## Abstract

Standard life cycle techniques such as life cycle warranty cost (LCWC) analysis and life cycle analysis (LCA) are used to respectively quantify the relative economical and environmental advantages of remanufactured goods while simultaneously identifying avenues for improvement. In this paper, we contribute to the literature on life cycle studies by incorporating reliability into LCWC analysis and LCA with the goal of improving long-term/multiple life cycle decision making. We develop a branched power-law model to incorporate the physical degradation mechanisms leading to reduced reuse rates of system parts over multiple life cycles. We then follow a standard LCA protocol to quantify the difference between a new unit and its remanufactured version in terms of environmental impact items such as abiotic depletion potential, global warming potential, and energy consumption. We then devise four practical warranty policies that vary in the choice of replacement and/or provision for extended warranty. All possible replacement scenarios for multiple life cycles are explored for each policy and a mathematically rigorous framework is provided, where the reliability information is used to calculate probabilistic LCWC and life cycle impact items. This reliability-informed LCWC analysis and LCA framework enables design engineers to compare design options and warranty policies by quantifying both economical and environmental impacts to aid in decision making. Although the framework is presented in a general form applicable to any engineered system, we demonstrate the utility of this framework by using a case study of an infinitely variable transmission used in agricultural equipment.

## 1 Introduction

Sustainability is being widely pursued by the industry to improve competitiveness on mitigating the environmental impacts, reducing economic costs, and enhancing social benefits [1,2]. Life cycle warranty cost (LCWC) analysis estimates the economic costs associated with the replacement of a failed product within a warranty period, whereas life cycle analysis (LCA) is typically used for capturing the environmental impacts of a product by considering the material extraction and processing, manufacturing, and transportation. Both LCWC analysis and LCA are commonly used in evaluating the sustainable capability of industrial products [35]. Remanufacturing plays an important role in enabling sustainability to put used or end-of-life products back into an “as new” functional state [6,7]. Distinguished from the other end-of-life strategies such as landfills and recycling, remanufacturing offers better preservation of value-added during the original fabrication process including labor, energy, and equipment expenditures [810], paving the way for implementing green/sustainable manufacturing. Particularly, remanufacturing is attractive for engineered systems in which a large fraction of components can be reused [11,12]. A report published by the United States International Trade Commission (USITC) in 2012 [13] identifies the United States as the largest remanufacturer in the world, particularly in the aerospace, heavy-duty and off-road equipment, and motor vehicle sectors. Canada, the European Union, and Mexico are important export markets for the U.S. remanufactured goods.

To the best of our knowledge, most of the research presenting LCWC analysis only considers replacements with new system units. The warranty policies are classified into renewing and non-renewing policies [14,15] that differ in whether a replacement unit is covered by an extended warranty. The expected warranty costs under non-renewing policies for both repairable and non-repairable systems were informed by the ordinary renewal process-based product failure model [16,17]. In addition to the expected warranty cost, Polatoglu and Sahin [18] also derived the probability distributions of the warranty cost, profit, and revenue for the renewing policies. The warranty policy directly affects the life cycle cost by taking into consideration the possibilities of renewal with a new or a remanufactured unit. Huang et al. [19] considered the free replace-repair warranty policy defined in Ref. [15] and utilized the associated warranty cost model to minimize the life cycle cost.

The automotive, and the heavy-duty and off-road industries share a large stake in the remanufacturing sector [20]. Comparative studies related to the remanufacturing of components/machines such as injectors [21], diesel engines [9,10,22], manual transmissions [23], alternators [1,24], cylinder heads [25,26], camshafts [27], and loading machines [28] exemplify the environmental and/or economic advantage of remanufacturing against new products [29]. The goal of LCA is to systematically assess the requirements in terms of resources and the corresponding impacts of the technologies on the environment. Typically, industries/ researchers comply with internationally accepted ISO standards [3032] as a basis for decision making for the customers, researchers, and industrialists. LCA can be performed either using a (1) process-based or (2) economic input output-based method. The process-based method, which is extensively used, requires material and energy workflow in the system boundary definition, whereas the input output-based method requires extensive data for several years and falls behind to accommodate quick adaption to newer technologies and fast policy changes [33].

Most of the comparative studies do not consider reliability when assessing the long-term benefits of adopting remanufacturing using LCWC analysis and LCA [3436]. One other issue with the comparative studies is that repeated remanufacturing allowing usage for multiple life cycles is rarely discussed. Products with low reliability would require frequent replacements leading to significant economic costs and environmental impacts. In some cases, the product design may fail to accommodate flexibility to modify/replace damaged components and therefore requiring complete product replacement for every failure [37,38]. In other words, connecting reliability, which provides statistical information regarding the expected failure rate of a product, and a theoretical LCWC analysis and LCA framework will provide a more realistic scenario to manufacturing companies. Therefore, as the industries embrace remanufacturing as a means for sustainable development, systematic reliability-informed LCWC analysis and LCA need to be performed which directly affect the decision making of the manufacturer in terms of replacing a failed product with a new product versus replacing with a remanufactured product [39,40]. To address this, we propose a reliability-informed LCWC/LCA framework that enables design engineers to compare design options and warranty policies by quantifying both economical and environmental impacts to aid the decision-making process. In the proposed framework, we perform both LCWC analysis and LCA with consideration of two replacement options during a system failure event: replacement with a newly manufactured (or new) system unit and replacement with a remanufactured system unit. The present work utilizes real data obtained from a transmission used in agricultural machines manufactured by John Deere and is an extension of our conference paper on reliability-informed LCWC analysis [41]. The highlights of the present work are:

1. LCWC analysis and LCA are considered for multiple remanufacturing cycles.

2. A branched power-law model is developed to characterize the degradation behavior of system parts upon repeated reuse for multiple life cycles.

3. A sales-based transportation model is developed which accounts for multiple transportation modes of both the system and its parts.

4. The reliability of the system is derived from the field time-to-failure data. The reliability model then serves as an input to both LCWC analysis and LCA. To this end, four practical warranty policies are explored to quantify both the warranty cost and the environmental impacts to aid in the decision-making process.

