Optimizing Two-Dimensional Renewable Warranty Policies for Sensor Embedded Remanufactured Products

Purpose: Remanufactured products, in addition to being environment friendly, are popular with consumers because they can offer the latest technology with lower prices in comparison to brand new products. However, some consumers are hesitant to buy remanufactured products because they are skeptical about the quality of the remanufactured product and thus are unsure of the extent to which the product will render services when compared to a new product. A strategy that remanufacturers may employ to entice customers is to offer warranties on remanufactured products. To that end, this paper studies and scrutinizes the impact of offering renewing warranties on remanufactured products. Specifically, the paper suggests a methodology which simultaneously minimizes the cost incurred by the remanufacturers and maximizes the confidence of the consumers towards buying remanufacturing products. Design/methodology/approach: This study uses discrete-event simulation to optimize the implementation of a two-dimensional renewing warranty policy for remanufactured products. The implementation is illustrated using a specific product recovery system called the Advanced Remanufacturing-To-Order (ARTO) system. The experiments used in the study were designed using Taguchi’s Orthogonal Arrays to represent the entire domain of the recovery system so as to observe the system behavior under various experimental conditions. In order to determine the optimum strategy offered by the remanufacturer, various warranty and preventive maintenance


Introduction
In current times, the exponential rise in technological development and the customers' desire to repeatedly purchase newer device models and technological products is the impetus which culminates into diminished product life cycles and an upturn in their rate of disposal.As a result, landfill areas and the Earth's natural resources start reaching a critical apex.Therefore, when a technological device reaches the end of its life and becomes essentially no longer useful or just antiquated, manufacturing firms repossess these same products that they had produced prior, in order to manage to meet the new regulations imposed upon them and to enlighten customers' awareness of the pertinent environmental issues regarding this matter.The manufacturers of these technological devices construct specialized facilities specifically designed for the end-of-life (EOL) product recovery process in order to minimize the amount of mechanical waste sent to landfills.This is achieved by retrieving the mechanical materials, parts, and components from the end-of-life products (EOLPs) by way of the recycling, refurbishing, and remanufacturing processes.The economic benefits from such facilities make the process of product recovery more attractive.
In product recovery, disassembly is the most vital operation because it allows for the extraction of the desired components, subassemblies and materials from EOL products.There are various ways to execute the process of disassembling EOL products.They can be effectuated at a single workstation, in a disassembly cell, or on a disassembly line.Although utilizing single workstations and disassembly cells are more flexible, the operation that produces the highest yield is the disassembly line, which is also the most efficient operation for automated disassembly (Gungor & Gupta, 2002).
warranty analyses models depicting a remanufacturing line under various scenarios.Moreover, we will attempt to minimize the cost associated with warranty and to maximize the profit gained by remanufacturers by unearthing a warranty with an appealing price.
Because of the infinitely increasing levels of complexity and uncertainty associated with the remanufacturing process, the scope of this paper is limited to the following factors.EOL products and demanded components arrive at the remanufacturing facilities in accordance with the Poisson distribution.The disassembly and remanufacturing time exponentially assigned to each station are distributed accordingly.Imposing a cost for backorders will be calculated based on the duration of aforementioned backorder.Excessive and unessential EOL products and components are disposed of regularly according to a stringent disposal policy.A pull control production mechanism is used in all disassembly line settings contemplated and reviewed in this research study.Comparisons of warranty costs and temporal periods are made amongst different warranty policies.
The primary contribution offered by this paper is that it presents a quantitative assessment of the effect of offering warranties on remanufactured items from a remanufacturer's perspective in that it proposes an appealing price in the eyes of the buyer as well.While there are developmental studies on warranty policies for brand new products and a few on secondhand products, there exists no study that evaluates the potential benefits of warranties on remanufactured products in a quantitative and comprehensive manner.This paper studies and scrutinizes the impact of offering renewing warranties on remanufactured products.Specifically, the paper suggests a methodology which simultaneously minimizes the cost incurred by the remanufacturers and maximizes the confidence of the consumers towards buying remanufacturing products.
The rest of the paper is organized as follows: section 2 list all the related work from the literature review.
System descriptions and design-of-experiment study are presented in Section 3 and Section 4 respectively.Section 5 presents the renewable one-dimensional warranty.Assumptions and notations are given in Section 6. Section 7 describes the preventive maintenance analysis.The failure analysis and warranty formulation are presented in Section 8 and Section 9 respectively.Finally, results and conclusions are given in Section 10.

