Expected Warranty Cost Research Articles

Sustainability via Extended Warranty Contracts: Design for a Consumer Electronics Retailer

Warranty is one of the most important attributes of any product, from both manufacturer and consumer points of view. Although the retailers connect manufacturers to customers by selling goods, traditionally, they have isolated themselves from warranty-related matters such as customer complaints and maintenance costs. However, recent trends in consumer behavior toward extended warranty contracts have changed this approach. While retailers have started to generate considerable revenue from the sale of these contracts, sustainability is also achieved by longer product life cycles. This study analyzed the failure behavior of different classes of cell phone products and their related costs through a chain of consumer electronics retailer operating in Türkiye. To compete on pricing and customer service, a novel policy was designed for the retailer to honor the contracts in house rather than underwriting to a third party insurer as the industry standard. The maintenance records of 328 previous failures were analyzed to plot a failure model. Failure mode and effects analysis was carried out to identify failure classes and the respective costs for extended warranty design for cell phones. The expected warranty costs for coverage of the third, fourth, and fifth years of operation were determined. The results show that the retailer may achieve the same level of profit by increasing customer satisfaction along with the sustainability of the product through repair actions.

Warranty cost analysis for products protected by Lemon Laws

ABSTRACT This paper deals with warranty cost analysis for a warranted product protected by lemon laws during the warranty period. The product is declared a lemon if either of two conditions are met: (i) the product has been returned to the dealer k (e.g. k = 4) times to have the failed product fixed, and the manufacturer was unable to repair the problem satisfactorily, or (ii) the product has been out of service more than the prespecified threshold (e.g. 30 days) due to one or more failures. We study two cases – (i) refund and (ii) replacement cases. For (i), if the product turns out to be a lemon then the manufacturer refund the purchase price, and replace with a new one for (ii). Since the complexity involved in the formulation of the expected warranty cost (EWC), a simulation approach is used to evaluate the EWC for the two cases considered. We give numerical examples to illustrate the EWC for refunding and replacement cases and discuss the impact of a reliability and/or quality improvement to reduce the EWC for the two cases.

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.

Optimal block replacement policy for two-dimensional products considering imperfect maintenance with improved Salp swarm algorithm

Abstract Human society is entering Industry 4.0. Engineering systems are becoming more complex, which increases the difficulties in maintenance support work. Maintenance plays a very important role in the entire life cycle of a system, and in reality, maintenance is not always perfect, and its maintenance degree is between good as new and bad as old, which should be considered in the maintenance strategy. Under the framework of two-dimensional warranty, this work proposes an optimal two-dimensional block replacement strategy based on the minimum expected warranty cost. Two-dimensional block replacement maintenance is imperfect maintenance. The failure rate reduction method is used to describe the maintenance effect of two-dimensional block replacement. In case analysis, the grid search algorithm, genetic algorithm, particle swarm optimization algorithm, and improved salp swarm algorithm (SSA) are used to find the optimal warranty scheme for the laser module. The improved SSA can converge faster and find a warranty scheme that makes the warranty cost lower. Therefore, managers can use these results to reduce costs and get a win-win extended warranty cost. Rationalization suggestions are put forward for managers to make maintenance decisions through comparative analysis and sensitivity analysis.

Optimum specification limit coefficient setting based on the smaller-the-better quality characteristics

In this work, the authors propose the application of type I continuous sampling plan (CSP-1 plan) with expected inspection cost, expected replacement cost, expected warranty cost, expected quality loss for conforming product, and expected quality loss for nonconforming product per item. The quality characteristics of product is considered as the normal distribution with smaller-the-better characteristics. The quality loss function of product addresses the quadratic quality loss function. The CSP-1 plan is applied in the process control. The optimal combination of parameters is obtained from the minimum expected total cost per item produced under the specified average outgoing quality limit (AOQL) protection. One needs to have the optimal clearance number, sampling frequency, and specification limit coefficient.

The integrated application of acceptance sampling in the quality control of manufacturing process and quality assurance of shipment product

In this work, the authors propose the integrated application of CSP-1 plan and Dodge-Romig rectifying inspection plan with expected inspection cost, expected replacement cost, expected warranty cost, expected quality loss for conforming product, and expected quality loss for non-conforming product per item. The quality characteristics of product is considered as the normal distribution with nominal-the-best and symmetric quadratic quality loss function. The CSP-1 plan is firstly applied in the process control. The optimal combination of parameters is obtained from the minimum expected total cost per item produced under the specified average outgoing quality limit (AOQL) protection. One needs to have the optimal clearance number, sampling frequency, and specification limit coefficient. Then Dodge-Romig rectifying inspection plan is applied in the product improvement. The optimal sample size, clearance number, and quality investment are obtained by minimizing the expected total cost per lot under the specified consumer’s risk.