Figure 1 shows the proposed reliability-informed LCWC analysis and LCA framework, which consists of two parallel routes: (1) monetary (LCWC analysis) and (2) environmental (LCA). Both routes first require quantifying the difference between a new and a remanufactured unit, followed by integrating reliability information to obtain realistic long-term monetary and environmental implications of a particular design/policy. The remainder of the paper is organized as follows. In Sec. 2, we present the detailed process of conducting LCA using standard practices for both new and remanufactured transmissions for multiple life cycles. Several environmental impact items that are derived from the LCA are identified and formulated such as abiotic depletion potential (ADP), global warming potential (GWP), and energy consumption. In this section, we also partially present the results of a case study of an infinitely variable transmission used in agricultural equipment. In Sec. 3, we perform the reliability analysis based on the field time-to-failure data and the renewal process. Following this, four practical warranty policies are considered. Using the environmental impact items determined in Sec. 2, reliability-informed LCWC analysis and LCA are formulated with mathematical rigor. In Sec. 4, we present the final results of the proposed reliability-informed LCWC analysis and LCA on the case study. The proposed framework, however, is not limited to the case study and can be adopted for other engineered systems where field reliability data and remanufacturing reuse-rate data are available for analysis.

Fig. 1
Fig. 1
Close modal

## 2 Life Cycle Analysis of Newly Manufactured and Remanufactured Transmissions

The ISO 14040:2006 to ISO 14042:2006 [3032] standards require LCA to include (1) defining the goal and scope of the LCA [31], (2) identifying the life cycle inventory (LCI) [31], (3) quantifying the impacts through life cycle impact assessment (LCIA) [32,42], and (4) interpreting the results. We now present a detailed LCA study in accordance with these guidelines.

### 2.1 Goal and Scope Definition.

The goal of this study is to analyze and compare the energy requirements and environmental impacts of new and remanufactured transmissions for multiple life cycles. We first quantify the material and energy consumption for both new and remanufactured transmissions followed by the calculation of air emissions and environmental impact factors such as GWP and ADP.

The functional unit used in this study is an infinitely variable transmission used in agricultural machines manufactured by John Deere. The transmission consists of approximately 360 different components which include a hydrostatic module, planetary gears, shafts, etc. A cradle-to-grave approach [43,44] was selected to perform the analysis for multiple life cycles with reuse and recycling at the end of each life cycle. The scope and boundaries of the new and remanufactured transmissions of this study are shown in Fig. 2. The life cycle of a new transmission begins with material production, component manufacturing, assembly, and transportation to the dealers/customers. For remanufacturing, the process starts with transportation of the recalled transmission cores to the remanufacturing plant, followed by disassembly, inspection, cleaning, reassembly with new replacement parts while reusing other components, and transportation of remanufactured transmissions back to the customers. By the assurance of the manufacturer, we assume that the performance/reliability of the remanufactured transmission is as good as new, which will be discussed in detail in Sec. 3. The manufacturer confirmed that the past 20 years of operation had shown that transmission cores typically undergo a maximum of three remanufacturing cycles, and past that point, the demand for this type of service solution decreases among the targeted machine population. In this study, the first life cycle corresponds to a new transmission, whereas the second, third, and fourth life cycles correspond to remanufactured transmissions.

Fig. 2
Fig. 2
Close modal

### 2.2 Life Cycle Inventory.

The raw material requirement and energy consumption are quantified in the LCI. A bill of materials (BOM) was provided by the manufacturer which detailed the weights of all the parts and their corresponding materials used for a single transmission. Upon recalling the cores for remanufacturing, some components that only require minor refurbishment can be reused for the next life cycle. The probability of reusing a component is provided by the manufacturer, which we refer to as the reuse-rate α. The electricity consumption during disassembly, inspection, cleaning, and assembly at the manufacturing plants and the quantity of materials recycled have been provided by the manufacturer for the year 2019.

We now identify individual contributions to the energy consumption and emissions for completing the LCI study which includes raw material embodied energy $E$emb, electrical energy for manufacturing the components $E$manu, transportation of the components/transmission $E$transport, electrical energy for industrial processes such as cleaning and assembly, $E$process and energy savings arising from recycling $E$recycle. The net energy consumption per transmission can be determined by summing up the components
$E=Eemb+Emanu+Etransport+Eprocess+Erecycle$
(1)

#### 2.2.1 Embodied Energy.

Embodied energy is the energy required for converting a material into a final manufactured product. In this study, we define the embodied energy to be the equivalent of process energy requirement (PER) which corresponds to the amount of energy in MJ needed for the conversion of materials from mining to processed material blocks (which will then be used for manufacturing individual transmission parts). The transmission considered in this study primarily consists of about 70% of cast iron, 29% of steel, 0.9% of aluminum, and 0.1% of rubber by weight. The amount of rubber used is very small and is always replaced with a new part for every remanufacturing cycle. Therefore, we do not account for rubber in our comparative analysis. The embodied energy of the transmission $E$emb can be defined as
$Eemb=∑j=1Ntmjbejb(MJ)$
(2)
where Nt is the total number of transmission parts, $mjb$ is the mass of material block required to make each transmission part, and $ejb$ is the specific embodied energy defined by the material used to make the jth part. The specific embodied energy for each material is obtained from the calculator tool by the REMADE institute.3 Equation (2) is straightforward for quantifying the embodied energy for a new transmission. But for quantifying the same for a remanufactured transmission, we need to account for the effect of the reuse-rate α of each transmission part. Inspired by the binary tree architecture commonly used in the field of computer science [45], we developed a branched power-law model which is built on the backbone of a binary tree structure where each part for every life cycle can either be reused or replaced with the new. The manufacturer provided the reuse rates at the end of the first life cycle of all the parts in the BOM, denoted as αj, j = 1, 2, …, Nt. We expect that the reuse rates for successive remanufacturing cycles to decrease primarily due to two physical phenomena: (1) the interaction between the new parts and reused parts may not be “as new” and (2) successive reuse of the same part multiple times may cause material fatigue and change the part dimensions and hence decrease the reuse rate. For each part j in the BOM, we account for the former effect by considering a linear decrease of the base value of αj by about 10% for every remanufacturing cycle and the latter effect by including an exponent to αj depending on the number of successive reuses. It should be mentioned that during remanufacturing, whenever a part is reused, it is first restored through refurbishing/reconditioning to meet the original specification as a new part. As a result, a remanufactured unit has very similar reliability to that of a new unit. Moreover, a remanufactured unit can potentially have better reliability as (1) the cores returned for remanufacturing have mostly survived the infant mortality period, effectively lowering the probability of infant mortality failure, and (2) in practice, based on the inputs from remanufacturing experts at John Deere Reman, components are sometimes replaced with their upgraded designs that often have improved reliability. Figure 3 shows a schematic of the proposed branched power-law model for part j in the BOM for multiple life cycles. The reuse rate of part j at the end of the ith life cycle is now represented as $αj,ik$, where the superscript k is the number of successive reuses of the part. Figure 3 also lists the probability of each replacement status and the successive reuse of this part is shown by an increasingly darker shade, indicating a decrease in reuse rate. The branched power-law model, therefore, provides a discrete probability distribution accounting for the possibilities of using a new or a remanufactured unit at every reman cycle. To account for the uncertainty in whether a part is reused in a remanufactured transmission, the Monte Carlo simulation (MCS) is performed iterating over 3000 transmissions to arrive at an average material requirement $mjb¯$ for each life cycle i and then use Eq. (2) to obtain the embodied energy for remanufacturing at the end of each life cycle.
Fig. 3
Fig. 3
Close modal