Environmentally Conscious Manufacturing and Product Recovery
In recent years, the number of studies dealing with environmentally conscious manufacturing and product recovery (ECMPRO) issues have gained gratuitous attention from researchers (Gungor & Gupta 1999), (Ilgin, & Gupta 2010b).This is partially due to environmental factors, government regulations, and public demands, but on the other side it is also due to economical profits obtained by implementing reverse logistics and product recycling resolutions.Manufacturers respond to consumer awareness of environmental issues and stricter environmental legislations by establishing designated facilities designed for the purpose of minimizing waste amassment by recovering materials and components derived from EOL products (Gungor & Gupta 2002).Researchers have shed light on the panoptic environmentally conscious dilemmas involved in product manufacturing.As a result, researchers have released reviews of these panoptic issues involved in environmentally conscious manufacturing and product recovery (see for example, Moyer & Gupta, 1997;Gungor & Gupta, 1999;Ilgin & Gupta, 2010c;Gupta, 2013;Ilgin, Gupta & Battaïa, 2015).Disassembly is the most apex in the remanufacturing research area, which is due to its significant role in the all recovery system.For different aspects involved in disassembly, see the book by Lambert and Gupta (2005).

Disassembly to Order Systems
The objective of the disassembly to order systems (DTOs) is the determination of the optimal lot-sizes of EOL products to disassemble in order to satisfy the demand of various components from a mix of product types that have a number of components and/or modules in common (Gupta & Lambert, 2008).Kongar and Gupta (2002) proposed a single period integer Goal Programming (GP) model for a DTO system to determine the best combination of multiple products to selectively disassemble them to meet the demand for items and materials under a variety of physical, financial and environmental constraints and goals.Kongar and Gupta (2006) extended Kongar and Gupta (2002) study by using fuzzy GP to model the fuzzy aspiration levels of various goals.Langella (2007) developed a multi-period heuristic considering holding costs and external procurement of items.Gupta, Imtanavanich & Nakashima (2009) used neural networks (NN) to solve the DTO problem.Kongar and Gupta (2009a) proposed a LPPbased solution methodology which can satisfy tangible or intangible financial, environmental and performance related measures of DTO systems.Kongar and Gupta (2009b) developed a multi-objective tabu search (TS) algorithm by considering multiple objective functions, viz.maximizing the total profit, maximizing the resale/recycling percentage, and minimizing the disposal percentage.Inderfurth and Langella (2006) developed two heuristic procedures (i.e., one-to-one, one-to-many) to investigate the effect of stochastic yields on the DTO system.Imtanavanich and Gupta (2006) use the heuristic procedures developed by Inderfurth and Langella (2006) to deal with the stochastic elements of the DTO system.Then, they useed a GP procedure to determine the number of returned products that satisfy various goals.Ondemir, Ilgin & Gupta (2012) presented an Advanced Repair-to-Order and Disassembly-to-Order (ARTODTO) model.ARTODTO model deals with the products that are embedded with sensors and Radio-Frequency Identification (RFID) tags.The goal of the proposed model was to determine how to process each and every end-of-life product (EOLP) on hand to meet used product and component demands as well as recycled material demand.The model considered disassembly, repair, and recycling options for each EOLP in order to satisfy material and remaining-lifetime-based (sophisticated) component/product demands and minimize the total cost.Outside component procurement option was also assumed to be available.Ondemir and Gupta (2012) proposed a remanufacturing-to-order (RTO) system for end-of-life sensor embedded products (SEPs).An integer programming (IP) model was proposed to determine how to process each and every end-of-life product on hand to meet the quality-based product and component demands as well as recycled material demand while fulfilling the minimum cost objective.Ondemir and Gupta (2013) proposed an ARTODTO model for EOL processing of SEPs under demand and decision uncertainty.The proposed model was formulated as a fuzzy goal programming (FGP) model to achieve a variety of financial, environmental, and physical goals.Alqahtani, Gupta & Nakashima (2014) extended Ondemir and Gupta (2013) study using simulation discrete model.

