Reliability-Informed Economic and Energy Evaluation for Bi-Level Design for Remanufacturing: A Case Study of Transmission and Hydraulic Manifold

Nemani, Venkat P.; Liu, Jinqiang; Ahmed, Navaid; Cartwright, Adam; Kremer, Gül E.; Hu, Chao

doi:10.1115/1.4054160

Abstract

Design for remanufacturing (DfRem) is one attractive strategy that encourages the reuse of a product and extends the product's life cycle. Traditional design processes often only consider product reliability at an early design stage. However, from the perspective of environmental sustainability, it is becoming increasingly important to evaluate the long-term economic and environmental impacts of design decisions during early-stage design. We propose a bi-level DfRem framework consisting of system-level reusability allocation and component-level design tradeoff analysis, considering reliability and product warranty policy. First, a system-level reusability allocation problem aims at a theoretical exploration of the design space where all the components comprising the system are allocated certain reuse rates to achieve target energy savings with minimum cost. Following the theoretical exploration at the system level, a component-level analysis looks at practical design options for each component and trades-off between the overall cost and energy consumption for multiple remanufacturing cycles. Both levels of the framework require modeling component reuse for multiple remanufacturing cycles, which we achieve by using a branched power-law model that provides probabilistic scenarios of reusing the component or replacing it with a new part. We demonstrate the utility of this framework with the case study of an infinitely variable transmission (IVT) used by some agricultural machines manufactured by John Deere and show snapshots of a prototype software tool that we developed for easy use by designers.

1 Introduction

1.1 Literature Review.

The rapid industrial development and increasing consumerism are negatively impacting the environment [1] to the point that policymakers all over the world recognize the need to promote sustainable development through the concept of circular economy [2–4]. A consensus among researchers and industrialists is to improve resource utilization efficiency to minimize material consumption and energy consumption during manufacturing [5–7]. The life cycle of a manufactured good typically includes material extraction, component production, assembly, use by the consumer, and disposal at end-of-life (EOL). According to the US Environmental Protection Agency, about 294 million tons of municipal solid waste was generated in 2018 alone, 50% of which is attributed to common materials like paper, plastics, metals, and glass [8]. Industrial solid waste generation is expected to be at least an order of magnitude larger than household wastes. The 3R model of sustainability, viz. reuse, recycling, and remanufacturing, is the most effective way to process EOL equipment [9–11]. Both reuse and remanufacturing offer better preservation of the value added to a product during initial fabrication with minor additional processing [12]. Remanufacturing restores previously worn out or EOL products to an “as new” state [13]. This restoration leads to efficient utilization of resources for extending the life cycle of EOL products and promoting economic benefits and the world's transition toward a circular economy [14–17].

Remanufacturing is particularly attractive for engineered goods where a large fraction of components can be reused [18]. The typical remanufacturing process involves product disassembly, inspection, cleaning, and reconditioning of all components, followed by assembly and testing to ensure that the remanufactured product is comparable to its new counterpart [19]. A number of businesses and researchers have looked at the viability of remanufacturing equipment such as photocopiers [20,21], computers [22], appliances [13,23], and automobile parts [5,12,24–27]. Some researchers claim cost savings of over 50% when products are remanufactured instead of being replaced with entirely new parts [12,28]. Despite the economic and environmental advantages of remanufacturing, often the remanufacturing sector faces several challenges such as effective core retrieval, managing uncertainties of core quality, identifying the correct design factors such as ease of disassembly, buffer allocation, and the general consumer behavior toward remanufactured goods [29–35]. However, proper decision-making during the design stage can ease several of these challenges [30,36,37]. Facilitating remanufacturing to enable multiple life cycles of a product might require a different approach during the initial product design stage, and this forms the basis of design for remanufacturing (DfRem) [38,39]. In this regard, Yang et al. [40] provided detailed guidelines for product remanufacturing, and Hatcher et al. [41] provided a comprehensive literature review on DfRem. Most of these guidelines are qualitative in nature, and accounting for all the design factors during remanufacturing may not be feasible [42]. Hence, businesses achieve successful remanufacturing by considering only a few important factors such as choice of material, ease of disassembly and reconditioning, and operational factors such as the relationship between original equipment manufacturer (OEM)–remanufacturer and marketing [34,43–45]. It is important for the OEMs to carefully evaluate the benefits of DfRem as opposed to other potentially conflicting design for X strategies.

Economic [46,47], energy [24], and environmental [25,48] benefits are some of the key drivers for DfRem [49,50]. Life cycle cost (LCC) analysis and life cycle analysis (LCA) are commonly used techniques to quantify the economic and environmental impacts of a product throughout its life cycle, right from material extraction, processing, manufacturing to its EOL [51–54]. LCA is a commonly used tool to practically evaluate the benefits of remanufacturing for sustainable development [55–57]. Energy and material consumption has been the focus of most LCA studies [58]. Lee et al. reported that energy consumed in remanufacturing processes can be decreased as much as 85% when compared to new products [59]. Similarly, Lund reported an 80% reduction in energy consumption for remanufactured engines [19]. In addition to these, several researchers performed comparative studies on turbine blades [60], diesel engines [61], and machine tools [62]. In parallel to the LCA studies, the economic feasibility of remanufacturing is often evaluated [63–65]. Remanufacturing typically requires a lesser cost than manufacturing due to low material quantity requirements under the assumption that the damage is not severe and is serviceable [66]. In addition, Gutowski et al. [67] conducted 25 case studies and found that although remanufacturing is beneficial at the manufacturing stage, its advantage for some of the case studies is nullified when the remanufactured products have smaller use phase efficiency than nits newer generations. A complete LCC analysis requires accounting for processes in the product life cycle along with economics between manufacturers, government, and the consumers [68], making the process complicated and requiring sophisticated models [53].

Ideally, quantification of the environmental impacts and product reliability during the early design stage of a product is required for a strategic evaluation of design tradeoffs [34,69,70]. In this regard, Ye et al. [71] developed a tool to estimate the environmental impact of system architecture and support OEM decision-making while considering uncertainty in the development of system modules and supplier–OEM relationship. This study, however, focused on the single use of products without consideration of remanufacturing. Remanufacturing requires additional considerations such as the uncertainty in the quality of the returned product. To address this, Aydin et al. [72] proposed a methodology to optimize the product returns considering uncertainty in quality and quantity of returned cores. However, this work does not account for multiple remanufacturing cycles. In this article, we augment the previous research work by evaluating the environmental and economic impacts of early-stage design decisions while simultaneously modeling for change in the uncertainty of returned product quality for multiple cycles.

The comparative benefits of remanufacturing options, both economically and environmentally, are often presented on a per-product basis without accounting for the long-term implications of a particular product design option. The reliability of a product is not only important in measuring its quality [73,74] but also is a measure of how frequently the need for remanufacturing is triggered during the serviceable product life [75–77]. Low-reliability products require frequent replacements incurring additional costs and energy consumption. Conversely, if a product already has very high reliability, investing in DfRem to improve the product's remanufacturability leading to a higher production cost would undermine the profits as the likelihood of failure or the need for remanufacturing is very low. A product replacement rate depends on integrating a reliability model with varying population sizes of the remanufactured parts [78]. Murayama and Shu [79] estimated the number of products returned for remanufacturing based on a probability distribution of time-to-failure that was fitted to reliability data. However, these methods can only calculate an expected quantity of products to fail within a specific time period without considering multiple life cycles. In this article, we consider the effects of reliability when evaluating the economic and environmental impacts of several design options over multiple remanufacturing life cycles.

1.2 Our Contribution.

In an earlier study, we proposed a framework to include reliability, obtained from the field failure data, into life cycle warranty cost (LCWC) analysis and LCA to aid in the decision-making process when considering multiple life cycles [75–77]. In this article, we further expand this framework into exploring theoretical design targets as well as evaluating practical design options. The main contributions of this work are as follows:

Model the reuse rate of a component for multiple remanufacturing cycles using a branched power-law model. The branched power-law model was proposed in our previous work [76]. In this study, we expand on quantifying the uncertainty associated with reuse or replacement with a new component for every remanufacturing cycle.
Formulate a system-level reusability allocation problem. Solving this problem assigns a system's individual components optimal reuse rates to achieve target savings in energy consumption with a minimal increase in the initial production cost. This optimization problem explores the theoretical design space of component reuse rates while considering the feasibility of design changes for each component. We demonstrate the utility of this formulation through the example of an infinitely variable transmission (IVT) used in agricultural machines manufactured by John Deere.
We formulate a component-level design tradeoff analysis where practical design options for each component are evaluated, considering that the optimal reuse rates obtained from the theoretical system-level reusability allocation may not always be practically achieved. The design options are evaluated in terms of cost and energy consumed on a per-product basis and after including reliability for three remanufacturing cycles. We then evaluate the design options using multi-attribute utility theory (MAUT) with an exponential risk-based utility function. This tradeoff analysis combined with the system-level reusability allocation can help the designer identify which practical design options are worth exploring while effectively utilizing time and other resources. For the case study, we explore three practical DfRem options for a hydraulic manifold, an important component within the IVT. We find that design options that would apparently be the most preferred when performing a one-to-one comparison without considering reliability do not necessarily maintain their preferability after including reliability.
We also share details of a prototype software tool named data-driven design decision support (D4S), which evaluates and recommends DfRem options for high-value components in industrial and agricultural equipment [80]. This tool intends to provide a simple to use platform for the designer to perform reliability-informed LCWC and LCA, the system-level reusability allocation, and the component-level design tradeoff analysis for any general agricultural or industrial system.