#### 2.2.2 Manufacturing.

The manufacturing processes required for each part are highly varied and are impractical for a part-by-part quantification. Considering the shift of the industries toward more energy-intensive processes, we use estimated energy consumption for machining as em = 1.87 × 105 J/cm3 [45,46] with a net material removal of $γ=5%$ for steel and aluminum, and $γ=10%$ for cast iron (based on the manufacturer’s suggestions). The total energy consumption for remanufacturing can be stated as
$Emanu=∑j=1NtΔmjem/ρj(MJ)$
(3)
where Δmj is the material loss when machining a block of material with mass $mjb$ and density ρj to obtain the transmission part of mass $mjp=(1−γ%)mjb$ given as $Δmj=γmjb/100$. Equation (3) can also be used to quantify the energy consumption for making new part replacements for remanufacturing with the exception that the mass components are now replaced with average material requirements $mjb¯$ after considering the reuse rates of the parts (as discussed in Sec. 2.2.1). Following this, the average masses of the parts after manufacturing can be defined as $mjp¯=(1−γ%)mjb¯$.

#### 2.2.3 Transportation Model.

We conduct the LCI for the transmission sold in the U.S. only. John Deere manufactures the new transmissions in Waterloo, Iowa, and remanufactures in Edmonton, Canada. The current transportation scenario for both new and remanufactured transmissions is shown in Fig. 4. First, the raw materials are transported from the material supplier/mines to component/part suppliers. After manufacturing, the parts are shipped to the manufacturing plant in Waterloo, Iowa for inspection and assembly. The finished transmissions are then sent to seven distribution centers all over the U.S. from which the transmissions reach the local dealers, and customers purchase transmissions from the local dealers. Upon failure, the transmission cores are recalled to a central hub at Springfield, Missouri, where the cores are collected and then shipped to Edmonton, Canada, for remanufacturing. New parts for replacement are obtained from the Waterloo manufacturing plant. The manufacturer noted that the part suppliers are optimally located around the Waterloo plant for manufacturing, and for remanufacturing at the Edmonton plant, new parts are obtained from the Waterloo plant. Although the transportation distances ③, ⑤, and ⑥ from Fig. 4 are shown for a candidate distribution center in Texas, in reality, the distances ③, ⑤, and ⑥ are calculated by sales-based weighted average. Primarily two modes of transportation are used: a heavy-duty truck with specific energy consumption eroad = 2.48 MJ/(tonne.km) and rail transportation with specific energy consumption erail = 0.54 MJ/(tonne.km) [47,48]. As can be seen from Fig. 4, at present the transportation is dominated by heavy-duty trucks with some railroad connections, and the transportation route for the process of remanufacturing is completely driven by heavy-duty trucks. To this end, we propose two scenarios as a means to quantify and suggest modifications to the current protocol based on LCIA: (1) when transportation is exactly as shown in Fig. 4 and (2) when distances ⑦ and ⑧ are replaced with railroad transportation considering that the relevant locations are well connected by railroads. We find that, for transportation scenario 1, the total distance covered by the heavy-duty trucks is about 8500 km of which about 5000 km is substituted by rail in scenario 2. The transportation energy consumption associated with new transmission $Etransportnew$ (Eq. (4)), remanufactured transmission for scenario 1 $Etransportre,1$ (Eq. (5)), and scenario 2 $Etransportre,2$ (Eq. (6)) can be given as
$Etransportnew=∑j=1Ntmjbdj,1eroad+∑j=1Ntmjp(dj,2eroad+dj,3erail+dj,4eroad)$
(4)
$Etransportre,1=∑j=1Ntmjb¯(dj,1eroad)+∑j=1Ntmjp¯(dj,2eroad)+∑j=1Nt2mjperoad(dj,5+dj,6+dj,7)+∑j=1Ntmjp¯(dj,8eroad)$
(5)
$Etransportre,2=∑j=1Ntmjb¯(dj,1eroad)+∑j=1Ntmjp¯(dj,2eroad)+∑j=1Nt2mjp(eroaddj,5+eroaddj,6+eraildj,7)+∑j=1Ntmjp¯(dj,8erail)$
(6)
Fig. 4
Fig. 4
Close modal

We note that accounting for the transportation distance ⑧ from Fig. 4 is only necessary when a new replacement part is required (following the analysis of the branched power-law model presented in Sec. 2.2.1).

#### 2.2.4 Processing.

Electrical energy requirements at the manufacturing plants for processes like inspection, cleaning, assembly, and disassembly $E$process are provided by the manufacturer based on yearly data.

#### 2.2.5 Recycling.

During the process of remanufacturing, parts that cannot be reused are either recycled locally or discarded through a landfill. Since most of the components are metallic with very slow rates of degradation, we do not consider the GWP caused by the landfill. On the other hand, the process of recycling requires a certain amount of energy for melting and processing erecycle(kJ/kg) but adds to the benefit of the environment by replacing requirements for virgin materials which otherwise demand a higher specific energy eb (same embodied energy as described in Sec. 2.2.1). The recycling benefits can, therefore, be expressed as
$Erecycle=∑k=1Kmkrecycle(ekrecycle−ekb)$
(7)
where the recycle masses $mkrecycle$ of all the materials k are provided by the manufacturer and the embodied energy for recycling $ekrecycle$ is obtained from the calculator tool by the REMADE institute.4 We note that $E$recycle from Eq. (7) is negative indicating a net energy consumption benefit resulting from recycling.

