outcome for the product; and (2) a two-dimensional maintenance policy with respect to customers’ usage rate. In addition, in order to adapt the model to reality, we depart from the literature by considering the continuous nature of the usage rate variable. Finally, in order to confirm the effectiveness of the model, some comparative studies are carried out. The obtained results reveal that preventive maintenance (PM) activities lead to a considerable rise in cost savings. Besides, in comparison with one-dimensional PM policies based on product age and usage, using a two-dimensional PM policy improves the economic criteria. Furthermore, the presence of the agent has a great impact on reducing the customer’s cost as well as the failure rate after the basic warranty period.

Warranty Cost Analysis for Multi-State Products Protected by Lemon Laws

The implementation of lemon laws in America has played an important role in improving the quality of after-sales service. Nowadays, many countries, such as China, Canada, Europe, Australia, Singapore, and South Korea, have adopted lemon laws in various industries to protect the interest of consumers. From the perspective of manufacturers, accurate estimation of the cost of the warranty service is of great importance in guiding product pricing, quality control, and design of warranty policies. According to the terms of different lemon laws, two warranty models considering the repair time and numbers for failures are proposed in this paper. Products under these models are multi-state, and Markov processes are used to model the degradation processes of products. In the first model, a product will be replaced by a new one if the time for a repair or the number of failures exceeds their respective thresholds over the warranty period. Under the second model, both catastrophic and minor failures are considered. A product will be replaced if one of the following three conditions is met over the warranty period: the time of one repair action (regardless of failure type) is longer than a time threshold; the number of minor failures is larger than a preset threshold; a catastrophic failure occurs. The expected warranty cost rates under the two proposed warranty models are derived under the assumption of renewable warranty terms. Numerical examples are given to illustrate the results obtained.

A Flexible Two-Dimensional Warranty in Optimizing the Dealer and Customer Satisfaction

Nowadays, in competitive market, in order to increase confidence in the quality of products, dealers set a warranty for selling them. This issue seems to have a tremendous effect on attracting more customers, especially when it comes to purchasing second-hand products. In this regard, this paper tends to present a two-dimensional warranty policy for second-hand products containing age and usage in two cases, L-shaped and Rectangular. Since maximizing customer repurchase probability is directly linked with dealer’s profit as well as minimizing costs, dealers ought to consider customer satisfaction. In fact, customer satisfaction depends on warranty length and the expected numbers of failures in the post-warranty period. To demonstrate the characteristics of the model, two comparative studies are conducted to present the effect of bi-objective function on warranty models. Finally, in order to extend insights into the matter, a sensitivity analysis is carried out on the varying parameters.

A Bivariate Optimal Random Replacement Model for the Warranted Product with Job Cycles

A monitoring system (MS) has been used to monitor products’ job cycles. It is indicated that by incorporating the job cycle into the product’s life cycle, warrantors can devise novel warranty models and consumers can define and model random maintenances sustaining the reliability of the product through warranty. In this study, by incorporating limited job cycles and a refund into the traditional free repair warranty, a two-dimensional free repair warranty with a refund (2DFRW-R) is devised for guaranteeing the product reliability to consumers. Under the condition that 2DFRW-R is planned to guarantee product reliability, a bivariate random periodic replacement (BRPR) (i.e., a random periodic replacement where the accomplishment of the Nth job cycle and the replacement time T are designed as replacement limits) is modeled to sustain the post-warranty reliability from the point of view of the consumer. From the point of view of the warrantor, the warranty cost related to 2DFRW-R is derived, and the characteristics of 2DFRW-R are explored. From the point of view of consumers, the expected cost rate related to BRPR is constructed, and the existence and uniqueness of the optimal BRPR are summarized as well. By discussing parameters, several special cases are derived. The characteristics of the proposed models are analyzed in numerical examples.