When discussing the framework using the case study of the IVT and the hydraulic manifold, we use real data that the OEM has provided. The assumptions, which the remanufacturing experts at the OEM have reviewed, are listed at appropriate places. Hereafter, we refer to the IVT as a system or a unit and individual components of the IVT as components or parts. The remainder of this article is organized as follows. In Sec. 2, we detail the proposed bi-level DfRem framework, followed by a description of the branched power-law model. In Sec. 3, we formally introduce the system-level reusability allocation problem, and in Sec. 4, we describe the component-level design tradeoff analysis. In Sec. 5, we present the case study of the IVT and the hydraulic manifold component to demonstrate the utility of the framework presented in Secs. 3 and 4, respectively. We briefly describe our prototype software in Sec. 6 and conclude our analysis in Sec. 7.

2 Overview

In this section, we first present the proposed design framework, following which we describe the branched power-law model to model for variation in reuse rates for multiple remanufacturing cycles.

2.1 Proposed Framework.

Successful implementation of DfRem requires a system-level understanding of the design parameters to achieve target energy savings while also accounting for practical design options for each individual component. The overall schematic of the proposed framework is shown in Fig. 1. When a unit fails in the field, the core is retrieved by the remanufacturer, following standard remanufacturing procedures, such as disassembly, cleaning, inspection, and assembly. During the inspection stage, each individual component is analyzed for the severity of wear and assessed if the component can be reused with some reconditioning process or needs to be replaced by a newly manufactured component. The reuse rate (α) of a component is the probability that a component can be reconditioned and reused. It can be easily defined as the ratio of the number of components reused (N_reuse) and the total number of returned components (N_recall) stated as follows:

α = \frac{N_{reuse}}{N_{recall}}

(1)

Fig. 1

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Schematic of the proposed bilevel DfRem framework

Often the inspection process is manually performed by expert technicians and is, therefore, time intensive. During the inspection of each component, a detailed report stating any visual damage is filed, and the component is assessed for reuse capability (i.e., it may be sent to recycling or placed in inventory for future remanufacturing). The reuse rate of a component is influenced by the capability of the inspection procedures to reliably identify the condition of the component [81]. Recent research suggests automating the inspection process using computer vision [82,83], which could lead to a more consistent and reliable assessment of the component's condition. Depending on the design and function of the system, each component has a different reuse rate, which can be altered by applying the concepts of DfRem to the component. Based on the design complexity, the designer categorizes components in terms of the feasibility for design change (formally defined later in Sec. 3.1). DfRem strategies are most effective on components that have high feasibility for design change. By using the information of component-level reuse rates and feasibility for design changes, we propose an optimization problem that aims at theoretically exploring the design space of component reuse rates to determine the best combination of component reuse rates to achieve target savings in sustainability metrics (such as energy, global warming potential, and so on) for a minimum increase in initial production cost. Adding value at the initial production stage can be considered an investment for greater economic and environmental impact benefits at the end of multiple remanufacturing cycles. The outcome of the system-level reusability allocation is the assignment of target reuse rates to all the components. These reusability targets are to be met by various DfRem practices. However, in reality, the set of DfRem options for each component are discrete, and the theoretical reuse rates may not be achieved. The goal, however, is to quantify the cost and energy of each potential design option for the individual components while considering reliability, project those discrete design options onto the theoretically explored design space, and rank the design changes according to the optimized solution. This framework supports strong interaction between the real-field failure data and the designer and remanufacturing experts to achieve the best DfRem solution for the system. We note that this framework is unique in comparison to extant works. For example, some works evaluated the return rate for various quality levels but did not aggregate the gains to the system level (e.g., Aydin et al. [72]), while others considered sustainability goals at a system level during the design stage but omitted the potential of remanufacturability (e.g., Ye et al. [71]).

2.2 Modeling Reuse Rates for Multiple Remanufacturing Cycles.

When being inspected during remanufacturing, a component is either reconditioned for reuse or replaced with a new component if the damage is irreparable. This probability is captured in the reuse rate α. When considering multiple remanufacturing cycles, we expect that the reuse rate decreases from cycle to cycle due to (1) accumulated material fatigue if a component is reused successively for multiple remanufacturing cycles and (2) potential nonsmooth and/or not “as new” interaction between new and remanufactured parts within the system. To this end, we proposed a branched power-law model [76], where the probability of reusing a component is varied with successive remanufacturing cycles. In this article, we further explore the uncertainty aspects of the branched power-law model. This exploration was not presented in our earlier work, where we primarily used the expected values of reuse rates [76]. The reuse rate of a part at the jth remanufacturing cycle is denoted as

α_{i, j}^{k + 1}

⁠, where the exponent k refers to the number of successive reuses of the ith part. The effect of nonsmooth interaction between components is modeled as a linear decrease in reuse rate with an increasing number of remanufacturing cycles formulated as (dropping the subscript i) follows:

α_{j + 1} = α_{j} - Δ α_{j}, i > 1

(2)

where Δα_j is the expected decrease of the reuse rate for the j + 1th remanufacturing cycle when compared to the jth cycle. When a component is successively reused, the material accumulates excessive stress due to material fatigue and other damage mechanisms, which is captured in the exponent k that further reduces the probability of successive reuse. These two effects that cause a reduction in the reuse rate from cycle to cycle can be modeled as a decision tree as shown in Fig. 2, where each node has a certain probability associated with reusing the component and replacing the component. The branched structure in Fig. 2 explores all potential routes for reusing/replacing components while tracking the status history along a particular route. The status history of the part is tracked whenever it is replaced with a new part [N] and whenever the part is reused [R] and the reuse rate is determined accordingly. For example, if a new part undergoes three remanufacturing cycles, the probability of [N] during the first remanufacturing cycle is (1 − α₁), followed by a [R] in the second remanufacturing cycle with probability of (1 − α₁)α₂. The part's status history can now be stated as [N, N, R], and the reuse rate for the third remanufacturing cycle is

(1 - α_{1}) α_{2} α_{3}^{2}

⁠. As shown in Fig. 2, whenever a component is successively reused, the exponent k increases with the icon representing the component becoming increasingly darker.

Fig. 2

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Schematic of the branched power-law model for a single component along with probability distributions of reuse and/or replacement with new components for three remanufacturing cycles. The probability distribution is shown for two design examples.

To demonstrate the variability in reuse/replacement accounted by the branched power-law model, we show examples of two designs, design A with a high initial reuse rate but degrades fast $α_{1}^{A} = 0.8, Δ α_{j}^{A} = 50 % a_{j}$ (shown as the first group of the grouped bar chart in Fig. 2) and design B with a moderate initial reuse rate but low Δα: $α_{1}^{B} = 0.6, Δ α_{j}^{B} = 5 % a_{j}$ (shown as the second group of the grouped bar chart in Fig. 2). At the first remanufacturing cycle, there is an 80% chance that design A can be reused. For the second remanufacturing cycle, it is 13% probable that design A can be reused twice ([N, R, R]), whereas there is a 75% probability that design A can be reused only once with one new replacement ([N, R, N] and [N, N, R]) and a 12% probability that a new part will be required in both remanufacturing cycles. High Δα is the reason for such low probability for two successive reuses for design A. In the third remanufacturing cycle, it is almost unlikely that both designs can be reused three times. However, there is a 45% probability that design B can be reused twice within the three remanufacturing cycles ([N, N, R, R], [N, R, N, R], and [N, R, R, N]) as opposed to a lower value of 26% for design A. It is more likely that design A will require two new replacements within the three remanufacturing cycles. In essence, design B seems favorable for multiple reuses within three remanufacturing cycles making it a better DfRem option than design A. It is therefore important to model reuse rates for multiple remanufacturing cycles, and our proposed branched power-law model is a simple tool for evaluating the same. We would like to note that the decrease in the reuse rate from one cycle to the next, as shown in Eq. (2), is simplified. In some cases, Δα_j may increase with the length of the jth cycle. However, the effect of cycle duration is captured in Sec. 3.3 through the inclusion of the reliability function and calculation of the expected number of replacements for each cycle.