#### 2.2.6 Results and Interpretation.

We first present the effects of remanufacturing on energy consumption, following which we list the inputs and outputs of LCI. The branched power-law model for the reuse rates enforces a probabilistic nature to the energy consumption associated with remanufactured transmissions. Figure 5(a) shows the probability distributions of energy consumption obtained from the MCS and Fig. 5(b) shows the individual energy contributions for four life cycles. For the second life cycle (or first remanufacturing cycle), the mean value of the total energy consumption is about $70%$ of a new transmission $E$new. As can be seen from Fig. 5(b), the primary source for energy savings for the second life cycle arises from $E$emb with a $50%$ decrease with respect to a new transmission (life cycle 1). However, part of the energy savings obtained from the decrease of $E$emb is mitigated by an increase in $E$transport leading to a net energy savings of $35%$ for the second life cycle. Further, analyzing Figs. 5(a) and 5(b) for the third life cycle, we observe an increase in energy demand for remanufacturing when compared to the second life cycle and even more for the fourth life cycle where the energy consumption is similar to that of a new transmission. This is attributed to the decrease in the reuse rate with the life cycle number (Sec. 2.2.1). However, we note that the magnitude of the difference between the distributions of life cycles 2 and 3, as shown in Fig. 5(a), is highly dependent on the decrease of the base value of reuse-rate α with the life cycle number (which was assumed to be 10% here as mentioned in Sec. 2.2.1). Designing the components that maintain material integrity would minimize the decrease of α, thus decreasing the energy gap between life cycles 2 and 3. To further demonstrate the sensitivity toward the decrease of α, we perform an analysis similar to that of Fig. 5(b) but assume the base values of the reuse-rates α to be constant, and only account for material degradation through the power-law exponent reflected by the number of successive reuses of each of the parts. The energy consumption contributions for this hypothetical scenario are shown in Fig. 5(d), where $E$emb shows smaller increases over multiple remanufacturing cycles when compared to Fig. 5(b). On the other hand, using materials that corrode/fatigue faster would restrict the benefits of remanufacturing by requiring the replacement of almost all the components with new parts for every attempted remanufacturing cycle. This sensitivity analysis (i.e., by comparing Figs. 5(b)5(d)) motivates a design problem which we plan to investigate in the future. At present, the manufacturer does not distinguish the life cycle number of a remanufactured transmission. To provide an average estimate of the remanufactured energy consumption $Ere¯$, we assume the transmissions from life cycle 2 to 4 be available in a proportion of 4:2:1 and perform a weighted sum to determine $Ere¯$. In Fig. 5(c), the various energy components identified in Secs, 2.2.12.2.5 and Fig. 5(b) are quantified for a new transmission and a remanufactured transmission with transportation scenarios 1 and 2 (defined in Sec. 2.2.3). As stated previously, we can observe from Fig 5(c) that although the reuse of parts greatly decreases the embodied energy $E$emb from 80% of $E$ for a new transmission to about 45% for a remanufactured transmission, this benefit is partly nullified by the long transportation distances to Edmonton, Canada especially by road ($Ere¯$ S 1). Adopting rail transportation whenever possible ($Ere¯$ S 2) greatly reduces $E$transport and provides more than 30% net energy consumption benefit when compared to $E$new, which is 10% additional benefit when compared to $Ere¯$ S 1.

Fig. 5
Fig. 5
Close modal

A detailed listing of all the inputs and outputs for the LCI is provided in Table 1 for both new and remanufactured transmissions. Part of the required resources, such as crude oil and natural gas, is estimated based on yearly resource consumption data provided by the manufacturer. We also included the resources and emissions arising from the raw material [49], U.S. electric supply [50], and transportation [51,52]. As can be observed from Table 1, remanufacturing shows a clear advantage in most departments except for the high dependence on heavy-duty truck transport. Although the branched power-law model provides a discrete probability distribution (see Sec. 2.2.1), we only list the expectation values for the entries corresponding to the remanufactured transmissions in Table 1.

Table 1

Inputs and outputs for LCI of the new and remanufactured (reman) transmissions

CategorySubstanceNewRemanSavings
InputsMaterial (kg)Cast iron930.50429.85500.65
Steel358.99186.15172.84
Aluminum8.144.833.31
Transportation (km)Heavy truck21008500−6400
Energy (MJ)Net value6.69e45.05e41.64e4
Resources (kg)Crude oil250.16131.42118.74
Natural gas781.26414.46366.80
OutputsAir emissions (kg)CO15.768.517.25
CO216,603.869217.07386.9
NOx50.3431.7618.58
CategorySubstanceNewRemanSavings
InputsMaterial (kg)Cast iron930.50429.85500.65
Steel358.99186.15172.84
Aluminum8.144.833.31
Transportation (km)Heavy truck21008500−6400
Energy (MJ)Net value6.69e45.05e41.64e4
Resources (kg)Crude oil250.16131.42118.74
Natural gas781.26414.46366.80
OutputsAir emissions (kg)CO15.768.517.25
CO216,603.869217.07386.9
NOx50.3431.7618.58

### 2.3 Life Cycle Impact Analysis.

Using the information from Table 1, we estimate three environmental impact factors: ADP, GWP, and energy consumption presented in Table 2. Both ADP and GWP are calculated by using characterization factors consistent with CML 2002 [53]. The results show that the process of remanufacturing causes a decrease of 35% ADP, 25% GWP, and 25% energy requirements.

Table 2

Characterization results of new and remanufactured (reman) transmissions

Impact itemSubstance(s)New quantityReman quantityCharacterization factorUnitNewReman
ADP CML2002Steel and cast iron1289.49 kg616.00 kg1.66E−6kg Sb-eq10.3E−35.4E−3 (52%-new)
Aluminum8.14 kg4.83 kg2.53E−5
Crude oil250.16 kg131.42 kg9.87E−6
Natural gas781.26 kg414.46 kg7.02E−6
GWP CML2002CO216,603.86 kg9217.0 kg1kg $CO2−$ eq32,744.1819,397.04 (60%-new)
NOx50.34 kg31.76 kg320
CO15.76 kg8.51 kg2
Energy consumptionNet6.69e4 MJ5.05e4 MJ1MJ6.69e45.05e4 (75%-new)
Impact itemSubstance(s)New quantityReman quantityCharacterization factorUnitNewReman
ADP CML2002Steel and cast iron1289.49 kg616.00 kg1.66E−6kg Sb-eq10.3E−35.4E−3 (52%-new)
Aluminum8.14 kg4.83 kg2.53E−5
Crude oil250.16 kg131.42 kg9.87E−6
Natural gas781.26 kg414.46 kg7.02E−6
GWP CML2002CO216,603.86 kg9217.0 kg1kg $CO2−$ eq32,744.1819,397.04 (60%-new)
NOx50.34 kg31.76 kg320
CO15.76 kg8.51 kg2
Energy consumptionNet6.69e4 MJ5.05e4 MJ1MJ6.69e45.05e4 (75%-new)

## 3 Reliability-Informed LCWC Analysis and Life Cycle Analysis Framework

In this section, we first determine the reliability function from the time-to-failure data. This reliability function is then incorporated into the LCWC analysis and LCA for various practical policies, following which we present algorithms in trying to numerically determine the expected LCWC and life cycle impact items (LCIIs) as well as their analytical solutions whenever possible. The LCIIs consist of LCA-derived ADP, GWP, and energy consumption but with the inclusion of reliability.