Sensor Embedded Products
Manufacturers are now able to build sensors in smaller sizes and at lower costs due to the expansion of technology.The use of sensor-based technologies on after-sale product condition monitoring is an active research area.Starting with the study of Scheidt and Shuqiang (1994), different methods of data acquisition from products during product usage were presented by the researchers (Karlsson, 1997(Karlsson, , 1998;;Klausner, Grimm & Horvath, 1999;Petriu, Georganas, Petriu, Makrakis & Groza, 2000;Simon, Bee, Moore, Pu & Xie, 2001).Cheng, Huang, Chen and Hung (2004), developed a generic embedded device that could be installed in different types of equipment, including manufacturing equipment, portal servers, and automated, guided vehicles.This device has the ability of retrieving, collecting, and managing equipment data with the help of an embedded real-time operating system and several software modules.Yang, Moore, Pu and Wong (2009c) and Yang, Moore and Chong (2009b) developed an intelligent product model for discovering product service systems for consumer products, such as fridge/freezer appliances and game consoles for PlayStation2.In this model, an intelligent data unit was installed in each product to acquire data during usage and the distribution stages of its life cycle.The procurement of the essential life-cycle components of a product with sensors embedded in it is presented by Vadde, Kamarthi, Gupta and Zeid (2008).Additional studies aim to further explore whether or not the use of embedded sensors increases product life-cycle management effectiveness.A comprehensive survey on the commercial sensor systems used in health management for electronic products and systems was reported by Pecht (2008).Fang, Ong and Nee (2014), who investigated the modern practices leading toward the eventual development of embedded sensors in products in two primary categories, (viz., embedding sensors in products and representing and interpreting sensor data).
Another avenue of research hinges on the life cycle data analysis obtained via the implementation of various sensor-based data acquisition methods.In this scope, Mazhar, Kara and Kaebernick (2005) presented an integrated, two-stage approach which combined the Weibull analysis and multiple linear regression to assess the component reliability in refurbished products based on their life cycle data.Mazhar, Kara and Kaebernick (2007) carried out a similar analysis by integrating Weibull analysis with neural networks.Herzog, Marwala and Heyns (2009) compared the performance of several neural network variations in the prediction of the residual life of machines and components.
Although the majority of the studies presented above focus on the development of SEP models that enable product data acquisition during their life cycle and/or in their EOL phase, only a select few number of researchers have conferred a cost-benefit analysis.Klausner, Grimm and Hendrickson (1998a) analyzed the trade-off between the higher initial manufacturing costs caused by using an electronic data log (EDL) in products and the cost savings from the reuse of used motors.Simon et al. (2001) improved the cost-benefit analysis of Klausner, Grimm and Hendrickson (1998b) by taking into consideration the limited lifespan of a product's design.It was revealed that under certain circumstances, product servicing offers more readily reusable components in contrast to EOL recovery of parts.

Warranty Analysis
A warranty is a contractual obligation incurred by a manufacturer (vendor/seller) in connection with the sale of a product.The purpose of a warranty is to establish liability in the rare event that a purchased item fails prematurely or is unable to perform its intended function.These contracts specify the promised product performance and when this expected performance level is not met, a return of compensation is available to the buyer as compensation (Blischke, 1993).Product warranties have different main functions.One of the functions is insurance and protection, permitting buyers to transfer the risk of product failure back to the sellers (Heal, 1977).Secondly, product warranties can also signal product reliability to customers (Balachander, 2001;Gal-Or, 1989;Soberman, 2003;Spence, 1977), and lastly, the sellers can use warranties to extract additional profitability (Lutz & Padmanabhan, 1995).
In contrast with massive literature on warranty policies for new items, up to now study on warranty policies for second-hand items receives less attention.Modelling the warranty cost analysis for used products is a novel field of research with a limited number of publications.The optimal upgrade strategies for second-hand items under both the virtual age along with the screening test reliability development methods are presented by Saidi-Mehrabad, Noorossana and Shafiee (2010), and Shafiee, Chukova, Yun and Akhavan-Niaki (2011a) who built a stochastic model designed to examine the optimal degree of investments for increasing the reliability of secondhand products under free repair warranty (FRW) policies.They concluded that a larger number of investments meant larger declines in the virtual age and greater reliability levels of the upgraded product.A stochastic reliability improvement model for used products with warranties and Cobb-Douglas-Type production function to reach the optimal upgrade level was presented by Shafiee, Finkelstein and Chukova (2011b).A study to determine the optimal upgrade, selling price and maximum expected profit with restrictive assumptions about the age distribution was conducted by Naini and Shafiee (2011).They built a mathematical model to implement a parametric analysis on the items' chronological ages to detect and determine the best policies.Yazdian, Shahanaghi and Makui (2014) adopted an integrated mathematical model that was not reliant on the specific age of the received item in order to determine the typically experienced remanufacturer decisions.The warranty policy and its effect on consumer behavior from the perspective of consumers has been studied by Liao, Li and Cheng (2015).A novel mathematicalstatistical model was proposed where decisions involving the pricing of returned used products (cores), with the degree of their remanufacturing, selling price, and warranty period for the final remanufactured products was to investigate the joint optimization of remanufacturing, pricing and warranty decision-making for end-of-life products (Yazdia et al., 2014).Kuik, Kaihara and Fujii (2015) presented mathematical models to examine two types of the proposed extended warranty policies for manufacturers so that they could make the comparisons of their possible gained profits of remanufactured products by the manufacturers who supplied them.In contrast, the analysis of warranty costs for remanufactured products has not yet received any significant attention.However, there are few papers that consider the warranty for the remanufactured products' reverse and closedloop supply chain management.Base and extended one-dimensional warranty can be offered for remanufacturing products using Free Replacement Warranty (FRW) and Pro-Rata Warranty (PRW) policy (Alqahtani & Gupta, 2015a, 2015b, 2015c).Also, renewable, nonrenewable, one-and two-dimensional warranty policies can be offered for EOL derived products (Alqahtani & Gupta, 2016a, 2016b, 2016c).