Optimal condition-based warranty policy for multi-state products with three guarantees service

ABSTRACT Within a certain period of time after products are sold, many manufacturers offer free repairing, replacing and refunding for the defective products, referred to as three guarantees service. Under the assumption that the working states of the product can be partitioned into three non-overlapping sets and its degradation can be modeled by homogeneous Markov chain, a three-stage and conditioned-based warranty model is proposed. Under the model, the whole warranty period is divided into a compulsory replacement period, a condition-based maintenance period, and a minimal repair period. Over the condition-based maintenance period, depending on the state set that the working state before the failure belongs to, failed products are rectified minimally, imperfectly, replaced by an identical one and the warranty terms are renewed, respectively. Markov process and renewal process theories are used to analyze the failure process and the warranty servicing cost over the whole warranty period. Based on double Riemann sum, a recursive algorithm for finding the optimal partition method of working states and the warranty period is proposed. A numerical example is given to illustrate the validity of the warranty strategy.

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.

Optimal maintenance strategies for coherent systems: A warranty dependent approach

We investigate optimal maintenance models for warranted coherent systems consisting of n components (n≥1). The system is under a warranty policy with two consecutive phases under which the manufacturer’s commitment goes in two different forms. In Phase I, upon the system failure, the failed components are replaced with new ones and a corrective maintenance is conducted on the whole system. If the system failure occurs during Phase II, only minimal repair is performed on the components. Following expiration of the warranty time, the customer is solely responsible for maintaining the system who, for a fixed length of the time period, replaces the failed components and preventively maintains the system at the end of such period. During the maintenance period, the same maintenance as that of in Phase I of the warranty period is conducted. Such a maintenance model can be considered as a generalization of the age-based maintenance model for a system under warranty model. We investigate, from the manufacturer’s and customer’s perspectives, the optimal length of each phase in the warranty period, and the optimal planned time of preventive maintenance based on some imposed cost functions, respectively. Numerical examples are provided to illustrate the proposed optimal maintenance models.

A customized warranty model by considering multi-usage levels for the leasing industry

In addition to the high acquisition cost of large-scale equipment, firms may also have to pay for costly repairs and maintenance for subsequent conditions of inadequate reliability and malfunctions. Therefore, instead of purchasing, many firms have considered obtaining large-scale equipment through leasing. Considering customization for heterogeneous consumers, which allows consumers to choose different leasing programs, firms can meet customer demands by enhancing their degree of satisfaction. This study considers customized leasing services and develops a pricing model for the leasing industry, in which the heterogeneity of customers, two-dimensional warranties, and preventive maintenance are taken into account for the purpose of establishing a customized leasing contract. Customers are categorized into three types according to their levels of usage of the leasing product: high, moderate, and low, and the lessor respectively provides the three corresponding leasing services. The various leasing services consist of different lease fees and preventive maintenance policies. The objective of this study is to assist the lessors in developing an optimal lease contract for heterogeneous lessees with different usage types. The results of the study show that when the penalties for higher usage customers who purchase lower-usage services are managed, offering a customized lease contract will elevate lessee willingness toward purchasing lease services, and therefore increase the total profit of the lessor.

Optimal maintenance strategies for warranty products with limited repair time and limited repair number

Nowadays, to protect the interests of customers, many warranty policies take into account the limit of repair time and the limit of repair number. Under a rebate warranty policy, the seller has to give a refund to the customer according to the rebate warranty contract if the number of product failures or a single repair time for failure exceeds some certain limits. Minimal repair is conducted when the product fails, and the repair cost is charged to seller during the warranty period. After warranty expires, the product continues operating for a period of time before being replaced. The repair cost during the post-warranty period is undertaken by the customer. From the customer’s perspective, the expected life cycle cost rate of the warranty product is derived. By minimizing the expected cost rate, the existence and uniqueness of the optimal maintenance strategy for the warranty product are proven theoretically. Finally, as an example, the warranty car under the protection of “lemon laws” is studied to illustrate the proposed rebate warranty model.