### 3.1 Reliability Function and Renewal Process.

Reliability data usually contain information about the time-to-failure values of the system units. The time-to-failure distribution can be derived from such information which can then serve as an input to model the reliability of this system [5456]. Amongst various possible distribution fits, we use the most commonly used Weibull distribution to model the time-to-failure distribution. The probability density function of the Weibull distribution can be expressed as
$f(x)=βλ(xλ)β−1exp[−(xλ)β]$
(8)
where β is the shape parameter that determines the shape of the function f(x), x is the time-to-failure, and λ is the scale parameter. The probability of failure (Pf) of the system is measured by the cumulative Weibull distribution function, given as
$Pf(x)=F(x)=∫0xf(x)dx=1−exp[−(xλ)β]$
(9)
The reliability/survival function is then calculated as
$R(x)=1−Pf(x)=∫x∞f(x)dx=exp[−(xλ)β]$
(10)

The parameters in the Weibull distribution, β and λ, are determined using the maximum likelihood estimation to provide the best fit to the field time-to-failure data.

In this study, we assume the replacements to be instantaneous (zero downtime), and the choice of replacement depends on the renewal process. In a renewal process, a system used to replace a failed system can have a different reliability function than the failed system. This enables modeling the LCWC for a warranty policy where a new system, once failed, is replaced with a remanufactured system that could have a different reliability function when compared to the new system. The schematic of the renewal process is shown in Fig. 6. The failure events and the corresponding replacement events are considered to occur randomly. The time between two consecutive failure events tj, j = 1, 2, …, R, is assumed to be an independent and identically distributed random variable following the Weibull distribution.

Fig. 6
Fig. 6
Close modal
The time from the beginning-of-life of a system to the Rth renewal is defined as
$TR={0,R=0∑j=1Rtj,R≥1$
(11)
The number of renewals N(t) within time t is then defined as
$N(t)=sup{R|TR≤t}$
(12)
where sup is the supremum function. The probability mass function of N(t) is calculated by
$P(N(t)=R)=P(N(t)≥R)−P(N(t)≥R+1)=P(TR≤t)−P(TR+1≤t)=FR(t)−FR+1(t)$
(13)
where FR(t) is the R-fold convolution of F with itself [57], defined as
$F0(t)=1$
$F1(t)=F(t)$
$FR(t)=∫0tF(t−u)dFR−1(u),R=2,3,..$
(14)

### 3.2 Warranty Policies.

Four warranty policies are considered in this study, which are summarized in Table 3. A regular warranty of Tw = 2000 h (starting from the beginning-of-life or life cycle 1) applies to all four policies. For the first three policies (Policies 1–3), the customers get one additional 2000 h of extended warranty after replacement if the replacement occurs within the regular/extended warranty period. Whereas for the fourth policy (Policy 4), no extended warranty is provided after replacement. Policies 1–3 differ in whether a new or remanufactured unit is used for replacement.

Table 3

Four warranty policies considered in this study

Policy indexExtended warrantyRenewal strategy
1YesA new unit replaces the first failed unit if the failure occurs within Te = 500 h of regular warranty. Remanufactured units are used for subsequent replacements.
2All failed units are replaced with new units.
3All failed units are replaced with remanufactured units.
4NoAll failed units are replaced with remanufactured units.
Policy indexExtended warrantyRenewal strategy
1YesA new unit replaces the first failed unit if the failure occurs within Te = 500 h of regular warranty. Remanufactured units are used for subsequent replacements.
2All failed units are replaced with new units.
3All failed units are replaced with remanufactured units.
4NoAll failed units are replaced with remanufactured units.

During the event of a failure, different policies associated with different renewal affect the LCWC and the LCIIs for the four policies. For example, through Fig. 7 we depict four possible failure scenarios and renewal strategies for Policy 1 for the first three life cycles along with the warranty cost and environmental impact items at each renewal. Please note that the environmental impact items also exist at t = 0 but are not shown in Fig. 7 to avoid congestion. When the first failure occurs within Te = 500 h of regular warranty, a new unit will be used for replacement of the failed unit (see the solid diamond in scenarios 1 and 3) at the cost of the manufacturer, which adds to the warranty cost. Such replacements also incur environmental impact items for that of a new transmission (see the left three bars in scenarios 1 and 3). When a failure occurs either between Te = 500 h and Tw = 2000 h of regular warranty or during the extended warranty, a remanufactured unit will be used for replacing the failed unit (see the solid triangles in scenarios 2–4) at the cost of the manufacturer, which again adds to the warranty cost and also the environmental impact items for that of a remanufactured transmission (see the left three bars in scenarios 2 and 4). On the other hand, when a failure occurs outside the regular/extended warranty (hollow triangles in scenarios 1 and 2), a remanufactured unit will be used to replace the failed unit at the cost of the customer, which results only in the addition of the environmental impact items for the remanufactured unit but not the warranty cost (see the right two bars in scenarios 1 and 2).

Fig. 7
Fig. 7
Close modal

### 3.3 Formulations of LCWC and LCII.

For the reliability-informed LCA of the system, we set the total lifetime of the system operation to be TL = 8000 h, which is four times the regular warranty (could potentially correspond to 8 years of operation). The life cycle impact items LCIIs consist of the environmental impact items (such as energy consumption, ADP, and GWP) for all the renewals during the product’s lifetime. On the other hand, the LCWC only includes the warranty costs for all the renewals within the warranty period. These formulations are capped by either placing a limit on the number of renewals R or by TL, whichever comes first (R = 4 for the case of transmission used in this study).