Maintenance Analysis
Maintenance has a significant role in product reliability and quality.In the literature, maintenance is classified into two main types viz., corrective maintenance (CM) and preventive maintenance (PM).CM occurs when item fail and it performs to restore a failure item to an operational state; PM is performed before item fail in order to reduce degeneration and failure rate.In case of short product's remaining life, the warranty is also comparatively short and only CM actions are offered.Where in a product with long remaining life, warranty could be relatively long and warranty servicing costs can be reduced by carrying out PM actions.Thus, there is a relation between warranties, CM and PM.
The literature on maintenance policies is extensive.Several review papers on maintenance policies have appeared (Wang, 2002;Garg & Deshmukh, 2006;Sharma, Yadava & Deshmukh, 2011).We refer the reader to book by Nakagawa (2006) for the detailed information on the general area of maintenance theory.An extensive review of modelling maintenance policies can be found in book by Nakagawa (2008).
Maintenance policies for second-hand products during the warranty were not receiving researchers' interest.(Shafiee & Chukova, 2013).Yeh, Lo and Yu (2011) proposed two periodical age reduction PM models to decrease the high failure rate of the second-hand products.Kim, Lim and Park (2011) studied the optimal periodic PM policies of a second-hand item following the expiration of warranty.
From the manufacturer perspective, it is meaningful to carry out PM actions only when the saving of warranty servicing cost exceeds the additional cost occur by performing PM activities.Therefore, developing PM policies for remanufactured products still needs further researches (Alqahtani & Gupta, 2017).

