Design Engineering Laboratory,
School of Mechanical, Industrial, and
Oregon State University,
Corvallis, OR 97331
Douglas L. Van Bossuyt
Department of Mechanical Engineering,
Colorado School of Mines,
Golden, CO 80401
Rob B. Stone
Design Engineering Laboratory,
School of Mechanical, Industrial, and
Oregon State University,
Corvallis, OR 97331
Irem Y. Tumer
Complex Engineered Systems
School of Mechanical, Industrial, and
Oregon State University,
Corvallis, OR 97331
The Function-Based Design
for Sustainability Method
Over the last two decades, consumers have become increasingly aware and desiring of
sustainable products. However, little attention has been paid to developing conceptual
design methods that explicitly take into account environmental impact. This paper con-
tributes a method of automated function component generation, and guided down-
selection and decision-making based upon environmental impact. The environmental
impact of functions has been calculated for 17 of the products found in the Design Repos-
itory using ReCiPe scoring in SimaPRO. A hierarchical Bayesian approach is used to
estimate the potential environmental impacts of speciﬁc functions when realized into
components. Previously, product environmental impacts were calculated after a product
was developed to the component design stage. The method developed in this paper could
be used to provide a criticality ranking based on which functional solutions historically
have the greatest risk of causing high environmental impact. The method is demonstrated
using a simple clock system as an example. A comparative case study of two phone charg-
ers for use in third-world countries demonstrates the decision-making capabilities of this
method, and shows that it is possible to compare the environmental impact of alternative
function structures during the conceptual stage of design. With the method presented in
this paper, it is now possible to make early functional modeling design decisions speciﬁ-
cally taking into account historical environmental impact of functionally similar
products. [DOI: 10.1115/1.4035431]
Keywords: sustainability, environmental impact, functional modeling, design decision-
making, product design
Sustainability in manufactured products is an increasingly
important consideration that design engineers must take into
account when designing new consumer products. A small but sig-
niﬁcant segment of the consumer market (15–30 million people in
the USA as of 2009) will pay a premium for consumer products
that are more sustainable than functionally identical competitor
products . However, efforts to create sustainable products often
do not occur until after most major design decisions have been
made, and manufacturing processes selection has begun [2,3].
This results in unsatisfactory sustainability due to compromises
foisted upon sustainable manufacturing efforts .
Efforts to connect early phase conceptual design functional
modeling with later analysis tools—such as for risk and reliability
analysis, and for mission stage planning—have brought signiﬁcant
analytic capabilities earlier in the design process to help shape
important early phase design decisions [5–8]. Analyzing signiﬁ-
cant design and manufacturing considerations in the very early
stages of a design process can mitigate the risks of costly redesign.
Thus, a method to analyze environmental impact during the ear-
liest stages of design has the potential to improve product or sys-
tem sustainability and may be used to make design tradeoff
1.1 Specific Contributions. This paper contributes the
function-based design for sustainability (FDS) method, which
enables automated functional solution generation and guided
down-selection and decision-making based on environmental
impact. The environmental impact of functions has been calcu-
lated for 17 of the products found in the Design Repository (a
product library where products are decomposed to the component
and functional level) using SimaPRO  (a lifecycle assessment
software product) and the ReCiPe  lifecycle assessment scor-
ing method and dataset. This product data was created during a
separate study of the relationship between sustainability and inno-
vation , and we use it in this manuscript to demonstrate the
FDS method. ReCiPe scores for every component are calculated
based on the material, the manufacturing process, and the mass of
the part. The ReCiPe method itself accounts for impacts during
material extraction through end of life . FDS uses a hierarchi-
cal Bayesian modeling approach to identify low environmental
impact functional solutions for products during the early phases of
design by using historical function–component information via
mean and standard deviation statistics. Previously, product envi-
ronmental impacts were calculated after a product was developed
to the component design stage. The FDS method makes it possible
to make early function-based modeling design decisions speciﬁ-
cally taking into account environmental impact of the product or
More speciﬁcally, FDS is used to rank the importance of func-
tion alternatives or function-to-component design choices with
respect to their potential to affect the ﬁnished product’s environ-
mental impact. The goal is similar to that of a risk priority number
(RPN) in a failure modes and effects analysis (FMEA) . The
RPN is an aggregate score created for each potential failure
Contributed by the Design Theory and Methodology Committee of ASME for
publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 2,
2016; ﬁnal manuscript received November 22, 2016; published online February 20,
2017. Assoc. Editor: Shapour Azarm.
Journal of Mechanical Design APRIL 2017, Vol. 139 / 041102-1Copyright V
C2017 by ASME
identiﬁed in an FMEA, and it creates a basis for ranking the
importance of potential failures. RPN ranking allows designers to
prioritize their focus on mitigating the most important potential fail-
ures. Similarly, the FDS method provides a way to prioritize early
design decisions based on their potential environmental impacts.