We first define key terms that will lead to formulating the expected LCWC and LCII. The time-to-failure distribution (probability density function) and the probability of failure (cumulative distribution function) for the new and remanufactured transmissions are denoted as fnew/re(t) and Fnew/re(t), while the probability mass function of N(t) (see Eq. 13) for the new and remanufactured transmissions are denoted as Pnew(N(t) = R) and Pre(N(t) = R). The impact items (expectation values) for the new and remanufactured units are denoted as $Iinew$ and $Iire$, where the index i = 1, 2, 3 corresponds to environmental impact items like energy consumption (i = 1), ADP (i = 2), and GWP (i = 3), respectively. The warranty costs for the new and remanufactured transmission renewals are denoted as Wnew and Wre.

For Policy 1, the expected LCWC can be formulated as
$E[LCWC]=Fnew(Te)Wnew+[Fnew(Tw)−Fnew(Te)]Wre+Fnew(Te)Fnew(Tw)∑j=24[Fre(Tw)]j−2Wre+[Fnew(Tw)−Fnew(Te)]∑j=24[Fre(Tw)]j−1Wre$
(15)
where the first and second terms on the right-hand side (RHS) of the equation represent the expected warranty costs of new and remanufactured replacements within the regular warranty period. The third term on the RHS represents the expected warranty cost of remanufactured replacements within the subsequent extended warranty period when the original unit fails within Te. The fourth term on the RHS represents the expected warranty cost of the remanufactured replacements in the extended warranty periods when the original unit fails within Te < TTw.
For Policy 2, the LCWC is only composed of the warranty costs of new replacements. The expected LCWC can be calculated using
$E[LCWC]=∑j=14[Fnew(Tw)]jWnew≈Fnew(Tw)1−Fnew(Tw)Wnew$
(16)
The LCWC for Policy 3 only consists of the warranty costs of replacement with remanufactured units. The expected LCWC can be stated as
$E[LCWC]=Fnew(Tw)Wre+Fnew(Tw)∑j=24[Fre(Tw)]j−1Wre≈Fnew(Tw)1−Fre(Tw)Wre$
(17)

The probability of replacements beyond three replacements decreases by orders of magnitude. Therefore, as a numerical artifact, the approximate terms in Eqs. (16) and (17) are derived assuming infinite replacements. However, we use the exact form of Eqs. (16) and (17) when presenting our results.

For Policy 4, the LCWC includes the warranty costs of remanufactured replacements within the regular warranty. The expected LCWC is thereby stated as
$E[LCWC]=WreFnew(Tw)+∫0TwWrefnew(t)∑j=14jP(N(Tw−t)=j)dt$
(18)
where the first term on the RHS indicates the expected warranty cost of the first remanufactured replacement after the failure of the original unit. The second term on the RHS indicates the warranty cost of the subsequent remanufactured renewals occurring within the warranty period.
The formulations of expected LCII are similar in structure to Eq. (18). The expected LCII for Policy 1 is only related to Te and TL, which can be formulated as
$E[LCIIi]=Inewi+InewiFnew(Te)+Irei∑j=14j∫TeTLfnew(t)Pre(N(TL−t)=j)dt+Irei∑j=14j∫t1=0Te∫t2=t1TLfnew(t1)fnew(t2−t1)×Pre(N(TL−t2)=j)dt2dt1$
(19)
where the first term on the RHS indicates the initial impact item for the new transmission at t = 0, the second term indicates the impact of the first renewal before 500 h (replacement with a new unit), the third term denotes the impact when the first renewal is after 500 h (replacement with a remanufactured unit), and the fourth term corresponds to the impact of the subsequent renewals after the first new renewal.
The expected LCII for Policy 2 only involves the impact of new renewals, which can be formulated as
$E[LCIIi]=Inewi+Inewi∑j=14jPnew(N(TL)=j)$
(20)
where the second term on the RHS indicates all the new renewals before TL.
Because each LCII is independent of the warranty period, the expected LCII for Policies 3 and 4 take the same form, given as
$E[LCIIi]=Inewi+IreiFnew(TL)+Irei∑j=14j∫0TLfnew(t)Pre(N(TL−t)=j)dt$
(21)
where the second term on the RHS captures all the remanufactured renewals before TL.

### 3.4 Calculating LCWC and LCIIs Using Monte Carlo Simulation.

The calculations of expected LCWC (Eqs. (15)(18)) only require the cumulative distribution functions Fnew(t) and Fre(t), whose analytical solutions can be easily determined. However, the calculations of the expected LCWC for Policy 4 and all the LCIIs (Eqs. (19)(21)) require the probability mass functions of N(t) and its implicit integration, whose analytical solutions are not viable. We, therefore, use MCS to provide approximated values for these equations. The probability distributions of LCWC and all the LCIIs are determined based on the direct simulation of a large number of failure scenarios.

We now present an example of MCS implementation to determine the expected LCII for Policy 1 (Table 4). For each of the K simulated scenarios, the algorithm starts by generating the S random failure times (which simulates S units sold in the market) according to the time-to-failure distribution of the new transmission fnew(t) before the first renewal while also initializing the counts of new/remanufactured renewals to be zeros (lines 1–3). Then, for each of the S random failure times, if a failure occurs before 500 h, the failed unit will be renewed by a new unit following which another failure time is generated according to fnew(t), and the new renewal count increments by 1 (lines 4–6). If a failure occurs after 500 h, the failed unit will be renewed by a remanufactured unit, another failure time is generated according to fre(t), and the remanufactured unit count increments by 1 (lines 7–11). For the subsequent failures (j = 3:R + 1), all the renewals will be with remanufactured units. For each j, we generate S random failure times according to fre(t). By counting the number of cases where exactly j − 1 failures occur between 500 h and 8000 h, the remanufactured unit renewal count is updated. This process (lines 12–17) is repeated until the total number of renewals reaches R. In this case, the total number of new and remanufactured renewals are identified. We can calculate the average LCWC for the S transmissions to be the LCII for scenario k (line 18). After this process is repeated K times, we will get the probability distribution of LCII based on the K random scenarios (lines 19–20).