System Description
This study used discrete-event simulation to optimize the implementation of a two-dimensional renewing warranty policy for remanufactured products.The implementation is illustrated using a specific product recovery system called the Advanced Remanufacturing-To-Order (ARTO) system.The experiments used in the study were designed using Taguchi's Orthogonal Arrays to represent the entire domain of the recovery system so as to observe the system behavior under various experimental conditions.In order to determine the optimum strategy offered by the remanufacturer, various warranty and preventive maintenance scenarios were analyzed using pairwise t-tests along with one-way analysis of variance (ANOVA) and Tukey pairwise comparisons tests for every scenario.
The Advanced Remanufacturing-To-Order (ARTO) system deliberated on in this study is a sort of product recovery system.A sensor embedded air conditioner (AC) is considered here as a product example.Based on the condition of EOL AC, it goes through a series of recovery operations as shown in Figure 1.Refurbishing and repairing processes may require reusable components in order to meet the demand of the product.This requirement satisfies both the internal and the external component demands.Thus, both will be satisfied using disassembly of recovered components.There are three different types of items arrivals in the ARTO system; either the EOL products for recovery process, failed SEP need to rectify or SEP due for maintenance activities.First, EOL ACs arrive at the ARTO system for information retrieval using a radio frequency data reader that is stored in the facility's database.Then the ACs go through a six-station disassembly line.
Complete disassembly is performed for the purpose of extracting every single component.Table 1 represents the precedence of relationships between the AC components.There are nine components in an AC: the evaporator, control box, blower, air guide, motor, condenser, fan, protector, and compressor.Exponential distributions are used to generate the station disassembly times, interarrival times of each component's demand, and interarrival times of EOL AC.All EOLPs after retrieval of the information are shipped either to station 1 for disassembly or, if EOLP only needs a repair for a specific component, it is instead sent to its corresponding station.Two different types of disassembly operations, viz., destructive or nondestructive, are used depending on the component's condition.If the disassembled component is not functional (broken, zero percent of remaining life), then destructive disassembly is utilized in such a way that the other components' functionality is not damaged.Therefore, unit disassembly cost for a functional component is higher than for a nonfunctional component.After disassembly, there is no need for component testing due to the availability of information regarding components' conditions from their sensors.It is assumed that the demands and life cycle information for EOLPs are known.It is also assumed that the retrieval of information from sensors costs less than the actual inspecting and testing.Recovery operations differ for each SEP based on their overall condition and estimated remaining life.
Recovered components are used to meet spare parts demands, while recovered or refurbished products are used for consumer product demands.Also, material demands are met using recycled products and components.Recovered products and components are characterized based on their remaining lifespans and are placed in different life-bins (e.g. one year, two years, etc.) where they wait to be retrieved via a customer demand.Underutilization of any product or component can happen when it is qualified for a higher life-bin but is placed in a lower life-bin because the higher life-bin is full.Any product, component, or material inventory that is greater than the maximum inventory allowed is assumed to be of excess and is instead used for material demand or is simply disposed of.
In order to meet the product demand, repair and refurbish options could also be chosen as presented in Figure 2. EOLP may have missing or nonfunctional (broken, zero remaining life) components that need to be replaced or replenished during the repairing or refurbishing process in order to meet certain remaining life requirements.EOLP may also consist of components having lesser remaining lives than desired, and, for that reason, might also have to be replaced.In case of failure SEP during warranty period, The failed ACs arrive at the ARTO system for information retrieval using a radio frequency data reader that is stored in the facility's database.Then the failure ACs goes through the recovery operations explain before same as an EOLP.
Finally, in order to reduce the risk of failure, PM actions are carried out during the warranty period.Here, if the remaining life of a remanufactured AC reaches a pre-specified value the remanufactured SEPs arrive at the ARTO system for information retrieval using a radio frequency data reader that is stored in the facility's database.Then, the SEPs go through four maintenance activities based on the information from the sensor about their condition.These maintenance activities include measurements, adjustments, parts replacement, and cleaning.When PM actions are performed with degree δ, the remaining life of the remanufactured ACs will be δ units of time more than before as shown in Figure 3.Meanwhile, any failures between two successive PM actions during warranty period are rectified at no cost to the customer.

Design-of-Experiments Study
According to a comprehensive study for the quantitative evaluation of the SEPs on the performance of a disassembly line conducted by Ilgin and Gupta (2011), it was show that smart SEPs are a favorable resolution in handling remanufacturing customer uncertainty.To test this claim on ARTO, we built a simulation model to represent the full recovery system and observed its behavior under different experimental conditions.ARENA program, Version 14.5, was used to build the discrete-event simulation models.A three-level factorial design was used with 51 factors that were considered each at 3 levels.
These were identified as low, intermediate, or high levels.The reason that the three-level designs were proposed was to model possible curvature in the response function and to handle the case of nominal factors occurring at 3 levels.The parameters, factors, and factor levels are given in Table 2 and Table 3 Furthermore, for validation and verification purposes animations of the simulation models were built along with multiple dynamic and counters plots.2,000 replications with six months (eight hours a shift, one shifts a day and 5 days a week) were used to run each experiment.Arena models calculate the profit using the following equation: ( where SR is the total revenue generated by the product; component and material sales during the simulated run time; CR is the total revenue generated by the collection of EOL ACs during the simulated run time; SCR is the total revenue generated by selling scrap components during the simulated run time; HC is the total holding cost of products, components, material and EOL ACs during the simulated run time; BC is the total backorder cost of products, components and material during the simulated run time; DC is the total disassembly cost during the simulated run time; DPC is the total disposal cost of components, material and EOL ACs during the simulated run time.TC is the total testing cost during the simulated run time; RMC is the total remanufacturing cost of products during the simulated run time; TPC is the total transportation cost during the simulated run time; PMC is the total preventive maintenance cost during the simulated run time and WC is the total warranty cost.
In each EOL AC, there are three types of scraps that need to be recovered and sold.The evaporator and condenser are sold as copper scrap, Chassis and metal covers are sold as steel scraps and blowers, fan and air guides are sold as fiberglass.All the other components are considered to be waste components.Scrap revenue from steel, copper, and fiberglass components is calculated by multiplying their weight in pounds by the units of scrap revenue produced by each metal type.Disposal cost is calculated as well by multiplying the waste weight by the unit disposal cost.The time of retrieving information from smart sensors is assumed to be 20 seconds per AC.The transportation cost is assumed to be $50 for each trip taken by the truck.There are different prices in the secondary market of recovery product due to different level of quality.