3 System-Level Reusability Allocation

In this section, we first state the problem definition, followed by expressions to quantify production cost and energy consumed during manufacturing/remanufacturing. We then provide an algorithm to estimate the overall energy consumed for multiple remanufacturing cycles. Following this, we present the results for the case study demonstrating the utility of the optimization formulation.

3.1 Problem Definition.

The system consists of multiple components, each with its own set of remanufacturability factors such as the reuse rate. Designers are often required to decide which components to improve to achieve the target sustainability metrics (such as energy savings) with the minimum cost. Consider a system consisting of n components with reusability

α = {α_{1}, α_{2}, . . α_{n}}

⁠. The objective is to allocate reuse rates to all or some of these n components to meet the goal of energy savings

E

_target with minimum initial production cost

C^{prod}

⁠. This allocation problem can be formulated as a nonlinear programming problem as follows:

min_{α} C^{prod} (α, f) = \sum_{i = 1}^{n} c_{i} (α_{i}, f_{i})

(3)

subject to α_{i, min} \leq α_{i} \leq α_{i, max}, E (α, m) \leq E_{target}

(4)

where the total unit cost ℂ^prod is the sum of individual component costs

c_{i}

and

E

is the total energy consumed during m remanufacturing cycles. In Sec. 3.3, we argue that

E

is the reliability-informed estimate of total energy consumption. Each component cost is a function of the reuse rate α_i and feasibility f_i for design changes to increase the component's reuse rate. The minimum reuse rate α_i,min is the current reuse rate, and the maximum attainable reuse rate α_i,max is set by the designer (ideally close to 1). The feasibility f_i is a number between 0 and 1 set by the designer to quantify the degree of difficulty in improving the reuse rate to attain its maximum value. Feasibility of 0 means that heavy investment is needed to achieve α_i,max, whereas a component with f_i = 1 requires the minimum cost to achieve the maximum reuse rate. The individual component cost can be formulated as follows [84]:

c_{i} (α_{i}; f_{i}, α_{i, \min}, α_{i, \max}) = c_{i}^{0} e^{ϕ_{i} [(1 - f_{i}) (\frac{α_{i} - α_{i, min}}{α_{i, max} - α_{i}})]}

(5)

where

c_{i}^{0}

is the present cost of the component and ϕ_i is a stretch parameter that the designer can choose to suit the expected cost model for the component. Depending on the design complexity and technological limitations, the feasibility factor f and the stretch parameter ϕ can be adjusted for the components. The exponential behavior of the cost function and its variation with f_i for a part with α_min = 0.6 and α_max = 1.0 is shown in Fig. 3. Modifying the design to obtain a reuse rate of 0.8 requires cost increments of 125%, 50%, and 10% for f = 0.2, 0.6, and 0.9, respectively, for ϕ = 1.

Fig. 3

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Variation of the cost function with feasibility for ϕ = 1 and 0.6

3.2 Energy Quantification.

The total energy

E

consumed in m remanufacturing cycles by the system can be expressed as a sum of individual component energies with making a new part

e_{i}^{new}

and remanufacturing energy for the jth remanufacturing cycle

e_{i, j}^{reman}

as follows:

E (α, m) = \sum_{i = 1}^{n} e_{i} (α_{i}, m) = \sum_{i = 1}^{n} (\sum_{j = 1}^{m} e_{i, j}^{reman})

(6)

As explained in Sec. 2.2, the probability of reuse/replacement depends on the status history of the components. The reuse/replace status for a component i in remanufacturing cycle j can be considered as a Bernoulli random variable X_i,j,k:

X_{i, j, k} \sim Ber (α_{i, j}^{k + 1})

(7)

where an outcome of 0 represents a replacement and an outcome of 1 refers to reusing the component. During the m remanufacturing cycles, a component can take any route shown in Fig. 2 with the status history at jth remanufacturing cycle stored in the variable

X_{i, j}^{*}

⁠.

X_{i, j}^{*} = 1

if the component is reused in the jth remanufacturing cycle and 0 otherwise. The energy consumed by the component i in m remanufacturing cycles can be calculated as follows:

e_{i, j}^{reman} = \sum_{k = 0}^{j - 1} (1 - X_{i, j - k - 1}^{*}) \cdot \prod_{l = 1}^{k} X_{i, j - k}^{*} \cdot (X_{i, j, k} \cdot e_{process, i}^{reman} + (1 - X_{i, j, k}) \cdot e_{i}^{new})

(8)

where

e_{process, i}^{reman}

is the energy consumed during the reconditioning step when the component is reused. The term

\prod_{l = 1}^{k} X_{i, j - k}^{*}

in Eq. identifies the number of successive reuses in the component history and the term

(1 - X_{i, j - k - 1}^{*})

ensures that the (j − k − 1)^st component must be new and all consecutive cycles from j − k to j are reused. For example, if a part has the status [N, R, N], the energy consumed in first remanufacturing cycle is

e_{i, 1}^{reman} = (1 - X_{i, 0}^{*}) \cdot (X_{i, 1, 0} \cdot e_{process, i}^{reman} + (1 - X_{i, 1, 0}) \cdot e_{i}^{new})

with

X_{i, 0}^{*} = 0

(as component is new). If the component is reused at this cycle, then

X_{i, 1}^{*} = X_{i, 1, 0} = 1

⁠. Note that the

\prod_{l = 1}^{k} X_{i, j - k}^{*}

becomes an empty product that equals 1. For the second remanufacturing cycle,

e_{i, 2}^{reman} = (1 - X_{i, 0}^{*}) \cdot X_{i, 1}^{*} \cdot (X_{i, 2, 1} \cdot e_{process, i}^{reman} + (1 - X_{i, 2, 1}) \cdot e_{i}^{new})

and

X_{i, 2}^{*} = X_{i, 2, 1} = 0

as the component is replaced with new. In this example, however, we are exploring only one path of [N, R, N] with probability of status update depending on the Bernoulli variables X_i,1,0 and X_i,2,1. Multiple evaluations of Eq. would account for all possible status updates for the component leading to an expected probability of each state as mentioned in Fig. 2. The sum of p successive independent and identically distributed Bernoulli trials is a Binomial random variable. If the successive Bernoulli trials are independent but not identically distributed, their sum becomes a Poisson binomial variable. However, in our case, the Bernoulli trials are dependent and not identically distributed, which cannot be explained by a standard distribution. We, therefore, use Monte Carlo simulation (MCS) to estimate

e_{i, j}^{reman}

⁠, which is then used to calculate

E

⁠.

The energy needed to make a new component

e_{i}^{new}

consists of contributions from material usage/embodied energy

e_{i}^{emb}

and energy consumed during manufacturing

e_{i}^{manu}

given as follows:

e_{i}^{new} = e_{i}^{emb} + e_{i}^{manu}

(9)

Although there would be contributions from transport and processes like assembly, in this study, we neglect these contributions under the assumption that these contributions would be very similar across multiple design options.

e_{i}^{emb}

refers to the equivalent process energy requirement, which corresponds to the amount of energy in MJ needed to convert the raw materials from mining to processed material blocks. These blocks are then manufactured into individual components. The embodied energy

e_{i}^{emb}

can be defined as follows:

e_{i}^{emb} = m_{i}^{b} e_{i}^{b}

(10)

where

m_{i}^{b}

is the mass of the material required to manufacture the component and

e_{i}^{b}

is the specific embodied energy obtained from a calculator tool made by the REMADE Institute.^² The manufacturing process energy

e_{i}^{manu}

is determined by estimating a specific machining cost

e_{i}^{manu} = 1.87 \times 10^{5} J / c m^{3}

[85] and assuming a material removal of

ν %

from the original material block with a material density ρ, which is given as follows:

e_{i}^{manu} = ν % \frac{m_{i}^{b} e_{i}^{manu}}{ρ}

(11)

3.3 Reliability-Informed Energy Quantification.

In Sec. 3.2, we formulated the energy consumption of a new component and a remanufactured component. Although comparing the new and remanufactured energy consumption on a one-to-one basis is beneficial, such a comparison does not represent reality because (1) it does not consider core return rate and (2) cores may be returned for remanufacturing when there is a failure. In other words, the reliability of the product may determine the expected number of cores returned for remanufacturing. Products with high reliability are expected not to experience failure for a long period of time. For this reason, investment for DfRem of high-reliability components may not be profitable. Therefore, it is essential to take reliability into account for a fair evaluation of design options during the component's service life.