Optimum specification limit setting under the larger-the-better quality characteristics

In this paper, the optimal clearance number and sampling frequency of type I continuous sampling plan (CSP-1 plan) and specification limit coefficient of product are determined with the minimum expected total cost per item under the specified average outgoing quality limit (AOQL) protection. The expected total cost per item includes the expected inspection cost, the expected replacement cost, the expected warranty cost, the expected quality loss for conforming product, and the expected quality loss for non-conforming product per item. The quality characteristic of product is considered as the normal distribution with larger-the-better characteristics. The quality loss function of product addresses the quadratic quality loss function. The sensitivity analysis of numerical example will be provided for illustration.

Warranty cost analysis for a multi-component product protected by lemon laws

We study warranty cost analysis for a multi-component product protected by the lemon laws. The product is repairable and consists of critical and non-critical components. The failed product under warranty due to failure of any critical or non-critical component is minimally repaired. It is considered that the product turns to be a lemon when either the number of critical or noncritical component failures reaches k. We obtain the expected warranty cost and the optimal period of lemon laws which are of interest to the manufacturer when the product is protected by the lemon laws, and provide numerical examples to illustrate the expected warranty cost and the optimal lemon law period.

Optimum reliability acceptance sampling plan using Type-I generalized hybrid censoring scheme for products under warranty

PurposeThe purpose of this paper is to design an optimal reliability acceptance sampling plan (RASP) using the Type-I generalized hybrid censoring scheme (GHCS) for non-repairable products sold under the general rebate warranty. A cost function approach is proposed for products having Weibull distributed lifetimes incorporating relevant costs.Design/methodology/approachFor Weibull distributed product lifetimes, acceptance criterion introduced by Lieberman and Resnikoff (1955) is derived for Type-I GHCS. A cost function is formulated using expected warranty cost and other relevant cost components incorporating the acceptance criterion. The cost function is optimized following a constrained optimization approach to arrive at the optimum RASP. The constraint ensures that the producer's and the consumer's risks are maintained at agreed-upon levels.FindingsOptimal solution using the above approach is obtained for Type-I GHCS. As a special case of Type-I GHCS, the proposed approach is also used to arrive at the optimal design for Type-I hybrid censoring scheme as shown in Chakrabarty et al. (2019). Observations regarding the change in optimal design and computational times between the two censoring schemes are noted. An extensive simulation study is performed to validate the model for finite sample sizes and the results obtained are found to be in strong agreement. In order to analyze the sensitivity of the optimal solution due to misspecification of parameter values and cost components, a well-designed sensitivity analysis is carried out using a real-life failure data set from Lawless (2003). Interesting observations are made regarding the change in optimal cost due to change in parameter values, the impact of warranty cost in optimal design and change in optimal design due to change in lot sizes.Originality/valueThe research presents an approach for designing optimal RASPs using Type-I generalized hybrid censoring. The study formulates optimum life test sampling plans by minimizing the average aggregate costs involved, which makes it valuable in dealing with real-life problems pertaining to product quality management.

Cost analysis of a piece-wise renewing free replacement warranty policy

Nowadays, fierce competition and increasing customer requirements force manufacturers to continuously provide better after-sales services and supports. One such kind of after-sales services is product warranty which has been offered for almost all products in today’s market. In this paper, we study a new warranty policy, called piece-wise renewing free replacement warranty. Under this policy, the whole warranty period is divided into two sub-periods and once an item fails in a specific sub-period, it will be replaced by a new identical one and the warranty period is fully or partially renewed. The expected warranty cost and warranty cycle of this policy are derived from the manufacturer’s perspective. The proposed model is then modified by involving three sub-periods and a failure limit, respectively. In the latter scenario, when the number of item failures over a warranty cycle exceeds a pre-specified threshold, the manufacturer has to refund the item’s purchase price, and consequently the warranty ceases. A real-world case study is presented using warranty data of a battery manufacturer. It is found that for a given warranty period, the piece-wise renewing free replacement policy has a better performance than traditional fully renewing policy, in terms of expected warranty cost, warranty cycle, and cost rate.

Two-dimensional warranty period optimization considering the trade-off between warranty cost and boosted demand

Product warranty in the market has a significant role in both protection and promotion. The manufacturer faces a problem of optimizing the warranty period considering a trade-off between the warranty cost and marketing competition. Meanwhile, for a two-dimensional (2D) warranty, customers with different usage rates have various perceptions on warranty period. Based on the relationships between nominal usage rate and customer’s usage rates, three different cases of designed 2D warranty period are discussed. Considering the variations in customers perceptions, a demand function based on attractiveness index is proposed to describe the boosted sales volume. Meanwhile, the expected warranty cost of 2D warranty based on a bivariate approach is derived when the product failures are minimally repaired. A profit model is developed to estimate the manufacturer’s expected profit of providing a longer warranty period. The optimal extension of 2D base warranty period is obtained by maximizing the manufacturer’s expected profit. Numerical examples in the automobile market are also conducted to validate the proposed model.

