Replacement Warranty Research Articles

Optimization of a preventive maintenance strategy for a product with limited repair times

This paper proposes a base warranty and replacement warranty strategy for repairable products. It should be emphasized that the product failure rate is low in the early stage of the base warranty. Therefore, in order to reduce the manufacturer’s maintenance cost, the manufacturer does not carry out preventive maintenance in the early stage of the base warranty, and carries out regular preventive maintenance in the later stage of the base warranty. At the same time, if the number of product failures in the base warranty exceeds the specified limit, the manufacturer must replace products for customers free of charge according to the warranty contract. After the product is replaced, if the number of product failures does not exceed the limit, the manufacturer will continue to provide customers with the remaining base warranty period of the original product, and the warranty period will continue to be extended for a period of time. By minimizing the expected cost rate, it is shown that the optimal maintenance policy for warranty products is unique. Finally, we give a numerical example and study the effects of periodic preventive maintenance and other relevant parameters on the optimal solution.

Generalized non-renewing replacement warranty policy and an age-based post-warranty maintenance strategy

Nowadays, to protect the interests of customers, quite a few warranted products are sold with some kinds of repair thresholds. For example, a mobile phone manufacturer may provide a replacement service if the phone sold still cannot work after several repair attempts or the cumulative repair time reaches 7 days or 1 month. Motivated by this observation, we study a non-renewing replacement warranty policy with a repair number threshold and a repair time threshold, in which the manufacturer has responsibility for replacing a product when the number of failures is beyond the repair number threshold or the cumulative repair time reaches the repair time threshold, whichever occurs first. In addition, an age-based post-warranty maintenance strategy is developed for the non-renewing replacement warranted product, which provides a lower cost rate than the existing ones. Based on the indicator function method and renewal process theory, we derive the product’s life cycle cost rate. Finally, considerable numerical experiments are carried out to show the influences of various parameters on the proposed maintenance strategy.

A random maintenance last model with preventive maintenance for the product under a random warranty

Although renewing pro-rate replacement warranty (RPRW) can help producers obtain some compensation from users, there seldom exists a two-dimensional random RPRW with a refund (2D-RRPRW with R) where a refund can guarantee the fairness of users. In addition, although random periodic replacement last (RPRL) can extend the service span after the expiry of the warranty, RPRL considering preventive maintenance (PM) has been seldom modeled to further lengthen the service span after the expiry of the warranty. In view of these, a 2D-RRPRW with R is devised to guarantee the fairness of users by integrating the limited job cycles and a refund into RPRW. Under the case where 2D-RRPRW with R warrants products with job cycles, a RPRL with PM is modeled to further lengthen the service span after the expiry of the warranty and reduce the failure frequency. It shows that to shorten the warranty period can makes the warranty cost of 2D-RRPRW with R to be less than the warranty cost of classic RPRW; and the performance of RPRL with PM outperforms the performance of classic RPRL.

Optimal preventive maintenance for repairable products with three types of failures sold under a renewable hybrid FRW/PRW policy

This paper proposes the optimal preventive maintenance policy for products under a warranty policy, which combines fully renewable free replacement warranty (FRW) and pro-rata warranty (PRW). Replacement age is divided into three separate periods: within FRW, during PRW and post-warranty. Moreover, it is assumed the product is subject to three types of failures arriving according to a non-homogeneous Poisson process. The first type can be fixed by minimal repair, and the third type is a catastrophic failure that results in product replacement. If the failure is of the second type and the product is at age t, it is either minimally repaired with probability p(t) or replaced by a new one with probability 1−p(t). The aim of this study is to develop the long-run expected cost rate for both warranted and non-warranted repairable products as well as to derive the optimal replacement time such that the incurred costs are minimized. The proposed approach provides valuable information for the product customers, managers, or engineers to make better decisions about the preventive replacement time of such products. The proposed model covers some preventive maintenance policies in the existing literature. Numerical computations are also performed to investigate the effect of the model’s parameters on the optimal solutions. Eventually, a real-life application is discussed to demonstrate the applicability of the proposed policy.

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.

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.