The reliability function of a system can be determined from time-to-failure data collected from the field. The Weibull distribution is selected to model the time-to-failure distribution. The probability density function of the Weibull distribution can be expressed as follows:

f (x) = \frac{β}{λ} {(\frac{x}{λ})}^{β - 1} \exp [- {(\frac{x}{λ})}^{β}]

(12)

where x is the time to failure, and β and λ are the shape and scale parameters, respectively. The cumulative distribution function, F(x), measures the probability of failure (P_f), which is given as follows:

P_{f} (x) = F (x) = \int_{0}^{x} f (x) d x = 1 - \exp [- {(\frac{x}{λ})}^{β}]

(13)

The shape and scale parameters are estimated by fitting the Weibull distribution to the time-to-failure data using the maximum likelihood estimation method. The reliability function can be derived as follows:

R (x) = 1 - P_{f} (x) = \int_{x}^{\infty} f (x) d x = \exp [- {(\frac{x}{λ})}^{β}]

(14)

By using the reliability function, we estimate the expected number of new replacements and remanufactured replacements, which also depends on the warranty scheme of the OEM. Typical warranty policies state that a failure occurring within the first T_e working hours will be replaced by a new unit, and any other subsequent failures will be replaced with remanufactured units. The unit is assumed to have an average product life of T_L (from the first purchase) beyond which the unit is no longer remanufacturable and/or the consumer upgrades to an entirely newer design. The expected number of replacements with new units n^new is calculated as follows:

n^{new} = \int_{0}^{T_{e}} 1 \cdot f (x) d x + \int_{T}^{T_{L}} 0 \cdot f (x) d x = 1 - R (T_{e})

(15)

The expected number of remanufactured replacements for the jth remanufacturing cycle can be calculated as follows:

\begin{aligned} n_{j}^{re} = j \int_{T_{e}}^{T_{L}} f (t) P^{re} (N (T_{L} - t) = j) d t \\ + j \int_{0}^{T_{e}} \int_{t_{1}}^{T_{L}} f (t_{1}) f (t_{2} - t_{1}) P^{re} (N (T_{L} - t_{2}) = j) d t_{2} d t_{1} \end{aligned}

(16)

where f(t) is the probability density function of the time-to-failure distribution for both new and remanufactured units assuming that remanufactured units perform as well as new based on the definition of remanufacturing, N(t) is the number of renewals within time [0, t] given a time-to-failure distribution, and P^re(N(T_L − t) = j) is the probability that j renewals occur within the time [0, T_L − t] given the time-to-failure distribution of the remanufactured units. The number of remanufactured replacements n^re follows a discrete distribution until m cycles within T_L. The first term on the right-hand side of Eq. indicates the expected number of remanufactured replacements when the brand-new unit fails after T_e, while the second term calculates the expected number of remanufactured replacements when the unit fails within T_e but after the first new replacement based on the warranty policy.

The expected total energy consumption for remanufacturing of the system can be determined from Eqs. and as follows:

E (α, m) = \sum_{i = 1}^{n} e_{i} (α_{i}, m) = n^{new} \sum_{i = 1}^{n} e_{i}^{new} + \sum_{i = 1}^{n} \sum_{j = 1}^{m} n_{j}^{re} e_{i, j}^{reman}

(17)

We note that Eq. (17) is slightly different from Eq. (6) by accounting for the warranty policy of new and remanufactured replacements. It is this reliability-informed energy $E$ (α, m) from Eq. (17) that serves as constraint in Eq. (4).

3.4 Algorithm.

We use Latin hypercube sampling (LHS) to generate the possible set of reuse rates for all the components bounded by α_min and α_max. The MCS algorithm to perform the system-level reusability allocation is presented in Table 1. For each possible set of $α$ ⁠, the average energy required for multiple remanufacturing cycles is calculated using the branched power-law model and MCS. In lines 13 and 15 of Table 1, we store the energy of reusing or replacing the component while also storing the status history. The status history within the MCS loop affects the reuse rates for the next remanufacturing cycle following the branched power-law model. The average energy calculated for each component in line 18 can be a simple average over the m remanufacturing cycles or a weighted average. The cost of each component within one LHS sample is determined using Eq. (5).

Table 1

LHS—MCS algorithm for performing system-level reusability allocation

Inputs: Component reuse rates

α_{current} = {α_{1}, α_{2}, . . α_{n}}

Component feasibilities

f = {f_{1}, f_{2}, . . f_{n}}

Exponent factor ϕ

Remanufacturing cycles: m

Bill of materials: component masses m^b and material type

Remanufacturing process energy:

e_{process, i}^{reman}

Number of MCS-simulated scenarios: Q

Number of LHS cases: N_LHS

Energy target:

E

_target

Time to failure data

Output: Optimized

α

satisfying Eqs. and

1 Set

α_{min} = α_{current}

⁠,

α_{max} = 1

2 GenerateN_LHS samples of

α

bounded by

α_{min}

and

α_{max}

3 forn_LHS = 1 : N_LHS

4 for each component in the system

5

α_{i} = α {c o m p o n e n t}

6 Calculate

e_{i}^{emb}

⁠,

e_{i}^{manu}

and

e_{i}^{new}

using Eqs. (–)

7 Store

E (q = 1, c o m p o n e n t, c y c l e = 1) = e_{i}^{new}

for new component

8 Status [N]

9 forq = 2 :Q loop over the MCS points

10 forj = 2 :m+1 loop over the component life cycles

11 Calculate

α_{i, j}^{k}

from Fig. 2 and Eq. using component status

12 if rand() >

α_{i, j}^{k}

then replace with a new component

13

E (q, c o m p o n e n t, j) = e_{i}^{new}

⁠, Status = Status + [N]

14 else reuse the component

15

E (q, c o m p o n e n t, j) = e_{process, i}^{reman}

⁠, Status = Status + [R]

16 end for (line 10)

17 end for (line 9)

18 Calculate

(e_{i}, σ_{e_{i}})

energy used by the component in m cycles

19 Calculate

c_{i =} c_{i}^{0} e^{ϕ_{i} [(1 - f_{i}) (\frac{α_{i} - α_{i, min}}{α_{i, max} - α_{i}})]}

using Eq. . Here we choose

c_{i}^{0} \propto e_{i}^{emb}

20 Fit the Weibull distribution to the time-to-failure data [76]

21 Calculate n^new and

n_{j}^{re}

from the Weibull distribution and MCS of Eqs. and [76]

22 Calculate

E

(n_LHS) from Eq. and

C (n_{LHS}) = \sum_{i = 1}^{n} c_{i}

23 Perform grid search optimization as in Eqs. and using the constraint of

E

_target

4 Component-Level Design Tradeoff Analysis

The system-level reusability allocation, described in Sec. 3, sets theoretical targets of the reuse rates of all the components. Achieving the optimized reuse rates for all the components may not always be practically feasible. However, the allocated reuse rate of each component guides the designer in determining which design options from a set of practical design options could satisfy the energy savings. In other words, the allocated reuse rate serves as a lower bound in evaluating the reuse rate for practical design options. This way, the designer can more effectively explore worthy design options and discard others. Let us assume that for each component i, the designer provides P_i design alternatives. Each design option Dp_i:1 → P_i affects the component's initial reuse rate $α_{1, D p_{i}}$ and its decrease $Δ α_{D p_{i}}$ from cycle to cycle. It is possible that for some designs the initial reuse rate is high but has poor retention of reuse rate thus severely limiting remanufacturing for multiple cycles (as shown in Fig. 2). The change in reuse rates affects the cost $c_{D p}^{new}$ and energy consumption $e_{D p}^{new}$ of new component along with the remanufacturing process cost $c_{process, D p}^{reman}$ and energy consumption $e_{process, D p}^{reman}$ (dropping the subscript i). The reliability informed cost and energy consumption can be determined using the methodology described in Sec. 3.3. Broadly, the cost/energy terms have contributions from material acquisition, manufacturing/machining, electricity, and labor, which we will describe in detail for the case study. The overall cost $c_{D p}$ and energy consumption $e_{D p}$ can be used to determine the best design.