On phase type arithmetico-geometric process and its application to deteriorating systems with warranty

This research article makes an attempt to introduce a phase type arithmetico-geometric process and illustrate its applicability to a deteriorating system with fixed warranty. Properties, renewal function, second moment and variance of the underlying counting process are derived analytically and supplemented numerically in the case of three distributions: exponential, Erlang distribution of order 3 and Coxian distribution of order 2. Sensitivity analysis and graphical illustrations are provided to highlight the effect of various cost parameters on the expected warranty cost by means of the Exponential and Erlang distribution of order 2.

A Customized Two-dimensional Warranty Menu Design for Customers with Heterogeneous Usage Rates

Abstract Traditionally, a two-dimensional (2D) warranty is characterized by a single 2D warranty region with age limit as the x-axis and usage limit as the y-axis. However, customers with heterogeneous usage rate have various perceptions on the same 2D warranty region, which leads to dissatisfaction on warranty policy. This study proposes a customized 2D warranty menu for customers with heterogeneous usage rates to increase customers’ satisfaction on after-sales service. Customers are classified into several categories according to their usage rates, and the optimal 2D warranty regions in the menu are designed considering both the manufacturer’s total expected warranty cost and heterogeneous customers’ perceptions on the designed 2D warranty menu. We define an attractiveness index to quantify a customer’s perception on the 2D warranty region based on his usage rate. Meanwhile, design principles and procedures of designing the appropriate 2D warranty menu are proposed. By adopting the proposed menu, customer population has a better perception than a single region. Meanwhile, the manufacturer is more competitive by providing the proposed menu with a same total expected warranty cost.

K0-재생교체보증에 대한 보증분석

본 논문에서는 수리가 가능한 시스템 (repairable system)에 대한 kSUB0/SUB-재생교체보증 (kSUB0/SUB-renewing replacement warranty)을 제안하였는데, kSUB0/SUB-재생교체보증 하에서는 보증기간 동안 시스템에 발생되는 번까지의 고장에 대해서 각각 새로운 시스템으로 교체를 해주고 보증기간도 다시 시작한다. 본 논문에서는 이러한 kSUB0/SUB-재생교체보증이 주어지는 경우에 대하여 생산자 측면에서의 보증분석(warranty analysis)을 이론적으로 수행하였다. 이를 위해서 생산자 측면에서의 총기대보증길이 (expected total warranty length)와 총기대보증비용 (expected total expected warranty cost)을 유도하였다. 끝으로 수치적 예를 통하여 본 논문에서 제안된 보증정책을 설명하였다.

Investigating the effects of operators on warranty cost under sales delay conditions

PurposeDue to the fact that the non-standard products, being used by customers, may cause failures in products with sales delays, which naturally affect the warranty policy. Thus, it seems to be necessary to study these two concepts simultaneously. The paper aims to discuss these issues.Design/methodology/approachIn this paper, a model is developed for estimating the expected warranty costs under sales delay conditions when two operator costs (failing but not reported and non-failing but reported) are included.FindingsThe proposed model is validated using a numerical example for a two types of intermittent and fatal failures occur under a non-renewing warranty policy.Originality/valueSales delay is the time interval between the date of production and the date of sale. Most reported literature on warranty claims data analysis related to sales delay have mainly focussed on estimating the probability distribution of the sales delay.

Utilizing experimental degradation data for warranty cost optimization under imperfect repair

Manufacturers usually want to predict the warranty cost for new products under affordable maintenance policies. With insufficient reliability information, experimental degradation tests are commonly conducted to predict the field reliability before the products are put on the market. In this paper, we propose a novel warranty cost optimization framework based on degradation data within a finite warranty period under the assumption of imperfect repairs. The expected number of warranty claims is given in the analytical form. Two sources of uncertainty are considered to estimate the field reliability for more realistic warranty cost prediction: the uncertainty in experimental data and the variation in field conditions. Effects of imperfect repairs are assumed to be random. The warranty cost for a single repair is assumed to be associated with the improvement factor of imperfect repairs. Optimal imperfect repair policy is obtained by minimizing the expected warranty cost for each sold product. Further, the proposed framework can facilitate the interval prediction for warranty cost. Numerical results show that the proposed analytical method to evaluate warranty claims significantly outperforms simulation methods from the perspective of computational efforts. Finally, an application example of degradation tests along with sensitivity analysis is presented to illustrate the proposed framework.