Cumulative free replacement warranty with phase type lifetime distributions

This paper analyzes the stochastic process generated by unit failures, and the corresponding cash flows, for products with cumulative warranties where the seller offers warranty on the total useful life of a batch of units rather than the lifetimes of individual units. Relative to individual warranties, cumulative warranties reduce administrative cost to seller as well as buyer, and are expected to lead to lower selling price due to reduced cost of warranty to the seller. For products with phase type lifetime distributions, matrix-analytic methodology is used to develop algorithms to compute economic measures such as cost of warranty. Results indicate that savings in cost of warranty due to a cumulative warranty relative to individual warranties, increase with increasing product lifetime variability, and that the marginal savings in cost of warranty decrease with increasing batch size. Economic measures are proposed to establish the amounts of discounts that the seller may be willing to offer, or the buyer expects, in order to change from individual warranties to a cumulative warranty.

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.

Optimal pricing and production strategies for new and remanufactured products under a non-renewing free replacement warranty

Due to its economic and environmental benefits, the remanufacturing industry has become vital and popular worldwide. The demand for remanufactured products highly depends on their price and warranty coverage offered, as these two features are the two most important to customers for signaling value and quality of the remanufactured products. This paper identifies the conditions of the optimal pricing and production strategies for a monopolistic manufacturer under a non-renewing free replacement warranty for a two-period planning horizon. It is shown that the manufacturer’s engagement in the remanufacturing activities depends on the warranty length and the ratio of the production cost to the remanufacturing cost. Numerical experiments provide additional managerial insights and implications by investigating the sensitivity of the optimal solutions to changes in the length of the warranty period offered.

Two-stage optimization model for renewing warranty considering warranty deadline

Renewing warranty can provide customers with better service, and thus help manufacturers to gain market opportunities. In engineering practice, the cost for replacement is usually higher than the cost for maintenance, hence manufacturers often face huge challenge to reduce the warranty service cost. With consideration of the warranty deadline, we propose a two-stage optimization model for renewing warranty. In the first stage, a renewing warranty with deadline (RWD) policy is implemented, where the deadline represents the cumulative uptime threshold. When the cumulative uptime exceeds the deadline, the product will be minimally repaired and kept to the residual warranty period. When RWD is expired, the replacement warranty with limited repairs (RWLR) policy is applied. Under the free replacement and pro-rata warranty policy, the corresponding two-stage cost optimization model is established from the manufacturer’s perspective, the aim is to minimize the cost rate and obtain the optimal warranty period. A numerical example is provided to illustrate the validity of the proposed model, and the sensitivity analysis is also carried out.

Optimal overhaul\u2013replacement policy for a multi-degraded repairable system sold with warranty

In this research, we study an optimal overhaul–replacement policy of a multi-degraded repairable system sold with a free replacement warranty. In the proposed replacement policy, a maintenance action and failure are dependent on a system degradation level and the system age, and hence the replacement model will provide more effective maintenance decisions. Failure of the system is modeled using a rate of occurrence of failure for the system, which is as a function of a degradation level of the system and its age. We develop the optimal replacement policy for a multi-degraded repairable system from the buyer’s point of view, who plans to use the system for a horizon planning T. The buyer conducts a periodic evaluation and selects an appropriate maintenance option based on the revealed system condition together with the system operational age. At each evaluation point, three alternative decisions are available, i.e., keep running the system, overhaul, or replace it with a new one. We formulate the sequential decision (keep, overhaul, or replace) problem as a dynamic programming model and obtain an optimal policy that minimizes total cost over T. Numerical examples are presented using several hypothetical data sets to illustrate the structure of optimal solution and its sensitivity against the change in parameter values. The main contribution of the paper is to offer a decision tool that will help in deciding the overhaul–replacement action based on the degradation level and the operational age of the system.

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.

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.

수리가 가능한 시스템에 대한 k0-재생교체보증이 종료된 이후의 최적의 교체정책

수리가 가능한 시스템에 대한 k0-재생교체보증이 종료된 이후의 최적의 교체정책

Post-warranty maintenance optimization for products with deterioration depending on aging and shock