The FDS method presented in this paper enhances the ability of
the product design engineers to develop sustainable products. And
while the broad concept of sustainability includes environmental,
economic, and social factors, in this work, we focus speciﬁcally
on improving sustainability through reducing environmental
impact. Several key areas of existing research and industrial prac-
tice are relevant to understanding and implementing FDS. This
section reviews speciﬁc details of several topics important to the
method including: innovation and sustainability in design, life-
cycle assessment, functional modeling and the design repository,
functional and environmental impact, and hierarchical Bayesian
2.1 Innovation and Sustainability in Design. In recent deca-
des, growing attention has been paid to the development of sus-
tainable processes and products both for short and long-term
issues [1,13–16]. In addition to consumer-driven needs and desires
spurring companies to adopt sustainable design practices, compa-
nies wishing to participate in international markets must adhere to
a number of different regulations (e.g., Refs. [17,18]). Such regu-
lations have necessitated that many products be redesigned in
order that they may continue to be sold in the European market-
Several design tools have been developed to help companies
comply with new regulations in Europe and elsewhere . Most
of the currently available tools are TRIZ-derived [21–24] and
base their sustainability statistics on seven eco-innovation ele-
ments embodied in three categories including: (1) material reduc-
tion, (2) energy reduction, and (3) product durability [25–33].
While the TRIZ-based methods are useful for creativity and
ideation within the context of sustainability, they are not appropri-
ate for designers who wish to use a functional modeling approach
to early conceptual system design . Work has been done to
link TRIZ’s problem-solving approach with the philosophy of
functional modeling  and to merge TRIZ’s active principles
with functional modeling , among other efforts [37–39]; how-
ever, a linkage between TRIZ and functional modeling has not
been developed to allow sustainability information to move
between TRIZ and functional modeling. Rather than developing
such a linkage, we have chosen to develop a method (presented in
this paper) to assess sustainability directly in functional modeling.
2.2 Life Cycle Assessment (LCA). Life cycle assessment
(LCA) [40–42] has proven to be a valuable tool for a variety of
purposes and industries [43–46]. While it is recognized that LCA
can be applied to the design process , it is challenging to do so
in the conceptual stages of design when sunk costs are low. Vari-
ous applications of LCA into existing design methods have found
varying measures of success in practice. Quality function deploy-
ment (QFD) [48–52] and TRIZ have  also seen LCA integra-
tion, but injecting life cycle requirements at this stage (prior to
functional analysis) can artiﬁcially limit the solution space.
Another drawback of many QFD-based methods is that product
designers are not provided actionable solutions to design chal-
lenges. Instead, product designers must look to other sources for
eco-innovative design solutions. The FDS method is formulated
to address these issues by offering the designer actionable choices
via comparisons between options at the functional stage of design.
2.3 Functional Modeling and the Design Repository. Func-
tional modeling, the function-ﬂow taxonomy, and the functional
basis [13,14] have been developed in part to help product design-
ers to determine the functional design of a product in the early
stages of conceptual design [54–58]. As the design progresses,
libraries of abstract historical product data, such as the Design
Repository, allow for functional models to be developed into com-
ponent designs through semi-automated processes. A restricted
vocabulary of component types, which can be developed and
matched to these functions using reverse engineering data, facili-
tates this process [50–61]. Function-based design continues to be
extended [63–64] to allow interesting and useful analyses [65–76]
to be performed by designers early in the conceptual stages of
design [77–88]. Using traditional engineering approaches, such
analyses are not possible until much later in the design process
[89–93]. For example, efforts have been made to bring risk and
reliability analysis into the earliest phases of design to prevent
costly redesigns or retroﬁts from signiﬁcant risk or reliability
issues discovered late in the design process [5–8,94]. While
design repositories can suffer from limited size, approaches such
as information extraction and human computation have been used
to improve the size of product data sets [95–97] and thus improve
their predictive power.
2.4 Functional and Environmental Impact. Devanathan
et al. have shown that it is feasible to associate environmental
impact with a given function by using a function impact matrix
(FIM) [98,99] to isolate functions that dominate product environ-
mental impact. Individual component impacts can be determined
and then mapped back to the functions that the components solve.
FIM works by combining LCA with portions of QFD. FIM is
developed by combining environmental impact data for each com-
ponent in a product with a function component matrix, and then
distributing impact data to the functions that deﬁne the product.
FIM was developed to redesign existing products rather than
design new products [98,99].