Selection of the proper design from the various Dp_i:1 → P_i designs belongs to the multicriteria decision-making (MCDM) problem. Commonly used MCDM approaches include the weighted sum model, MAUT, the analytic hierarchy process, and the Technique for Order Preference by Similarity to Ideal Solution [86–91]. In this study, we rank the design changes using MAUT with the overall cost and energy as the attributes. We now formulate the utility-based approach for ranking the design options. Let the expectation values be the design matrix entries X_pz for the pth design option and zth attribute. An exponential utility function u_pz with risk factor γ_z is used in this study, which can be stated as follows:

u_{p z} = {\begin{matrix} \frac{(1 - e^{- γ_{z} {\overset{˘}{X}}_{p z}})}{sign (γ_{z})} γ_{z} \neq 0 \\ 0 γ_{z} = 0 \end{matrix}

(18)

where

{\overset{˘}{X}}_{p z}

is the normalized data entry. Since both objectives cost and energy consumption are nonbeneficial (i.e., these should be minimized), we use the following normalization for X_pz:

{\overset{˘}{X}}_{p z} = \frac{X_{p z}^{max} - X_{p z}}{X_{p z}^{max} - X_{p z}^{min}}

(19)

\begin{aligned} X_{p z}^{min} = min_{D p : 1 \to P} (X_{p z}) \\ X_{p z}^{max} = (m + 1) \times max_{D p : 1 \to P} (X_{p z}) \end{aligned}

(20)

where

X_{p z} = c_{D p}^{new}

for z = 1 and

X_{p z} = e_{D p}^{new}

for z = 2. The min–max definitions in Eq. are motivated by the probabilistic scenarios of reuse/replace (e.g., see Fig. 6) as opposed to traditional min–max purely based on the data entries X_pz. Equation ensures a utility u_pz = 1 for the idealistic scenarios where the manifold never fails. The utility value u_pz = 0 is obtained when the costliest design is always replaced with new part for three remanufacturing cycles (hence the factor 4 in Eq. ). The traditional min–max definition would lead to the relative scaling of X_pz data entries to 0 and 1 but fails to provide practical insight. Moreover, according to traditional min–max definition, the utility can be negative in scenarios where a component is replaced for every remanufacturing cycle (for the probability of 3N in Fig. 6).

The net utility score of each design U_p is defined as a weighted sum of the individual attributes:

U_{p} = \sum_{z} w_{z} u_{p z}

(21)

where w_z is the importance weight of each attribute. The design options are then ranked based on U_p with the best design option having the largest U_i. Based on the OEM's suggestion, cost-utility u_p1 is given more importance than energy consumption utility u_p2. We therefore select (w₁, w₂) = (0.65, 0.35). For demonstration, we consider that the designer is risk-averse when considering cost and risk seeking when considering energy consumption, with (γ₁, γ₂) = (1, − 0.5). We note that the two attributes, cost and energy consumption, are not independent and an additive form of the utility function is not strictly valid. However, for simplicity, we treat these two attributes as independent. Another limitation of the current approach is not considering process choice-related uncertainties of cost and energy. For example, if additive manufacturing is used to repair component wear, the degree of wear determines the additive manufacturing process cost leading to a distribution of U_p. In this work, we consider U_p to be deterministic, which may undermine the true benefit of the design alternatives subjected to varying degrees of wear. Strictly speaking, the practical design changes of each component may also influence the system-level reusability allocation, requiring another iteration of the reuse rate allocation as described in Sec. 3. However, after including the design changes, the system will already be close to achieving the target energy savings. Thus, the reuse rate allocation may not change significantly in the new iteration.

5 Case Study

In this section, we show the application of the proposed framework on a case study of a transmission for system-level reusability allocation and a hydraulic manifold (a component within the transmission) for component-level design tradeoff analysis.

5.1 Infinitely Variable Transmission (System Level).

We demonstrate the system-level reusability allocation on an IVT used in agricultural machines manufactured by John Deere. The transmission consists of over 350 different components such as gears, housings, shafts, and so on. The remanufacturer provided us with the following real data that we use in the optimization: (1) bill of materials with part weights and material types, (2) initial reuse rates estimated based on the historical data, (3) yearly data of the remanufacturing plant consumption such as electricity, use of fuels, oils, and so on, which we use to calculate the $e_{process, i}^{reman}$ by scaling the yearly data to the component mass, and (4) failure data from which we derive the reliability function [75,76]. To make the optimization simple to visualize, we choose the top four components of the IVT ranked by the amount of embodied energy needed to manufacture a component. In addition, the hydraulic manifold is considered as a fifth component, which is the case study of the component-level design tradeoff analysis in Sec. 5.2. We use the following assumptions in our study, after consultation with the remanufacturing experts: (1) the system undergoes at most three remanufacturing cycles, (2) all the cores are returned for remanufacturing upon failure during field use, (3) whenever a component is reused, the remanufacturing process energy $e_{process, i}^{reman}$ does not change with the remanufacturing cycle, (4) the cost of an individual component is proportional to its embodied energy $c_{i}^{0} \propto e_{i}^{emb}$ ⁠, and (5) there is no significant energy consumption difference when modifying the reuse rates. The parameters used in the system-level reusability allocation for this case study are presented in Table 2.

Table 2

Parameters used in the case study

Parameter(s)	Value(s)
$f$	$[0.8, 0. 5, 0. 3, 0. 7, 0.8]$
α_current	$[0.84, 0. 81, 0. 79, 0. 5, 0.82]$
Δα	$0.1 \times α$
ϕ	$0.5$
m	3
$E$ _target	$0.9 \times E_{current}$

This optimization study aims to allocate reuse rates to the four components of the IVT to obtain at least 10% energy savings with minimum cost. Figure 4(a) shows the variation of initial production cost and the total energy consumed all the way from the initial production to three remanufacturing cycles. The axes are normalized with respect to the current remanufacturing procedures followed by the remanufacturer. We also show the current status and optimized solution in Fig. 4(a). To achieve energy savings, a cost investment is needed, which is most effectively used when focused on improving the design of the most feasible components. As shown in Fig. 4(b), components 1, 4, and 5 have the best improvement in the reuse rate due to high feasibility. Component 3 is allocated only a small increase in the reuse rate due to low feasibility. For this case study, an additional cost of 11% for DfRem is expected to achieve an energy savings of 10%. We note that the cost increment is dependent on ϕ, and for this case study, we chose ϕ = 0.6, which leads to relatively larger costs. Also, we only adopted five components in this case study, and the current reuse rates of the selected components are already large, which is why we only see relatively smaller energy savings. The high reliability of the IVT reduces the likelihood of component replacements, effectively scaling down the benefits obtained during remanufacturing. From Fig. 4(b), we find that the hydraulic manifold (component 5) is allocated a reuse rate of 0.94 to meet the required energy savings. In the next section, we will explore several design changes for the hydraulic manifold and investigate which design changes will allow meeting the allocated reuse rate.

Fig. 4

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System-level reusability allocation for IVT case study: (a) design space exploration of cost and energy normalized by current remanufacturing scenario and (b) comparing reuse rates of the current design with the allocated reuse rates after optimization

5.2 Hydraulic Manifold (Component Level).

In Sec. 5.1, the various components are allocated reusability with the goal of cost minimization and energy conservation. To practically realize the allocated reuse rate for each component, several practically feasible design changes should be evaluated. We now present the case study of a hydraulic manifold, an important component of the IVT. Figure 5 shows the cross-sectional and side views of the hydraulic manifold. The primary purpose of the manifold is to regulate the fluid flow among various other components within the IVT. The manifold is primarily made of aluminum, and during its operation, metallic particles within the fluid are observed to cause abrasive wear. In addition, the disassembly and cleaning steps within the remanufacturing process may lead to the formation of dents or scratches. A significant amount of wear is focused along the gasket region marked in red in Fig. 5.

Fig. 5

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Cross-sectional and side views of the hydraulic manifold (photo courtesy: John Deere)

5.2.1 Design Explorations.

In this section, we state the practical design options for the manifold of interest. As pointed out previously, the major failure mode observed during remanufacturing is abrasive wear and denting in the gasket area and other functional regions of the manifold. Three design options, along with the current scenario of remanufacturing, are presented in Table 3. The proposed design options and the assumptions/analysis mentioned in Table 3 are verified with OEM's remanufacturing experts. The design options differ in the initial production cost, energy consumption, and reuse rate. The initial reuse rate of 0.82 for the current design is based on the field data. The other reuse rates mentioned in Table 3 are assumptions built upon the original reuse rate combined with reman experts’ anticipation of the effects of each design change on addressing the fundamental failure mechanism and the remanufacturing procedure. For the current remanufacturing procedure of basic cleaning and inspection, it is unlikely that the manifold will retain the reuse rate for successive reuses. When a cold spray repair technique is employed in Design#1, the initial reuse rate of 0.82 remains the same, but the repair technique helps retain the reuse rate better for successive reuses. On the other hand, Design#2 provides better material integrity than Design#1 and, therefore, has a better initial reuse rate and retention for multiple life cycles. Based on the physics of the failure mechanism, Design#3 (surface coating) offers the best solution in terms of a high initial reuse rate with the excellent reuse rate retention for multiple reuses. From our analysis in Sec. 5.1, we find that the allocated reuse rate for the hydraulic manifold is about 0.94, which is achieved by Design#2 and Design#3 with some error margin. Although Design#3 can be perceived to be the best design change from a failure mechanism standpoint, we will later show that the inclusion of reliability can potentially favor other design options.

