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 [3–5]. 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 [8–10], 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 [30–32] 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 [34–36]. 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:
LCWC analysis and LCA are considered for multiple remanufacturing cycles.
A branched power-law model is developed to characterize the degradation behavior of system parts upon repeated reuse for multiple life cycles.
A sales-based transportation model is developed which accounts for multiple transportation modes of both the system and its parts.
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.
2 Life Cycle Analysis of Newly Manufactured and Remanufactured Transmissions
The ISO 14040:2006 to ISO 14042:2006 [30–32] 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.
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.
2.2.1 Embodied Energy.
2.2.2 Manufacturing.
2.2.3 Transportation Model.
2.2.4 Processing.
Electrical energy requirements at the manufacturing plants for processes like inspection, cleaning, assembly, and disassembly process are provided by the manufacturer based on yearly data.
2.2.5 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 of a new transmission new. As can be seen from Fig. 5(b), the primary source for energy savings for the second life cycle arises from emb with a decrease with respect to a new transmission (life cycle 1). However, part of the energy savings obtained from the decrease of emb is mitigated by an increase in transport leading to a net energy savings of 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 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 , 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 . In Fig. 5(c), the various energy components identified in Secs, 2.2.1–2.2.5 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 emb from 80% of 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 ( S 1). Adopting rail transportation whenever possible ( S 2) greatly reduces transport and provides more than 30% net energy consumption benefit when compared to new, which is 10% additional benefit when compared to S 1.
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.
Category | Substance | New | Reman | Savings | |
---|---|---|---|---|---|
Inputs | Material (kg) | Cast iron | 930.50 | 429.85 | 500.65 |
Steel | 358.99 | 186.15 | 172.84 | ||
Aluminum | 8.14 | 4.83 | 3.31 | ||
Transportation (km) | Heavy truck | 2100 | 8500 | −6400 | |
Railroad | 1600 | 0 | 1600 | ||
Energy (MJ) | Net value | 6.69e4 | 5.05e4 | 1.64e4 | |
Resources (kg) | Crude oil | 250.16 | 131.42 | 118.74 | |
Natural gas | 781.26 | 414.46 | 366.80 | ||
Outputs | Air emissions (kg) | CO | 15.76 | 8.51 | 7.25 |
CO2 | 16,603.86 | 9217.0 | 7386.9 | ||
NOx | 50.34 | 31.76 | 18.58 |
Category | Substance | New | Reman | Savings | |
---|---|---|---|---|---|
Inputs | Material (kg) | Cast iron | 930.50 | 429.85 | 500.65 |
Steel | 358.99 | 186.15 | 172.84 | ||
Aluminum | 8.14 | 4.83 | 3.31 | ||
Transportation (km) | Heavy truck | 2100 | 8500 | −6400 | |
Railroad | 1600 | 0 | 1600 | ||
Energy (MJ) | Net value | 6.69e4 | 5.05e4 | 1.64e4 | |
Resources (kg) | Crude oil | 250.16 | 131.42 | 118.74 | |
Natural gas | 781.26 | 414.46 | 366.80 | ||
Outputs | Air emissions (kg) | CO | 15.76 | 8.51 | 7.25 |
CO2 | 16,603.86 | 9217.0 | 7386.9 | ||
NOx | 50.34 | 31.76 | 18.58 |
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.
Impact item | Substance(s) | New quantity | Reman quantity | Characterization factor | Unit | New | Reman |
---|---|---|---|---|---|---|---|
ADP CML2002 | Steel and cast iron | 1289.49 kg | 616.00 kg | 1.66E−6 | kg Sb-eq | 10.3E−3 | 5.4E−3 (52%-new) |
Aluminum | 8.14 kg | 4.83 kg | 2.53E−5 | ||||
Crude oil | 250.16 kg | 131.42 kg | 9.87E−6 | ||||
Natural gas | 781.26 kg | 414.46 kg | 7.02E−6 | ||||
GWP CML2002 | CO2 | 16,603.86 kg | 9217.0 kg | 1 | kg eq | 32,744.18 | 19,397.04 (60%-new) |
NOx | 50.34 kg | 31.76 kg | 320 | ||||
CO | 15.76 kg | 8.51 kg | 2 | ||||
Energy consumption | Net | 6.69e4 MJ | 5.05e4 MJ | 1 | MJ | 6.69e4 | 5.05e4 (75%-new) |
Impact item | Substance(s) | New quantity | Reman quantity | Characterization factor | Unit | New | Reman |
---|---|---|---|---|---|---|---|
ADP CML2002 | Steel and cast iron | 1289.49 kg | 616.00 kg | 1.66E−6 | kg Sb-eq | 10.3E−3 | 5.4E−3 (52%-new) |
Aluminum | 8.14 kg | 4.83 kg | 2.53E−5 | ||||
Crude oil | 250.16 kg | 131.42 kg | 9.87E−6 | ||||
Natural gas | 781.26 kg | 414.46 kg | 7.02E−6 | ||||
GWP CML2002 | CO2 | 16,603.86 kg | 9217.0 kg | 1 | kg eq | 32,744.18 | 19,397.04 (60%-new) |
NOx | 50.34 kg | 31.76 kg | 320 | ||||
CO | 15.76 kg | 8.51 kg | 2 | ||||
Energy consumption | Net | 6.69e4 MJ | 5.05e4 MJ | 1 | MJ | 6.69e4 | 5.05e4 (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.