Renewable Two-Dimensional Warranty
During the process of deciding to purchase a product, the buyer usually compare features of a product with other competing brands that are selling the same product.In some cases, the competing brands produce similar products bearing similar features such as the costs, special characteristics, quality, credibility of the product, and even insurance from the provider.In these cases, after sale factors come into effect, such as the discount, warranty, availability of parts, repairs, and other services.These factors will be very significant to the buyer in such a situation.So will the warranty since it further assures the buyer of the reliability of the product.
A warranty is an agreement that requires the manufacturer to correct any product failures or to compensate the buyer for any problems that may occur with the product during the warranty period in relevance to its sale.The objective of the warranty is to promote the product's quality and guarantee its performance in order to assure productivity for both the manufacturer and the buyer.For a given product, the warranty cost (in a statistical sense) is the same for all new items if the manufacturer has good quality control.In contrast, each EOL product is different due to factors such as age, usage, and maintenance history.This makes the warranty cost for each remanufactured product derived from an EOL item statistically different.
The importance of warranties for remanufactured products is increasing because consumers are becoming more demanding of product quality and the increase in customer's awareness of the environment will increase the demand for remanufactured products and future costs of replacement/repair in case of product failures.Therefore, warranty management has become very important to remanufacturers of remanufactured products.They need to estimate the warranty cost in order to factor it into the pricing structure.Failure to do so can result in the remanufacturers incurring loss, as opposed to profit, with the sale of remanufactured items.Analyses of warranty costs for remanufactured products are more complex when compared to new products because of the uncertainties in usage and maintenance history.Moreover, warranty policies similar to new and secondhand products may not be economically acceptable from the remanufacturer's point of view.
Therefore, there is a need to test and compare these warranty policies for remanufactured products and estimate the expected warranty cost associated with these policies.There are other related issues such as the servicing strategies involving remanufactured spare parts in the replacement/repair of failures during the warranty period.
In the two-dimensional warranty, a policy is defined by a region in a two-dimensional plane, typically with one axis representing time or age and the other axis representing the usage.For renewing policies, the warranty period begins anew with each replacement or repair.Therefore, the warranty period is uncertain as the warranty expires only when an item does not fail for a period W, as shown in

Assumptions and Notations
This section starts with the model assumptions.Then, the notation of all the parameters used in this paper.

Assumptions
The following assumptions have been considered to simplify the analysis: i.The failures are statistically independent.
ii.Every item failure under warranty period results in a claim.
iii.All claims are valid.
iv.The failure of a remanufactured item is only a function of its age.
v. The time to carry out the replacement/repair action is relatively small compared to the mean time between failures.
vi.The cost to service warranty claim (for repair/replacement of failed components) is a random variable.

W:
Warranty period;

Preventive Maintenance Analysis
Usually, a PM activities involve a set of maintenance tasks, such as, cleaning, systematic inspection, lubricating, adjusting and calibrating, replacing different components, etc. (Ben-Mabrouk, Chelbi & Radhoui, 2016).The right PM activities can be able to reduce the number of failures efficiently, as a result reduce the warranty cost and increased the customer satisfaction.This study, adopt the modelling framework proposed by Kim, Djamaludin and Murthy (2004) to model the effect of PM activities.
A series of PM activities of a remanufactured item are performed at remaining life RL 1 , RL 2 ,… RL j ,…, with RL 0 = 0. Here, the effect of PM results in a restoration of the item so that the item's virtual remaining life is effectively increase.The concept of virtual age is introduced in Kijima, Morimura and Suzuki, 1988; and then extended in Kijima (1989).In this study, the j th PM only reimburses the damage accrued during the time between the (j − 1) th and the j th PM activities, as a result an arithmetic reduction of virtual remaining life can be obtain (Martorell, Sanchez & Serradell 1999).Therefore, the virtual remaining life after performing the j th PM activity, i.e.RL j , is then given by ( 2) where m is the level of PM effort, and δ(m), m = 0, 1, …, M, is the remaining life increment factor of PM with effort m.Note that, the effect of PM depends on its level m, 0 ≤ m ≤ M, and its relationship with the remaining life is characterized by the age-incremental factor δ(m). Larger value of m represents greater PM effort, hence δ(m) is a increasing function of m with δ(0) = 0 and δ(M) = 1.More specifically, if m = 0, then v j = RL j , j ≥ 1, which means that the item is restored to as bad as old (ABAO); if m = M, the item is restored back to as good as new (AGAN); while in a more general case m  (0, M), the item is partially restored, i.e. the PM activity is imperfect.This concept will be used in the next section to derive the expected.