Table 3

Design scenarios for the hydraulic manifold

Design ID	New product design and remanufacturing procedure	Assumptions/analysis
Current	New: Same as Fig. 5 Reman: Basic cleaning and inspection	Poor reuse rate retention as there is no effective repair technique to extend component life The initial reuse rate is 0.82^{^a}, which decreases by 60% for every reman cycle
Design#1	New: Same as Fig. 5 Reman: Use cold spray additive manufacturing to treat dents/scratches followed by machining	Cold spray is relatively costly and potentially affects local material properties Spot repair and limitations on accessibility to the required repair location Fair retention of the reuse rate. The initial reuse rate is 0.82^{^a}, which decreases by 20% for every reman cycle
Design#2	New: Thicker gasket area Reman: Machining/material removal of the gasket area	Avoids additive manufacturing as in Design#1 Ensures multiple remanufacturing cycles Cannot repair in other regions The initial reuse rate is 0.9, which decreases by 15% for every reman cycle.
Design#3	New: Surface coating (anodizing) Reman: Brush anodizing or re-anodizing	Effectively addresses the failure mechanism Best reuse rate and retention The initial reuse rate is 0.95, which decreases by 5% for every reman cycle.

Design ID	New product design and remanufacturing procedure	Assumptions/analysis
Current	New: Same as Fig. 5 Reman: Basic cleaning and inspection	Poor reuse rate retention as there is no effective repair technique to extend component life The initial reuse rate is 0.82^{^a}, which decreases by 60% for every reman cycle
Design#1	New: Same as Fig. 5 Reman: Use cold spray additive manufacturing to treat dents/scratches followed by machining	Cold spray is relatively costly and potentially affects local material properties Spot repair and limitations on accessibility to the required repair location Fair retention of the reuse rate. The initial reuse rate is 0.82^{^a}, which decreases by 20% for every reman cycle
Design#2	New: Thicker gasket area Reman: Machining/material removal of the gasket area	Avoids additive manufacturing as in Design#1 Ensures multiple remanufacturing cycles Cannot repair in other regions The initial reuse rate is 0.9, which decreases by 15% for every reman cycle.
Design#3	New: Surface coating (anodizing) Reman: Brush anodizing or re-anodizing	Effectively addresses the failure mechanism Best reuse rate and retention The initial reuse rate is 0.95, which decreases by 5% for every reman cycle.

a

Based on actual reuse data collected during remanufacturing

In this study, the reliability of the various design options mentioned in Table 3 is assumed to be similar for all remanufacturing cycles. Strictly speaking, each design change can potentially yield a different reliability level associated with the manifold. But assuming the transmission to be a series system of multiple components, of which the manifold is one component, it is not likely that a minor difference in the reliability of the manifold will significantly change the overall reliability of the transmission system. We would also like to note that the need for remanufacturing is triggered upon the failure of the entire transmission; therefore, in assessing the design changes, we use the reliability of the entire transmission based on the time-to-failure data collected from the field [76]. Also, based on the definition of remanufacturing to produce “as new” goods, the reliability of the transmission is assumed to be constant across multiple life cycles.

5.2.2 Formulating Cost and Energy Consumption.

DfRem changes for the hydraulic manifold mentioned in Table 3 modify the cost $c^{new}$ and energy $e^{new}$ of new manifold along with the remanufacturing process cost $c_{process}^{reman}$ and energy consumption $e_{process}^{reman}$ ⁠. We list the various contributions to cost and energy consumption for making a new manifold and the remanufacturing procedures in Table 4. The aluminum manifold is made by die casting followed by machining/finishing processes. Therefore, the cost and energy for the current design $c_{D 0}^{new} & e_{D 0}^{new}$ have contributions from material acquisition $c_{D 0}^{emb} & e_{D 0}^{emb}$ ^³ [92], die casting $c_{D 0}^{cast} & e_{D 0}^{cast}$ [93,94], machining $c_{D 0}^{mach} & e_{D 0}^{mach}$ [95,96], electricity $c_{D 0}^{elec} & e_{D 0}^{elec}$ [85,95] and labor $c_{D 0}^{labor}$ for both casting and machining. Alternatively, one could also write the cost equation in terms of machine burden for both die casting and machining. We have verified with the OEM that our implementation of the cost model of the current design is 95% accurate with respect to the market price of the hydraulic manifold by considering a 15% profit margin on the manifold cost.

Table 4

Cost and energy consumption formulation for the various design options

Design ID	Cost	Energy consumption
Current/ Design#0	New: $c_{D 0}^{new} = c_{D 0}^{emb} + c_{D 0}^{cast} + c_{D 0}^{mach} + c_{D 0}^{labor} + c_{D 0}^{elec}$	New: $e_{D 0}^{new} = e_{D 0}^{emb} + e_{D 0}^{cast} + e_{D 0}^{mach} + e_{D 0}^{labor} + e_{D 0}^{elec}$
Current/ Design#0	Reman: $c_{process, D 0}^{reman} = c_{D 0}^{r, elec} + c_{D 0}^{r, oil} + c_{D 0}^{r, labor}$	Reman: $e_{process, D 0}^{reman} = e_{D 0}^{r, elec} + e_{D 0}^{r, oil}$
Design#1	New: (same as current design) $c_{D 1}^{new} = c_{curr}^{new}$	New: (same as current design) $e_{D 1}^{new} = e_{D 0}^{new}$
Design#1	Reman: $c_{process, D 1}^{reman} = c_{process, D 0}^{reman} + c_{D 1}^{r, emb} + c_{D 1}^{r, spray} + c_{D 1}^{r, labor}$	Reman: $e_{process, D 1}^{reman} = e_{process, D 0}^{reman} + e_{D 1}^{r, emb} + e_{D 1}^{r, mach}$
Design#2	New: $c_{D 2}^{new} = c_{D 0}^{new} + c_{D 2}^{emb} + c_{D 2}^{mach}$	New: $e_{D 2}^{new} = e_{D 0}^{new} + e_{D 2}^{emb} + e_{D 2}^{mach}$
Design#2	Reman: $c_{process, D 2}^{reman} = c_{process, D 0}^{reman} + c_{D 2}^{r, mach} + c_{D 2}^{r, labor}$ `	Reman: $e_{process, D 2}^{reman} = e_{process, D 0}^{reman} + e_{D 2}^{r, mach}$
Design#3	New: $c_{D 3}^{new} = c_{D 0}^{new} + c_{D 3}^{coat} + c_{D 3}^{labor}$	New: $e_{D 3}^{new} = e_{D 0}^{new} + e_{D 3}^{coat}$
Design#3	Reman: $c_{process, D 3}^{reman} = c_{process, D 0}^{reman} + c_{D 3}^{r, coat} + c_{D 3}^{r, labor}$	Reman: $e_{process, D 3}^{reman} = e_{process, D 0}^{reman} + e_{D 3}^{r, coat}$

Design#1 is different from the current scenario by the inclusion of the cold spray additive manufacturing technique during remanufacturing. Since only part of the gasket area would require reconditioning, we assume that for every remanufacturing cycle, about 20% of the gasket area is subjected to cold spray to develop a thickness of 0.03 in. followed by machining. These processes add the cost of material $c_{D 1}^{r, emb}$ ⁠, process cost $c_{D 1}^{r, spray}$ ⁠, and additional labor cost $c_{D 1}^{r, labor}$ to the current remanufacturing cost $c_{process, D 0}^{reman}$ ⁠. In these formulations, the superscript r refers to remanufacturing step. Design#2 modifies the original manifold design by having a 0.09 in. thicker gasket (leading to additional $c_{D 2}^{emb} & e_{D 2}^{emb}$ and $c_{D 2}^{mach} & e_{D 2}^{mach}$ ⁠) and the remanufacturing process is the material removal of 0.03 in. thickness for every remanufacturing cycle $(c_{D 2}^{r, mach} & e_{D 2}^{r, mach})$ ⁠. This design change ensures at least three remanufacturing cycles while also avoiding the costly additive manufacturing technique of Design#1. Design#3 has an additional step of hard anodizing to create a layer of thickness 0.001 in., leading to additional $c_{D 2}^{coat} & e_{D 2}^{coat}$ ⁠. The remanufacturing procedure, in this case, is re-anodizing or brush anodizing. The electricity and time requirements for anodizing are determined using the 720 anodizing rule [97]. The labor costs $c^{labor}$ are set at $ 20/h, and the labor time is determined appropriately for each process based on the OEM's recommendations. We assume that the remanufacturing process costs and energy consumption of the design options are similar across multiple remanufacturing cycles. However, there is a variation from cycle to cycle because of the reuse rate and its retention, which we model using the branched power law as described in Sec. 2.2. To determine the reliability-informed cost and energy consumption for the manifold, the formulations in Table 4 are subjected to the reliability-informed framework described in Sec. 3.3.