Table 4

Procedure for approximating the LCII with MCS for Policy 1

 Algorithm: Approximating LCII with MCS Inputs: Number of simulated scenarios: K Number of renewals: R Number of random failure times: S Time-to-failure distribution of new/remanufactured transmission: fnew(t)/fre(t) Output: LCII 1 fork = 1:K 2  Generate S random failure times $tsk,1,s=1:S$ based on fnew(t) 3  Initialize new impact items counter cnew = S and remanufacturing impact item    counter cre = 0 4  fors = 1:S 5   if$tsk,1<500$ 6    Generate a random failure time $tsk,2$ based on fnew(t) 7    cnew = cnew + 1 8   else 9    Generate a random failure time $tsk,2$ based on fre(t) 10    cre = cre + 1 11   end 12  end for 13  forj = 3:R + 1 14   Generate S random failure times $tsk,j,s=1:S$ based on fre(t) 15   Calculate the simulated times when j − 1 and j failures occur, respectively$Tsk,j−1=∑l=1j−1tsk,l$⁠, $Tsk,j=∑l=1j−1tsk,l$ 16   Find the cases where exactly j − 1 failures occur between Te and TL$Sj−1={s|Te$Tsk,j$ > TL} 17   $cre=cre+size(Sj−1)$ 18  end for 19  Calculate the LCII for the k-th scenario   LCII(k) = (Inewcnew + Irecre)/S 20  end for 21  Get the probability distribution of LCII based on the K random scenarios
 Algorithm: Approximating LCII with MCS Inputs: Number of simulated scenarios: K Number of renewals: R Number of random failure times: S Time-to-failure distribution of new/remanufactured transmission: fnew(t)/fre(t) Output: LCII 1 fork = 1:K 2  Generate S random failure times $tsk,1,s=1:S$ based on fnew(t) 3  Initialize new impact items counter cnew = S and remanufacturing impact item    counter cre = 0 4  fors = 1:S 5   if$tsk,1<500$ 6    Generate a random failure time $tsk,2$ based on fnew(t) 7    cnew = cnew + 1 8   else 9    Generate a random failure time $tsk,2$ based on fre(t) 10    cre = cre + 1 11   end 12  end for 13  forj = 3:R + 1 14   Generate S random failure times $tsk,j,s=1:S$ based on fre(t) 15   Calculate the simulated times when j − 1 and j failures occur, respectively$Tsk,j−1=∑l=1j−1tsk,l$⁠, $Tsk,j=∑l=1j−1tsk,l$ 16   Find the cases where exactly j − 1 failures occur between Te and TL$Sj−1={s|Te$Tsk,j$ > TL} 17   $cre=cre+size(Sj−1)$ 18  end for 19  Calculate the LCII for the k-th scenario   LCII(k) = (Inewcnew + Irecre)/S 20  end for 21  Get the probability distribution of LCII based on the K random scenarios

## 4 Case Study—Transmission in Agricultural Equipment

### 4.1 Reliability Analysis of the Transmissions Based on Field Data.

The time-to-failure data were obtained from the agricultural machines in the field that were equipped either with the new or remanufactured transmissions. Most of the observed failures occur before 4000 h. During the maximum likelihood estimation of the Weibull parameters, the units that have not failed are considered to be right-censored at 4000 h. The reliability data and the best-fit Weibull distribution are shown in Fig. 8. The exact number of failures (nf) and the time-to-failure data are not shown for confidentiality purposes. Reliability analysis based on the field data provided by the manufacturer shows no significant difference between the time-to-failure distributions of the new and remanufactured transmissions.

Fig. 8
Fig. 8
Close modal

### 4.2 Results: Reliability-Informed Life Cycle Analysis.

To demonstrate the utility of the LCWC and LCII models in evaluating the economic cost and environmental impacts for different warranty policies, we consider two different cases as shown in Table 5. In Case 1, the reliability levels of the new and remanufactured transmissions are the same and obtained from the field reliability data. We also perform a reliability sensitivity test by artificially setting a 5% lower reliability to the new/remanufactured transmissions in Case 2. Further, we assume the replacement cost of the remanufactured transmission to be 75% of the cost of a new transmission, which is determined based on the energy consumption comparison presented in Table 2. We would like to note a few key differences between our conference paper [41] and the work presented here which uses the same field time-to-failure data. In the conference paper, we neglected infant mortality of the transmissions when calculating the reliability numbers and also the replacement cost of the remanufactured transmission was set arbitrarily. However, in this study, we consider all types of failures for all time intervals, and the ratio of the cost of a remanufactured transmission to that of a new transmission is set to be similar to the ratio of the energy consumption of a remanufactured transmission to that of a new transmission (from Table 2).

Table 5

Costs and impact items of new and remanufactured transmissions in Cases 1 and 2

CaseCondition of the replacement unitReliability at 4000 hReplacement cost ($)ADP (kg Sb-eq)GWP (kg CO2-eq)Energy (MJ) 1New0.934340,00010.3E−332,744.186.69e4 Reman0.934330,0005.4E−319,397.045.05e4 2New0.917440,00010.3E−332,744.186.69e4 Reman0.917430,0005.4E−319,397.045.05e4 CaseCondition of the replacement unitReliability at 4000 hReplacement cost ($)ADP (kg Sb-eq)GWP (kg CO2-eq)Energy (MJ)
1New0.934340,00010.3E−332,744.186.69e4
Reman0.934330,0005.4E−319,397.045.05e4
2New0.917440,00010.3E−332,744.186.69e4
Reman0.917430,0005.4E−319,397.045.05e4

The expected LCWC and LCIIs calculated for the four warranty policies in Cases 1 and 2 are summarized in Table 6. Due to the random nature of the MCS, we perform 20 independent runs and report the means and standard deviations of the LCWC and LCIIs. We note that the values in Table 6 and subsequently the plots shown in Fig. 9 are only averaged for the renewals and do not consider the constant initial impact value of a new transmission, viz. the first term in Eqs. (19)(21), to highlight the differences in renewal strategies. For all the entries, the standard deviation of the mean value capturing the run-to-run variation of MCS is at least two orders of magnitude lower than the mean value for LCA and one order of magnitude lower for LCWC, indicating the stability of the MCS approach. We note that for Policies 1–3, the calculations of expected LCWC only require the cumulative distribution functions Fnew(t) and Fre(t), whose analytical solutions can be easily acquired. This is not true for other entries that require probability mass function N(t) within an integrand and we, therefore, report only the values obtained from MCS. For all the cases, the analytical LCWC solutions are within one standard deviation of the MCS-estimated means and the difference between the analytical LCWC and MCS-estimated LCWC is less than 1.7% which verifies our implementation of the MCS algorithm.