ABSTRACTDue to the non-substitutability of the product, the monopoly manufacturer designs warranty to reduce maximally warranty cost. Although the monopoly manufacturer maintains responsibly product reliability in warranty, the consumer still confronts a problem about how to sustain product reliability after the designed warranty expires. Goal of this paper is, from the consumer’s perspective, to propose a reliability maintenance policy after expiry of the monopoly manufacturer’s warranty. First, a renewable repair-limit pro-rata replacement warranty (RRLPRRW) policy is considered from viewpoint of the monopoly manufacturer and used as a quality guarantee of the product with the deterioration affected by internal aging and external shock. Second, depreciation cost is earlier considered in the process of modeling life cycle cost, which differs from the traditional works on the consumer’s post-warranty reliability maintenance problem. Third, the consumer’s discounted cost rate model considering depreciation cost is derived to achieve optimal maintenance policy. Finally, a numerical example is provided to illustrate our approach. It was found that the proposed maintenance policy is more effective and the depreciation cost considered in life cycle cost has significant effect on extension of the post-warranty period.

Optimizing under and out of warranty products’ decisions in the finite planning horizon

In this paper, we consider a manufacturer that produces products in a finite horizon time and sells products with non-renewing free replacement warranty policy. The manufacturer is responsible to provide spare parts for failed products, whether the products are under or out of warranty. Previous research on warranty optimization has focused on maximizing manufacturer profit without considering the spare part market for out-of-warranty products. This study proposes a novel nonlinear model that maximizes manufacturer profit by optimization of price, warranty length and spare part inventory for under- and out-of-warranty products in a manufacturing/remanufacturing system. Due to the model’s unique structure, we propose a new two-stage approach that combines metaheuristic and an exact method, in which the first stage is to determine product’s prices and warranty length with metaheuristic algorithm and in the second stage the remaining inventory related problem is transferred to a Minimum Cost Network Flow Problem which is solved for spare part inventory control. To illustrate the effectiveness of the suggested method, the model is solved for a case study of Iranian SANAM electronic company with two different metaheuristic algorithms and a sensitivity analysis is conducted to study the effect of various parameters on the optimal solution.

Optimal warranty design and post-warranty maintenance for products subject to stochastic degradation

ABSTRACTWarranty policy, as a marketing strategy, has been widely studied for several decades, but warranty models incorporating condition-based maintenance are still rare. In condition monitoring, product reliability in the warranty period can be tracked and predicted based on its degradation path. In this article, we first propose a condition-based renewable replacement warranty policy through the integration of Inverse Gaussian degradation model. The goal is to maximize the manufacturer's profit by optimizing the warranty period, sale price, and replacement threshold. In a monopoly market, we show that it is more profitable to let the replacement threshold equal the failure threshold. However, in the competitive market the optimal replacement threshold should be below and no more than the failure threshold. Second, depending on whether the historical degradation level is observable or not to the customer, optimal post-warranty maintenance policy considering hybrid preventative maintenance effect (i.e., both age and degradation level reduction) is derived. Numerical experiments show that a larger replacement threshold can increase the manufacturer's profit, reduce sale price and prolong warranty period, but it has less effect on saving the consumer's cost or extending the replacement age.

Warranty analysis of a two-component system with type I stochastic dependence

This article develops the warranty cost analysis of a two-component in-series system with stochastic dependence. From the perspectives of both the manufacturer and the consumer, the short-run total profits and costs under the non-renewing free replacement (non-renewing free replacement warranty) policy and the renewing free replacement warranty policy are derived, respectively. Numerical examples are given showing the impact of the failure dependence to both the consumer and the manufacturer.

One-Dimensional Renewable Warranty Management within Sustainable Supply Chain

Sensor embedded products utilize sensors implanted into products during their production process. Sensors are useful in predicting the best warranty policy and warranty period to offer a customer for remanufactured components and products. The conditions and remaining lives of components and products can be estimated prior to offering a warranty based on the data provided by the sensors. This helps reduce the number of claims during warranty periods, determines the right preventive maintenance (PM) policy, and eliminates unnecessary costs inflicted on the remanufacturer. The renewing, one-dimensional Free Replacement Warranty (FRW), Pro-Rata Warranty (PRW), and combination FRW/PRW policies’ costs for remanufactured products and components were evaluated with/without offering PM for different periods in this paper. To that end, the effect of offering renewable, one-dimensional, Free Replacement Warranty (FRW), or Pro-Rata Warranty (PRW), or combination FRW/PRW warranty policies for each disassembled component and sensor embedded remanufactured product was examined, and the impact of sensor embedded products on warranty costs was assessed. A case study and varying simulation scenarios is examined and presented to illustrate the model’s applicability.

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.