Optimal replacement strategies for warranty products with multiple failure modes after warranty expiry

The optimal replacement problem for a warranty product subject to (M + 1) types of mutually exclusive failure modes, including M repairable failure modes and a catastrophic failure mode, is investigated in this paper. When the product fails with a repairable failure mode, a minimal repair will be conducted to remove the failure. However, if a catastrophic failure mode occurs, the failure product can only be replaced by a new one. Within the warranty period, the seller needs to complete each failure repair within a repair time limit. Once a failure cannot be repaired within the stipulated time, under the rebate warranty, the customer is refunded a proportion of the sale price of the product based on its working time, and the warranty terminates simultaneously; or under the free replacement warranty, the seller is obligated to provide a new product at no charge to the customer. Under both the warranty policies, the repair cost is free of charge to the customer within the warranty time, while the customer is responsible for all the cost for repairs within the post-warranty time. From the customer’s point of view, the expected life cycle cost rate of the product under the rebate and free replacement warranty are respectively derived. The existence and uniqueness of the optimal replacement strategies after warranty expiring are also proved theoretically by minimizing the cost rate. Finally, we give numerical examples to illustrate the two warranty models and show the effectiveness of proposed strategies.

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.

Warranty assessment of photovoltaic modules based on a degradation probabilistic model

AbstractEvaluating the probability of failure of a product during the warranty is key to estimating the cost of its entire life cycle. Photovoltaic (PV) modules are the most reliable elements of a PV system, and their high reliability translates into long warranty periods (typically 25 to 30 years). The number of PV modules that fail during warranty and when they failed is an important issue to estimate the life cycle cost of PV modules. In this paper, we propose a coupled degradation‐warranty model for PV modules. The proposed model is aimed to assess the probability of failure over time covered by warranty based on degradation data. This allows us to estimate the time of PV modules failure covered by the warranty. Although the warranty model has been applied to some forms of degradation and sales functions, our method can be applied to any real application. This allows the key parameters of the warranty to be obtained in a simple way. The required degradation parameters to fulfill warranty depend on the allowable ratio of warranted elements. However, the main conclusion of the influence of degradation rates on warranty is that it is not possible to fulfill 25 years of warranty if degradation rates are larger than 0.8%/year. The required degradation rates values, for 25 years of warranty, will be lower than 0.5%/year if the allowed warranted element is in the range of 1%.

Optimal Strategy for a Closed-Loop Supply Chain Considering Recycling and Warranty Channels

In this paper, four closed-loop supply chain (CLSC) game models with different recycling channels and warranty channels are proposed: (a) manufacturer recycling and warranty model, (b) manufacturer recycling and retailer warranty model, (c) retailer recycling and manufacturer warranty model and (d) retailer recycling and warranty model. The impacts of different recycling channels and warranty channels on the manufacturer, retailer and entire supply chain system are systematically analyzed from the perspective of the consumers, CLSC members and environment. The optimal strategies for remanufacturing systems under different channels are discussed and two contracts are proposed to coordinate supply chain members. By comparing and analyzing the optimal equilibrium solutions for different scenarios, the following conclusions are obtained: (1) The retailer recycling and warranty mode ( $$R-R$$ ) not only extends the warranty period of the product, but also improves the recovery rate of the CLSC system. (2) Under certain sharing ratios, the revenue-sharing contract and cost-sharing contract can effectively coordinate the manufacturer and retailer in the worst scenario. (3) Compared with the manufacturer recycling mode, the optimal profit of each CLSC member under the retailer recycling mode is significantly higher. Eventually, a set of numerical examples is provided to verify the above conclusions and conduct the sensitivity analysis on the optimal decisions in the proposed four different remanufacturing scenarios.