Failures and Renewal Process
Most products are complex and multipart so that an item can be viewed as a system consisting of several components.The failure of an item occurs due to the failure of one or more components.A remanufactured products or component is categorized in terms of two states viz., working or failed.
The time intervals between consecutive failures are random variables and modelled by proper distribution functions.Interchangeably, the number of failures over time can model by a suitable counting process.
The actions to make a failed item operational depend on whether the failed component(s) are repairable or not.In the case of a repairable component, the remanufacturer has the option of repairing or replacing it by a remanufactured working component if available.If not a new component will be used to rectify the claim.In case of repairable components, the characterization of subsequent failures depends on the type of repair (e.g., minimal repair, imperfect repair and so on).Similarly, in the case of a non-repairable component, the remanufacturer can use a remanufactured working component in the replacement to make the item operational.
In two-dimensional warranty policies, remanufactured item failures can be viewed as random points occurring over a two-dimensional region.Time to first failure of a remanufactured component depends on the mean remaining lifetime (MRL) and the PM of the component at the time of sale of the remanufactured product.If the sensor information about EOL component indicates that it has never failed, or was always minimally repaired, then the remaining life of the component at sale is the same as that of the item.Usually, the MRL of remanufactured component at sale differs due to the replacement or repair and maintenance actions.Therefore, the time to first failure under warranty needs to be defined.Let RL i denote the remaining life of remanufactured component, i.There are two cases: either RL i is known because of embedded sensor or RL i is unknown because it is a conventional product.
The sensor embedded in the item provides the remanufacturer with the MRL of the item at sale and the virtual remaining life due to upgrades and maintenances information.The item failure is modelled by a point process with intensity function Ʌ(RL) where RL represents the remaining life of the item.
Ʌ(RL) is a decreasing function of RL indicating that the number of failures increases with remaining life decrease.The failures over the warranty period occur according to a non-stationary Poisson process with intensity function Ʌ(RL).This implies that N (W; RL), the number of failures over the warranty period W for an item of remaining life RL at the time of sale and virtual remaining life v, is a random variable with (3) The expected number of failures over the warranty period is given by ( 4) The expected number of renewals over the warranty period is given by the two-dimensional renewal

Renewing 2D Free Replacement Warranty Policy
Under this policy whenever a remanufactured item fails in the warranty region; Ω, the remanufacturer replaced all failures with a remanufactured one at no cost to the buyer.The replacement comes with a new warranty identical to the original one.There are four different warranty regions under FRW policy as shown in Figure 5.The expected warranty cost per remanufactured item is given by ( 7)

Renewing FRW with Infinite Strips Region
The warranty region is characterized by two infinite dimensional strips as shown in Figure 5(b).Under this warranty region, the policy assures the buyer is guaranteed a minimum coverage for W units of time after sale and for U units of usage.The warranty expires the first time instant both time and usage exceeds the limits W and U respectively.As a result, the number of replacements under warranty is given by (8) As a result, the expected warranty cost per remanufactured item is given by ( 9)

Renewing FRW with Four Parameters Region
The warranty region is characterized by four parameters (W 1 , W 2 , U 1 and U 2 ) as shown in Figure 5(c).
Under this policy, a buyer is assured of warranty coverage for a minimum time period W 1 and for a minimum usage U 1 and for a maximum cover for W 2 unit of time and U 2 unit of usage.As a result the number of replacements under warranty is given by (10) As a result, the expected warranty cost per remanufactured item is given by (11)

Renewing FRW with Triangle Region
The warranty region is characterized by a triangle shape as shown in Figure 5(d).The number of replacements under warranty is given by ( 12) As a result, the expected warranty cost per remanufactured item is given by ( 13)

Renewing 2D Pro-Rata Warranty Policy
Under this policy, if the remanufactured item fails in the warranty region, Ω, a remanufactured replacement is supplied at reduced price.This can be viewed as a conditional refund since the refund is tied to a remanufactured replacement purchase.Similar to FRW policy, two different forms for warranty region and refund function, R(t, x) are been consider for PRW.