Gilchrist et al.  developed a method to compare the func-
tional impact of existing products by directly linking functions to
environmental impacts through FIM using ReCiPe 2008 , a
dataset and LCA computational method, and information from
SimaPRO , a LCA software package. Their work determines
the most common component used to solve a particular function
and investigates the method of manufacture of the average com-
ponents [4,100]. From the work of Gilchrist et al., it was found that
innovative products often fare worse in sustainability metrics than
common products that solve the same functional design. While Gil-
christ et al. method is useful for existing products that can be
decomposed to a functional level, it allocates historical environmen-
tal impact evenly across all functions that a type of component has
performed. This simple assumption detracts from the predictive
power of the method when developing new products.
2.5 Hierarchical Bayesian Modeling. Hierarchical Bayesian
modeling is a statistical modeling approach that combines Bayes-
ian inference with hierarchical statistical modeling . This
approach has been applied to solve problems in a wide range of
domains including geochemical parameter estimation ,
growth rate forecasting , speech recognition , relational
learning , and reliability forecasting .
Gelman et al.  describe the hierarchical Bayesian model-
ing approach. They present an example in which a joint probabil-
ity model is created for an overall rat population using (1) a
noninformative hyperprior distribution representing current
beliefs about rat tumor incidence and (2) new results from a series
O’Halloran  use this hierarchical Bayesian approach—
along with historical reliability data, the functional basis, and the
component taxonomy—to develop a methodology for reliability
prediction. Their methodology enables a designer to consider the
probable reliability of candidate systems at the functional model-
ing stage of design. Each observation in O’Halloran’s work is a
041102-2 / Vol. 139, APRIL 2017 Transactions of the ASME
failure rate for a real component. These observations are organ-
ized hierarchically according to their function classiﬁcations and
component classiﬁcations. Failure rate probability distributions
are calculated for each top-level function according to the compo-
nent subpopulations within, which enables predictions about the
future failure rates of any given function. Others have previously
used hierarchical Bayesian approaches for a variety of purposes in
engineering design in applications that include consumer prefer-
ence modeling and marketing decision support (e.g., see Refs.
The function-based design for sustainability (FDS) method con-
sists of three distinct steps as shown in Fig. 1. The ﬁrst stage
requires collection and preparation of historical environmental
impact data. The second stage establishes predictive probability
distributions of environmental impact for each
function–component combination in the historical dataset. The
third stage uses these probability distributions to provide guidance
to design engineers.
3.1 Step 1: Data Preparation. The data preparation phase
involves the collection of historical product data from the design-
er’s domain. This reﬂects the approach used in function-based
failure prediction methodologies based on the historical failure
data [5–8,89,112–116]. In the example and case study presented
in Sec. 4, a convenience sample of 17 consumer products is used
(with ReCiPe scores calculated for each component) to demon-
strate the approach. These products are cataloged in the Design
Repository  and were used in a previous sustainability study
. To create this test set, cradle-to-grave environmental impact
scores are queried from SimaPRO based on the materials and
manufacturing processes that make up each component. The end-
of-life scenario is assumed to be landﬁlling, and packaging and
shipping are assumed to be equal across all products. The three
ReCiPe endpoint indicators are aggregated into a single unitless
performance metric using the hierarchist weighting and normal-
ization method. Use phase impacts are estimated for each type of
component based on expected lifetimes and duty cycles of the
product and component.
Given a set of products similar to the product being designed,
each component in each product is assigned a functional basis func-
tion, a component taxonomy type, and an environmental impact
score. Impact scores are aggregated by shared function–component
pairings within each product and normalized to product mass.
The data preparation procedure begins by processing each prod-
uct separately. For each product, each component’s impact score
in Iis divided by its parent product’s total mass (mp) as shown in
Eq. (1). The mass normalization produces a vector of impact den-
sity observations (y) that enables comparison of general compo-
nent taxonomy types across multiple products. For example, if all
other factors are held equal, the environmental impact of two elec-
tric motors that comprise 20% of a product’s mass will be identi-
cal in this analysis, regardless of whether that product’s mass is
10 kg or 100 kg. For any analysis that uses this data, the outcome
is interpreted as a relative historical likelihood that a given type of
component will contribute signiﬁcantly to a product’s overall
environmental impact. Figure 2provides an example of the data
preparation stage. The ReCipE score of the ﬁrst gear in the Polar-
oid Pogo (3.05 10
) is divided by 218 g to produce a normal-
ized ReCiPe score of 1.40 10
. The normalized scores for both
gears in the Polaroid Pogo are then summed together to create a
single entry for (gear, change mechanical). This entry is grouped
with the corresponding score from the Garage Door Opener to
produce a vector of observations for (gear, change mechanical)
In the remaining discussion, yijk will refer to one normalized
impact observation (i) within one function–component pair (j)
Fig. 1 FDS methodology overview
Journal of Mechanical Design APRIL 2017, Vol. 139 / 041102-3
within one product (k). The vector y*jrepresents an outcome of
the data preparation stage, containing a normalized set of environ-
mental impact observations ifor a speciﬁc function–component
pairing j. In Fig. 2,y1;ðgear;change mechanicalÞ;Poloroid Pogo ¼1.4010
and y2;ðgear;change mechanicalÞ;Poloroid Pogo ¼3.56 10
y;ðgear;change mechanicalÞ¼[1.43 10
, 2.40 10
The mass normalization builds in the implicit assumption that
in a given problem domain, the nuances of that domain have a
strong effect on the range of masses in potential alternatives. It is
not useful to compare the environmental impact of a car engine to
the environmental impact of a lawnmower engine; the mass of the
car engine will almost always be larger (and therefore lead to a
higher environmental impact) because the car engine has more
mass to move. When generalizing the impact of engines in gen-
eral, it is more useful to examine each component’s contribution
as a percentage of its mass in the system because it abstracts away
some of this domain speciﬁcity.