Evaluation of the warranty cost of a product with type III stochastic dependence between components

• Warranty policy analysis. • Two component system with stochastic dependency. • Renewal theory and Manufacturer and User cost calculation. • Non constant Failure rate and Accumulative damage. This paper analyses respectively the expected warranty costs from the perspectives of the manufacturer and the consumer. For a two-component series system with stochastic dependence between components, both the non-renewing free replacement policy and the renewing replacement policy are examined. It is assumed that whenever component 1 fails, a random damage to component 2 is occurred while a component 2 failure causes the system failure. Component 2 fails when its total accumulative damage exceeds a pre-determined level L . By considering the consumer’s behavior and the product service time, the warranty costs allocations between the manufacturer and the consumer are presented. Numerical examples are given to demonstrate the applicability of the methodology. It is proved that, independent of the type of the warranty policy, the failure interaction between components impacts the manufacturer profits and the consumer costs. The initial warranty length has also an impact on the product quality preferences to both the consumer and the manufacturer.

Using accelerated life tests data to predict warranty cost under imperfect repair

For new products that have not been put on the market, manufacturers usually want to predict the warranty cost to forecast its influence on future profit. In the test phase of new products, accelerated life tests (ALT) are commonly used to predict the lifetime under use condition. In this paper, we present a framework to predict the warranty cost and risk under one-dimensional warranty by analyzing ALT experimental data. Two sources of variability are considered to make inferences of predicted warranty cost: the uncertainty of estimated parameters from ALT data and the variation in field conditions. Under these assumptions, the expected warranty cost and warranty risk is computed by Markov chain Monte Carlo (MCMC) sampling based on the approximated lifetime distribution. We assume that the warranty guarantees imperfect repairs. The framework could be easily repeated for ALT data based on log-location-scale lifetime distributions and both constant-stress and step-stress ALT data. Compared with original Monte Carlo (MC) simulation, the proposed method provides comparable prediction accuracy with significantly less computational effort. A numerical example with sensitivity analysis is given to illustrate the effectiveness of the proposed methods.

Optimal maintenance strategy under renewable warranty with repair time threshold

In this paper, we consider a periodic preventive maintenance model, from the manufacturer's perspective, which can be implemented to reduce the maintenance cost of a repairable product during a given warranty period. The product is assumed to deteriorate with age and the warranty policy we adopt in this paper takes into account the two factors of failure time and repair time of the product when the product failure occurs. Under the proposed two-factor warranty, a repair time threshold is pre-determined and if the repair takes more time than that of the threshold, the failed product is replaced with a renewed warranty policy. Otherwise, the product is only minimally repaired to return to the operating state. During such a renewable warranty period, preventive maintenance is conducted to reduce the rate of degradation periodically while the product is in operation. By assuming certain cost structures, we formulate the expected warranty cost during the warranty period from the manufacturer's perspective when a periodic preventive maintenance strategy is adapted. Although more frequent preventive maintenance increases the warranty cost, the chance of product failures would be reduced. The main aim of this paper is to accomplish the optimal trade-off between the warranty cost and the preventive maintenance period by determining the optimal preventive maintenance period that minimizes the total expected warranty cost during the warranty period. Assuming the power law process for the product failures, we illustrate our proposed maintenance model numerically and study the impact of relevant parameters on the optimal preventive maintenance policy.

Optimum Time-Censored Modified Ramp-Stress ALT for the Burr Type XII Distribution with Warranty: A Goal Programming Approach

Accelerated life tests (ALTs) are used to make timely assessments of the life time distribution of highly reliable materials and components. Much of the previous work on ALTs has focused on constant-stress, step-stress, ramp-stress schemes and their various combinations. In the literature ramp-stress ALTs that have been formulated can be conducted when more than one test chambers are available; installation of which may prove to be costly. Even when one test chamber is used the stress rate remains constant throughout the duration of the experiment. It is not only necessary but imperative to examine if the test specimen is able to withstand differing stress conditions with the passage of time. This paper therefore, presents an optimal design of multi-objective modified ramp-stress ALT model with weighted goal programming approach. The modified ramp-stress uses one test chamber in place of the various chambers used in simple ramp-stress ALT thus saving experimental cost. With the market being increasingly competitive the emphasis today is on goal attainment with minimum deviations. Goal programming is a method to solve multi-objective problems that has applications in varied fields of engineering and operational research. The optimal plan consists in finding out relevant experimental variables, namely, stress rate, stress rate change point and warranty period, by using goal programming on weighted sum of variance of reliability function and expected warranty cost with pre-specified mission time under normal operating conditions. The Burr type XII life distribution and time-censored data have been used for the purpose. Burr type XII life distribution has been found appropriate for accelerated life testing experiments. The method developed has been explained using a numerical example and sensitivity analysis carried out. Comparative study has also been done to highlight the merits of the proposed model.