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.
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.
Policy index | Extended warranty | Renewal strategy |
---|---|---|
1 | Yes | A 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. |
2 | All failed units are replaced with new units. | |
3 | All failed units are replaced with remanufactured units. | |
4 | No | All failed units are replaced with remanufactured units. |
Policy index | Extended warranty | Renewal strategy |
---|---|---|
1 | Yes | A 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. |
2 | All failed units are replaced with new units. | |
3 | All failed units are replaced with remanufactured units. | |
4 | No | All 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).
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 and , 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.
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.
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).
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 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 |
6 Generate a random failure time based on fnew(t) |
7 cnew = cnew + 1 |
8 else |
9 Generate a random failure time based on fre(t) |
10 cre = cre + 1 |
11 end |
12 end for |
13 forj = 3:R + 1 |
14 Generate S random failure times based on fre(t) |
15 Calculate the simulated times when j − 1 and j failures occur, respectively , |
16 Find the cases where exactly j − 1 failures occur between Te and TL > TL} |
17 |
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 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 |
6 Generate a random failure time based on fnew(t) |
7 cnew = cnew + 1 |
8 else |
9 Generate a random failure time based on fre(t) |
10 cre = cre + 1 |
11 end |
12 end for |
13 forj = 3:R + 1 |
14 Generate S random failure times based on fre(t) |
15 Calculate the simulated times when j − 1 and j failures occur, respectively , |
16 Find the cases where exactly j − 1 failures occur between Te and TL > TL} |
17 |
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.
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).
Case | Condition of the replacement unit | Reliability at 4000 h | Replacement cost ($) | ADP (kg Sb-eq) | GWP (kg CO2-eq) | Energy (MJ) |
---|---|---|---|---|---|---|
1 | New | 0.9343 | 40,000 | 10.3E−3 | 32,744.18 | 6.69e4 |
Reman | 0.9343 | 30,000 | 5.4E−3 | 19,397.04 | 5.05e4 | |
2 | New | 0.9174 | 40,000 | 10.3E−3 | 32,744.18 | 6.69e4 |
Reman | 0.9174 | 30,000 | 5.4E−3 | 19,397.04 | 5.05e4 |
Case | Condition of the replacement unit | Reliability at 4000 h | Replacement cost ($) | ADP (kg Sb-eq) | GWP (kg CO2-eq) | Energy (MJ) |
---|---|---|---|---|---|---|
1 | New | 0.9343 | 40,000 | 10.3E−3 | 32,744.18 | 6.69e4 |
Reman | 0.9343 | 30,000 | 5.4E−3 | 19,397.04 | 5.05e4 | |
2 | New | 0.9174 | 40,000 | 10.3E−3 | 32,744.18 | 6.69e4 |
Reman | 0.9174 | 30,000 | 5.4E−3 | 19,397.04 | 5.05e4 |
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.
Policy | Energy consumption (MCS: μ, σ) | ADP (MCS: μ, σ) | GWP (MCS: μ, σ) | LCWC (MCS: μ, σ) | LCWC (analytical) | |
---|---|---|---|---|---|---|
MJ | kg Sb-eq | kg CO2 − eq | $ | $ | ||
Case 1 | 1 | (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 2 | 1 | (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 |
Policy | Energy consumption (MCS: μ, σ) | ADP (MCS: μ, σ) | GWP (MCS: μ, σ) | LCWC (MCS: μ, σ) | LCWC (analytical) | |
---|---|---|---|---|---|---|
MJ | kg Sb-eq | kg CO2 − eq | $ | $ | ||
Case 1 | 1 | (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 2 | 1 | (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.
Footnotes
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.