5.2.3 Results.

We now present the results comparing the cost and energy consumption of the design strategies mentioned in Table 3. We also include a case of “no remanufacturing” (by always replacing with new) to highlight the importance of remanufacturing in general. We first look at the probability of reusing the manifold or replacing it with a new part for three remanufacturing cycles for all design scenarios in Fig. 6. This probability distribution results from applying the branched power-law model (Sec. 2.2) to the reuse rate assumptions listed in Table 3. We also show an approximate remanufacturing cost and energy consumption for the various reuse/replace with new situations (these are approximate because of the variations with designs). The current remanufacturing scenario mostly encourages single reuse within three remanufacturing cycles with an expected remanufacturing cost of 2.06 times the new manifold cost $c_{D 0}^{new}$ (i.e., $2.06 \times c_{D 0}^{new}$ ⁠). Although this is better than using all-new replacements, Design#1 and Design#2 favor two reuses within the three cycles, making them more beneficial in terms of cost (about $1.4 \times c_{D 0}^{new}$ ⁠) and energy (about $1.2 \times e_{D 0}^{new}$ ⁠), with Design#2 performing slightly better than Design#1. Design#3 is the best design that favors reusing the manifold two or three times. Because of this, the expected remanufacturing cost is about $0.88 \times c_{D 0}^{new}$ ⁠, and remanufacturing energy requirements average at $0.6 \times e_{D 0}^{new}$ ⁠.

Fig. 6

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Probability of manifold reuse R or replacement with new N for three remanufacturing cycles. Approximate remanufacturing costs and energy consumption are also shown for each of the remanufacturing scenarios.

We now compare the results of the various design scenarios without considering reliability. Figure 7 shows the overall cost and energy consumption for the various design options for three remanufacturing cycles. Although the current remanufacturing scenario (Design#0) seems to greatly decrease the cost and energy consumption of the first remanufacturing cycle, this benefit quickly diminishes for subsequent remanufacturing cycles due to the poor retention of reuse use. The use of cold spray (Design#1) provides slightly better cost and energy savings for the three remanufacturing cycles due to better retention of reuse rate. However, the additive manufacturing technique is relatively costly, slightly negating the benefit from better reuse rate retention. Design#2, however, avoids additive manufacturing and maintains the material integrity by simple machining, albeit a slightly bulkier design. We have verified with the OEM that this design change does not alter the hydraulic mechanism of the manifold. Maximum benefit is achieved by Design#3, which addresses the fundamental problem of abrasion/denting using a conventional anodizing process. The $c_{D 3}^{new}$ and $e_{D 3}^{new}$ for Design#3 are slightly higher owing to more labor time spent for surface coating (the surface coating process itself is cost-efficient when the parameters are calculated using the 720 rule for anodizing [97]). It can be observed from Fig. 7 that Design#3 can achieve as much as a 27% reduction in cost and a 42% reduction in energy consumption when compared to the current remanufacturing scenario for three remanufacturing cycles. We would like to note that the assumptions on the reuse rate and its retention for multiple life cycles from Table 3 majorly influence the comparisons shown in Fig. 7. Apart from the additional costs associated with each design change, the reuse rates dictate the sizes of similarly colored bars across the design options. A higher reuse rate reflects a smaller contribution to the cost and energy consumption. The assumptions regarding the reuse rate retention affect the relative magnitude of the cost and energy consumption for successive remanufacturing cycles within the same design option. For example, in each design scenario $C_{1}^{re} (red) < C_{2}^{re} (yellow) < C_{3}^{re} (purple)$ ⁠, and a poor reuse rate retention reflects as a larger difference in the inequality. In the limit of a very low reuse rate and retention, each design option approaches the “all-new” design scenario.

Fig. 7

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Normalized cost and energy consumption for the various design options for three remanufacturing cycles

However, the benefits of each of the design scenarios differ after considering reliability. Figure 8 shows the reliability-informed cost $c^{rel}$ and energy consumption $e^{rel}$ considering a product lifetime of T_L = 8000 h (see Eqs. (15) and (16)). The number of cores retrieved for remanufacturing is small due to the high reliability of this case study and hence the effective contributions of $c^{reman}$ and $e^{reman}$ are significantly smaller when compared to $c^{new}$ and $e^{new}$ ⁠, respectively. Consequently, the differences between the various design scenarios are also largely reduced. In fact, contrary to our observation from Fig. 7, Design#3 seems to be disadvantageous after including reliability. This can be attributed to the increase in the initial cost due to surface coating and additional labor, and the rise in initial energy consumption is due to additional electricity. Similarly, the higher energy consumption of Design#2 stems from using more aluminum, an energy-intensive material, in the gasket region. However, both Figs. 7 and 8 clearly establish the advantage of remanufacturing, in general, over always using new replacements. We note that the reliability function is time-dependent. When considering longer time periods T_L, we can expect a greater number of failures and hence more demand for remanufacturing. To this end, we plot the variation of the $c^{rel}$ and $e^{rel}$ with T_L as shown in Fig. 9(a). From the perspective of energy consumption, both Design#2 and Design#3 only show small variations from T_L = 4000 h to 20, 000 h because of good reuse rate retention. However, this advantage is not enough to overcome the initial offset in energy consumption arising from the design modifications. To further elaborate the understanding, we also show a hypothetical case in Fig. 9(b) with low reliability where the scale parameter λ is decreased by ten times and the shape parameter β is increased by a factor of three. In this case, we see the crossover of $c^{rel}$ and $e^{rel}$ at some T_L between the design options. For example, in Fig. 9(b), Design#3 seems to me unfavorable if the component is designed for T_L = 8000 hrs, whereas if considering T_L = 20, 000 h, the current remanufacturing scenario is the most inefficient next to always new replacements. Both Figs. 8 and 9 show the importance of considering reliability in decision-making relevant to DfRem. We also note that the results shown in Figs. 7–9 are expectation values of an otherwise probabilistic formulation.

Fig. 8

View large Download slide

Reliability-informed cost and energy consumption for the various design options for three remanufacturing cycles at the end of T_L = 8000 hrs

Fig. 9

View large Download slide

Variation of and with T_L for (a) true reliability with (β,λ) = (0.6569,323,700) and (b) pseudo reliability function with (β,λ) = (0.6569 × 3,323,700/10). A reference line marking T_L = 8000 h is marked to represent Fig. 8.

The net utility score for each design option is shown in Fig. 10(a), along with the utility score associated with the reuse remanufacturing scenario (from Fig. 6). The sizes of the symbols in Fig. 10(a) are proportional to the corresponding probability values from Fig. 6. The current design has the lowest utility of 0.28 because of the high probability of 1R2N. The net utility score of Design#1 is only slightly lower than Design#2 because of the costs associated with additive manufacturing in Design#1. Design#3 has the highest score because the high reuse rate and reuse retention lead to the high probability of 2R1N and 3R. We also show the different design options marked on a net utility contour heatmap in Fig. 10(b). We note that the utility-based analysis shown in Fig. 10 does not include reliability. We then rank the design options using the same method with and without reliability in Table 5. Following our arguments from Figs. 7 and 8, by not considering reliability, the surface-treated Design#3 seems to have the best rank, but the ranking drastically changes after considering reliability, where Design#3 is now ranked last. In the limit of low reliability, we expect that the design ranks with and without considering reliability merge together, but low reliability is something the designer wants to avoid in the first place. Through this example, we highlight the importance of considering reliability in ranking the design options.

Fig. 10

View large Download slide

(a) Utility score of the four design options along with the multiple remanufacturing scenarios of reuse/replace with new. The symbol size is proportional to the probability of the reuse/replacement. (b) A utility heat map with markings of the design options.