A complimentary extended warranty: Profit analysis and pricing strategy

This paper aims to investigate the emerging trend of a new warranty policy in industries, namely, complimentary extended warranty. For the warranty with complimentary extended service, customers can enjoy a free extended warranty if they register online before expiration of the base warranty. At present, with frequent technological innovations, customers are more willing to replace the product instead of repair, which makes traditional warranty less attractive. Since the warranty with complimentary extended service does not charge extra fees for the customers and the option of online registration is open to customers, it can attract a broad range of customers. Compared with traditional warranties, the proposed warranty provides flexibility for customers in their post-purchase choice of online registration. We develop a warranty model to investigate the popularity of the warranty. It turns out that the proposed warranty model exhibits advantages over the traditional warranties. The proposed warranty is profitable for risk averse customers and for products that heap benefits from customer information. We design and price the warranty for unit product when the customers have heterogeneous risk attitudes. In addition, we analyze the total profit and determine the optimal selling price considering the customer demand. Finally, a numerical example is presented to illustrate the effectiveness of the proposed warranty policy.

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.

새로운 연장된 이단계 보증모형에 대한 보증비용분석

새로운 연장된 이단계 보증모형에 대한 보증비용분석

Pricing and warranty decisions in a two-period closed-loop supply chain

For a two-period closed-loop supply chain (CLSC) consisting of a manufacturer and a retailer, Stackelberg game analyses are conducted to examine pricing and warranty decisions under two warranty models depending on who offers warranty for new and remanufactured products and the corresponding benchmark models with a warranty for new products only. Next, we identify the conditions under which warranty for remanufactured products is offered and investigate how this warranty affects the CLSC operations. Subsequently, comparative studies are carried out to examine equilibrium decisions, profitability and consumer surplus of the CLSC between the two warranty models. Analytical results show that offering warranty for remanufactured products does not affect new product pricing in period 2, but influences the pricing of new products in period 1 and remanufactured products in period 2, thereby enhancing remanufacturing, individual and channel profitability, and consumer surplus. Compared to the retailer warranty for remanufactured products, the manufacturer warranty can attain a more equitable profit distribution. If the warranty cost advantage of the manufacturer (retailer) is significant relative to that of the retailer (the manufacturer), the manufacturer (retailer) arises as a natural choice to offer warranty for remanufactured products as this decision enhances both profitability and consumer surplus.

Software for warranty optimization

The research article is associated with warranty optimization. Warranty is one of the most important factors for each organization because it accounts for a large profit in the organizations. In the past research articles, the models developed are only for specific problems of warranty optimization. In this research, a generic model is developed that can be applied to any system for calculating the optimal alternatives, optimal types of warranty policy and optimal warranty durations for various components within a system. The constraints considered in the past by the researches are either related to customer’s criteria or related to manufacturer’s criteria. For the first time, this research article is able to provide solution for warranty optimization considering both the criteria as major constraints together. In this research article, an optimized model of warranty is developed. The model is made in the form of software (OptiW) for easy implementation for the users. This software can be applied to any system having various components like Weibull distribution or exponential distribution. This software can determine the type of warranty policies, type of alternatives used and optimum warranty duration period for various components within a system. In this model, life cycle cost is a non-linear objective function of minimization type subjected to two constraints. The constrains are mean time between failure (MTBF) taking into account the customer’s perspective and spare parts cost taking into account the manufacturers’ perspective. First, the numbers of failures for various warranty plans are simulated using inverse function of the cdf of Weibull distribution. The results of the simulation were required in the optimization model. Genetic algorithm is used to solve non-linear optimization model in the MATLAB. Graphical user interface is developed using guide tool in MATLAB. The software exe file is developed using deploy tool to make this software applicable to any window. Using this software OptiW, an engine problem having 29 components as a case study is solved. The results obtained from the OptiW have reduced life cycle cost as compared to existing model of warranty. The optimum warranty duration for 29 components was larger as compared to various existing warranty models. For the future scope, this research paper can be useful for other extended warranty models or for further research.