Renewing PRW with Rectangle Region
The warranty region is characterized by a rectangle shape as shown in Figure 5(a) and the refund function is given by ( 14) As a result, the expected warranty cost per remanufactured item is given by ( 15)

Renewing PRW with Infinite Strips Region
The warranty region is characterized by two infinite dimensional strips as shown in Figure 5(b) and the refund function is given by ( 16) As a result, the expected warranty cost per remanufactured item is given by ( 17)

Renewing FRW-PRW Combination Policy
In combination warranty, the warranty region, Ω, consists of two disjoint sub-regions Ω 1 and Ω 2 where the warranty terms are different for each region.If a failure occurs in Ω 1 , the buyer is entitle to FRW policy.While, if a failure occurs in Ω 2 , the buyer is entitle to PRW policy.The replacement is covered with a new warranty identical to that of the original item.Similar to PRW policy, two different forms for warranty region and refund function, R(t, x) are been consider for FRW-PRW combination policy as shown in Figure 6.The expected warranty cost per remanufactured item is given by ( 19)

Renewing FRW-PRW Combination with Infinite Strips Regions
The warranty region is characterized by two infinite dimensional strips regions as shown in Figure 6(b).
As a result the refund function is given by (20) As a result, the expected warranty cost per remanufactured item is given by ( 21)

Conclusions
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 the 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, twodimensional, Free Replacement Warranty (FRW) or Pro-Rata Warranty (PRW) or Combination FRW/PRW warranty policies to 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 were examined and presented to illustrate the model's applicability.

Figure 3 .
Figure 3. Scheme for PM policies for remanufactured Products

Figure 4 .
There are many different available two-dimensional consumer warranty policies which most products are sold with.The most famous renewing consumer warranties are the Renewing Free Replacement Warranty (FRW) and Renewing Pro-Rata Warranty (PRW), or a combination of the both FRW/PRW.

Figure 4 .
Figure 4. Parameters used in the ARTO system

F
i ( .): Marginal distribution function of F( ., .); F( ., .): Bivariate distribution function; F( .| .): Conditional distribution function; R( ., .): Refund function for two-dimensional warranty; N( .): Number of replacements under warranty; N( ., .): Tow-Dimensional renewal function associated with F( ., .); N(W; RL): Number of failures over the warranty period with remaining life, RL; τ ri : Time at which warranty expires; G( .): Distribution function of usage rate; E[.]: Expected value of expression within [.]; C d (W; RL): Total warranty cost to remanufacturer; used to generate the remaining life and usage of remanufactured item at failure; (ti, xi), using a bivariate random number generator and time history of replacements under warranty and repeat sales over the simulation time interval.The ARENA simulation program yields the remaining life and usage at failures under warranty; the virtual remaining life after preventive maintenance activities, the number of replacements under warranty for each purchase and the time between repeat purchases.

Figure 6 .
Figure 6.Warranty Regions for Combination Warranty Policy

Table 1 .
AC Components and precedence relationship

Table 2 .
Taguchi (1986)rial design with 54 factors at 3 levels requires an extensive number of experiments (viz., 5.815E+25).To reduce the number of experiments to a practical level, a small set of all the possible combinations was picked.The selection method of an experiment's number is called a partial fraction experiment, which yields the most information possible of all the factors that affect the performance parameter with minimum number of experiments possible.For these types of experiments,Taguchi (1986), enacted specific guidelines.A new method of conducting the experimental design was to use a special set of arrays called orthogonal arrays (OAs) that were built by Taguchi.Orthogonal arrays Parameters used in the ARTO system provided a way to only have to conduct a minimal number of experiments.In most cases, orthogonal array is more efficient when compared to many other statistical designs.The minimum number of experiments that are required to conduct the Taguchi method can be calculated based on the degrees of freedom approach.

Table 3 .
Factors and factor levels used in design-of-experiments study So, the number of experiments must be greater than or equal to a system's degrees-of-freedom.The Precisely, L 109 (3 54 ) (i.e., 109= [(Number of levels -1) x Number of Factors] +1) Orthogonal Arrays were chosen because the degree of freedom ARTO system is 101, meaning it requires 101 experiments to accommodate 54 factors upon three different levels.Additionally, orthogonal array assumes that there is no interaction between any two factors.

Table 4 .
Expected number of failures and cost for remanufactured AC and components for 2D Renewable FRW, PRW and Combination Policies