Fig. 9
Fig. 9
Close modal
Table 6

Results of expected LCWC and LCIIs calculated for the four policies in Cases 1 and 2

PolicyEnergy consumption (MCS: μ, σ)ADP (MCS: μ, σ)GWP (MCS: μ, σ)LCWC (MCS: μ, σ)LCWC (analytical)
MJkg Sb-eqkg CO2 − eq$$Case 11(5735.0, 6.28)(7.0e−4, 8.02e−7)(2326.1, 2.59)(1507.1, 73.4)1481.9 2(6747.0, 7.26)(10.0e−4, 10.3e−7)(3301.5, 3.43)(1773.7, 92.32)1771.8 3(5092.5, 5.23)(5.2e−4, 3.27e−7)(1953.4, 2.26)(1326.4, 64.5)1328.8 4(1276.6, 59.5)N/A Case 21(8171.5, 6.15)(9.0e−4, 7.12e−7)(3283.3, 3.13)(1599.7, 75.8)1581.9 2(9678.9, 7.06)(15.0e−4, 14.2e−7)(4751.0, 3.53)(1946.3, 91.8)1945.0 3(7329.5, 4.26)(8.2e−4, 4.47e−7)(2803.7, 2.09)(1462.2, 68.7)1458.7 4(1390.3, 68.5)N/A PolicyEnergy consumption (MCS: μ, σ)ADP (MCS: μ, σ)GWP (MCS: μ, σ)LCWC (MCS: μ, σ)LCWC (analytical) MJkg Sb-eqkg CO2 − eq$$
Case 11(5735.0, 6.28)(7.0e−4, 8.02e−7)(2326.1, 2.59)(1507.1, 73.4)1481.9
2(6747.0, 7.26)(10.0e−4, 10.3e−7)(3301.5, 3.43)(1773.7, 92.32)1771.8
3(5092.5, 5.23)(5.2e−4, 3.27e−7)(1953.4, 2.26)(1326.4, 64.5)1328.8
4(1276.6, 59.5)N/A
Case 21(8171.5, 6.15)(9.0e−4, 7.12e−7)(3283.3, 3.13)(1599.7, 75.8)1581.9
2(9678.9, 7.06)(15.0e−4, 14.2e−7)(4751.0, 3.53)(1946.3, 91.8)1945.0
3(7329.5, 4.26)(8.2e−4, 4.47e−7)(2803.7, 2.09)(1462.2, 68.7)1458.7
4(1390.3, 68.5)N/A

The probability distributions of the LCWC and LCIIs for different policies generated by a single MCS run are shown in Fig. 9. By comparing the LCWC and LCIIs from Table 6 and Fig. 9, three observations can be made. (1) The expected LCWC and LCIIs are the highest for Policy 2 where each failure event is followed by replacement with a new unit. This represents a scenario where remanufacturing is never adopted into the Policy. (2) The replacement with a remanufactured transmission, in Policies 1, 3, and 4, significantly reduces both LCWC and LCIIs when compared to Policy 2. The LCWC and LCIIs for Policy 1 are slightly higher than Policies 3 and 4 considering that new replacements are possible in Policy 1 if the failure occurs within the first 500 h, although in Case 1 with higher reliability, such early failures are unlikely. (3) The difference between policies with remanufactured replacements is significantly affected by the reliability numbers. When the reliability of the transmission is lower (Case 2), the difference between Policies 1 and 3/4 increases because lower reliability is synonymous with a greater number of failures and a possible new transmission replacement for Policy 1. On the other hand, the difference between Policies 1 and 3/4 is reduced when the reliability number is high (Case 1). When the product reliability level is high, Policy 1 may be attractive to the customer with the possibility of a new replacement upon early failure and from the perspective of the manufacturer, this can be achieved with a minimal increase in cost when compared to Policy 3 (which only considers remanufactured replacements). This analysis has the potential to enable manufacturers to quantify the expected LCWC and LCIIs whenever improvements are made to the remanufacturing process and make informed decisions regarding warranty policy design based on long-term calculations.

## 5 Conclusions

Although a direct comparison between a new and a remanufactured system unit gives a good idea about the benefits of remanufacturing local to every replacement, incorporating reliability data into LCWC analysis and LCA enables the manufacturer as well as the customer to evaluate the long-term implications of a particular policy economically as well as its impact on the environment. One of the R’s of sustainability, reuse, is the backbone of the remanufacturing process as it preserves the value-added into the parts during the original fabrication. One of the highlights of this work is to create a probabilistic workflow of the reuse rate for multiple cycles where the physical degradation mechanisms such as material fatigue, change in product dimensionality, and not “as new” interaction with other parts of the system lead to a decrease in the reuse rate for multiple remanufacturing cycles. As a consequence of this decrease in the reuse rate, we observe that the first remanufacturing cycle the embodied energy (or requirement for raw materials) only increases to the point that a remanufactured system does not show substantial benefit when compared to a new system. We propose and demonstrate a mathematical framework for a probabilistic estimate of LCWC and LCIIs for various policies by including reliabilities. This framework could potentially be extended to other engineered systems and influence the decision-making process. In many industrial settings, there is a disconnect between product designers and remanufacturers. The proposed framework will allow designers to perform early-stage design trade-off evaluations using real-world field and remanufacturing data that can be used as feedback to the design process. This framework also has the potential to initiate and facilitate conversations between product designers and remanufacturers about how to design products with end-of-life remanufacturing in mind.

For the particular case study of an infinitely variable transmission used in this study (based on real data provided by the manufacturers for sales within the U.S.), we find that the present state of remanufacturing weighted averaged over four life cycles decreases the impact on the environment by 47% for ADP, 40% for GWP, and 25% for energy consumption when compared to a brand new product. We find that although the embodied energy is significantly reduced due to remanufacturing, the transmission is transported across large distances by road which minimizes the benefit of remanufacturing. Suggestions are made to the remanufacturer to look into the possibility of switching to railroad transportation whenever possible and in such a scenario a further gain of 10% can be observed in each category. The long-term benefit observed after including reliability is a reduction of about 48% in ADP, 40% in GWP, 25% in energy consumption, and 30% LCWC when comparing policies that consider all-new replacements against policies that consider all-remanufactured replacements.

4

See Note 3.

## Acknowledgment

This material is based upon the work supported by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy (EERE) under the Advanced Manufacturing Office Award Number DE-EE0007897.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The authors attest that all data for this study are included in the paper.

## Disclaimer

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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