Table 5

Ranking of the design options with and without considering reliability

Design ID	Without reliability	With reliability
Design#0	4	2
Design#1	3	1
Design#2	2	3
Design#3	1	4

6 Data-Driven Design Decision Support Software Tool

The algorithms/models presented in this article and our related previous publications [75–77] have been implemented on a prototype of design decision analysis software called D4S [80,98]. This prototype software tool allows a designer to leverage real-world field reliability and remanufacturing reusability data to drive DfRem decisions, particularly for high-value components in industrial and agricultural equipment. As shown in Fig. 11, the D4S prototype has four modules, which can be summarized as follows:

The reliability analysis module fits the reliability function based on user inputs such as the time-to-failure data, different types of time-to-failure distributions (Weibull, Exponential, Gamma, Normal, etc.), and the ability to specify right-censored data.
The LCWC analysis module determines the expected LCWC with user inputs such as the reliability function (which can be automatically imported from the previous module), costs of new and remanufactured units, and warranty policy. By solving the system of equations described in Ref. [76], this module outputs the probability distribution of LCWC.
The LCA module quantifies the environmental impacts such as energy consumption, global warming potential, and abiotic depletion potential for multiple remanufacturing cycles while considering reliability. As shown in Fig. 12, the user inputs include the bill of materials, transportation of the raw materials/finished product (zip codes of key locations), specific energy consumption during manufacturing/remanufacturing processes, quantities of resources such as fuel, and the maximum number of life cycles. The reliability of the system is automatically imported from the first module. The reliability-informed environmental impacts are determined using the algorithms mentioned in Ref. [76].
The design decision module conducts the system-level reusability allocation and component-level design tradeoff analysis described in this article. For the system-level reusability allocation, the user inputs include the bill of materials, current and maximum achievable reuse rates of the components, feasibility for design change, and target energy savings with the output similar to Fig. 4. For the component-level design tradeoff analysis, the user inputs suggested design changes, and the software outputs results similar to Fig. 7 and 8.

Fig. 11

View large Download slide

Schematic of the D4S prototype software tool along with snapshots of four modules

Fig. 12

View large Download slide

User interface and output of the LCA module in the D4S software tool

The software tool is designed to be versatile and simple to use. The results are presented to assist the designer in understanding the long-term economic and environmental implications of DfRem decisions. We currently validated the D4S prototype on the IVT used in agricultural equipment. It is unclear how generalizable our validation findings can be to other high-value components. We plan to demonstrate the utility of the tool on an automotive part in the future.

7 Conclusions

This article emphasizes the importance of including reliability at an early design stage for DfRem by creating a two-stage framework. At the upper level, the framework sets theoretical reuse rate expectations on all the components of the system, and the lower level of the framework compares practical design options for each individual component and evaluates these design options with respect to the theoretical reuse rate expectation. To enable remanufacturing for multiple remanufacturing cycles, the component design should not only have a high initial reuse rate but also retain it for multiple reuses accounting for factors such as material fatigue. The branched power-law model is used to model variation of the reuse rates from cycle to cycle and determine the probability that a particular component will undergo a certain number of reuses. The feasibility of design change is an important parameter that the designer can choose for the components. Lower feasibility means that high-cost investment is needed for DfRem design modification, whereas higher feasibility indicates favorable design changes with low costs.

We explore the utility of the framework through the case study of an IVT used in some agricultural equipment manufactured by John Deere who provided us with the bill of materials, initial component reuse rates, and field time-to-failure data. By using an exponential cost function (with feasibility), we solve the reusability allocation problem and visualize the theoretical reuse rate design space of the components and how they affect the energy consumption and cost. Better reuse rates are allocated to components that have relatively high feasibility and we find that to obtain about 10% of energy savings with respect to the current state of IVT remanufacturing, there needs to be roughly 11% cost investment to improve the design of a few select components. These numbers, however, vary with the cost model used by the designer. We then take the case study of a hydraulic manifold, an important component of the IVT. Working closely with the OEM, we developed several design options for the manifold such as the use of cold spray additive manufacturing, having a bulkier design in the gasket region, and surface coating. When considering the overall cost and energy consumption for the initial new component and three remanufacturing cycles, the current state of remanufacturing is at least 25% more efficient than always using a new component for replacement. The surface coating technique is evaluated to be the best design modification with up to 27% savings in cost and 42% savings in energy consumption with respect to the current remanufacturing scenario. This, however, is true when not considering the reliability of the system. After accounting for reliability, the same surface coating technique is ranked the last. This is because the system already has relatively high reliability, and the probability of failure within the product service life of T_L = 8000 h (roughly 8–10 years) is very low. The additional cost and energy required to do the surface coating of the initial design now become significant and is not recovered during the multiple remanufacturing cycles. It is, therefore, crucial to consider product reliability when ranking design options as it could be significantly different when ranking the same designs in a traditional one-to-one manner without considering reliability (which is often the approach taken in current literature). In the limit of low reliability, the design ranks will be consistent whether or not reliability is considered.

In this article, the reuse rates of the parts were determined by the OEM's inventory data, which may not be available for other practitioners as it takes several months to years to develop a sufficiently larger inventory of returned cores with reliable end-of-life designators. Moreover, the current algorithm requires some active interaction from the designer, potentially limiting the identification of broader remanufacturing opportunities. The cost models developed in this article do not account for process uncertainty, which could significantly impact the results. Our future work is directed toward (1) conducting finite element modeling to evaluate the fatigue life and wear from which the remanufacturability potential can be approximated at the initial design stage, (2) automating the identification of components that provide the best remanufacturing advantage by using machine learning techniques for real-time cost and energy estimates, and (3) validating the D4S software tool on an automotive part.

Footnotes

2

https://remadeinstitute.org

3

See Note ².

Acknowledgment

This material is based upon 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.

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.

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.

Nomenclature

$c$ =: individual component cost
$e$ =: energy consumption for a part
$E$ =: total energy consumption of a system
$c^{0}$ =: present cost of a component
ℂ^prod =: total unit cost
f =: feasibility for a design change
R =: reliability function
u_pz =: utility function of the pth design option and zth attribute
D_p =: design alternative
N_reuse/recall =: number of reused/ recalled components
P_f =: probability of failure
T_e =: time covered by a warranty policy for a new replacement
T_L =: total product life
U_p =: net utility score of the pth design option
m^b =: mass of material required to manufacture a component
n^new/re =: expected number of replacements with new/remanufactured components
α =: component reuse rate
β =: Weibull shape parameter
γ =: risk factor
λ =: Weibull scale parameter
ν (%) =: % of material removal from a block to manufacture a product
ϕ =: stretch parameter

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Reliability-Informed Economic and Energy Evaluation for Bi-Level Design for Remanufacturing: A Case Study of Transmission and Hydraulic Manifold

Abstract

1 Introduction

1.1 Literature Review.

1.2 Our Contribution.

2 Overview

2.1 Proposed Framework.

2.2 Modeling Reuse Rates for Multiple Remanufacturing Cycles.

3 System-Level Reusability Allocation

3.1 Problem Definition.

3.2 Energy Quantification.

3.3 Reliability-Informed Energy Quantification.

3.4 Algorithm.

4 Component-Level Design Tradeoff Analysis

5 Case Study

5.1 Infinitely Variable Transmission (System Level).

5.2 Hydraulic Manifold (Component Level).

5.2.1 Design Explorations.

5.2.2 Formulating Cost and Energy Consumption.

5.2.3 Results.

6 Data-Driven Design Decision Support Software Tool

7 Conclusions

Footnotes

Acknowledgment

Disclaimer

Conflict of Interest

Data Availability Statement

Nomenclature

References

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Reliability-Informed Economic and Energy Evaluation for Bi-Level Design for Remanufacturing: A Case Study of Transmission and Hydraulic Manifold

Abstract

1 Introduction

1.1 Literature Review.

1.2 Our Contribution.

2 Overview

2.1 Proposed Framework.

2.2 Modeling Reuse Rates for Multiple Remanufacturing Cycles.

3 System-Level Reusability Allocation

3.1 Problem Definition.

3.2 Energy Quantification.

3.3 Reliability-Informed Energy Quantification.

3.4 Algorithm.

4 Component-Level Design Tradeoff Analysis

5 Case Study

5.1 Infinitely Variable Transmission (System Level).

5.2 Hydraulic Manifold (Component Level).

5.2.1 Design Explorations.

5.2.2 Formulating Cost and Energy Consumption.

5.2.3 Results.

6 Data-Driven Design Decision Support Software Tool

7 Conclusions

Footnotes

Acknowledgment

Disclaimer

Conflict of Interest

Data Availability Statement

Nomenclature

References

Get Email Alerts

Cited By

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