After normalization, components with the same functional basis
function and component taxonomy type (within each product) are
aggregated into a single function–component pair. Mass-
normalized impact scores with the same function–component des-
ignation are summed as shown in Eq. (2),whereNis the number of
observations for function–component pair j,andyijk is the impact
density of one function–component pair within a given product. In
Fig. 2, the normalized scores of the two “gear” components in the
Polaroid Pogo are summed to produce a single aggregated score for
(gear, change mechanical), in this case 1.4310
Normalizing and aggregating components into single
function–component pairs addresses component taxonomy cate-
gories that distribute their impact across many discrete component
observations within a single product. For example, the environ-
mental impact of a 20 g circuit board is assumed to be roughly
comparable to the environmental impact of two 10 g circuit
boards. Summing impact observations with identical function and
component types creates a raw aggregated impact observation for
each unique function–component pair in a product.
Next, each yijk score is binned such that every unique
function–component pair has a vector of environmental impact
densities gathered from all products in the dataset. Equation (3)
describes this process wherein each product’s summed impact
score yjkKis one element in the vector yj. For example, Fig. 2
shows the creation of a two-element vector of normalized
scores—one from the Polaroid Pogo and one from the Garage
Door Opener—for the (gear, change mechanical) pair. This vector
will contribute to predicting the impact of the “change mechani-
As a result of aggregating the mass-normalized impact scores
in this manner, design guidance that uses this data is based on
the share of a product’s overall environmental impact contributed
by any given function–component pair. A key difference
between using historical data to predict environmental impact
instead of reliability [107,117] is that environmental impact is
sensitive to component mass, while the failure modes and mech-
anisms that drive reliability are more consistent with respect to
mass. As such, while historical reliability methods can ignore
component mass, environmental impact scores must account for
The outcome of the data preparation stage is a set of historical
observations that describe the environmental impact for each
function–component pairing in each product. Using
function–component pairings at this stage rather than grouping
each impact observation directly under functions supports the
hierarchical approach used in the probability prediction stage.
3.2 Step 2: Probability Prediction. The second step of the
method applies a hierarchical Bayesian approach  to generate
probability distributions of environmental impact for each func-
tion. This approach builds on the approach developed by O’Hal-
loran  that uses a hierarchical Bayesian approach to generate
function-level hyperdistributions for reliability prediction. Equa-
tions (4)–(9) in this paper are reproduced from O’Halloran’s work
The inputs to the probability prediction stage are the impact
scores from the data preparation stage and an expected sample
variance of environmental impact for each type of component.
The outputs are sets of Bayesian hyperparameters (mean and
standard deviation) for function-level normal probability distribu-
tions describing the probability density of environmental impact
for each function.
Fig. 2 Data preparation
041102-4 / Vol. 139, APRIL 2017 Transactions of the ASME
A hierarchical Bayesian approach is selected for this method
because of the natural hierarchy that exists between functions and
components. A single function can often be satisﬁed by a variety
of components. As a consequence, each group of children in this
natural hierarchy (groups of components) provides information to
make predictions about its parent (function).
Different components performing the same function can exhibit
nonrandom covariance over a wide range of properties such as
mass, material, and manufacturing process. This leads to natural
divisions in groups of components that perform the same function.
For example, the environmental impact of components in the
function–component pairing (import electrical energy, battery) is
much different than that of components in (import electrical
energy, electric cord). All distributions in this methodology are
assumed to be unimodal and normal, although this is not always
an accurate assumption when these component subgroups exist.
To combat the issue of nonrandom variation amongst different
components that perform the same function, components under
each function are clustered into natural groups. A
function–component pair’s membership in a cluster is determined
using the mean value of its normalized scores.
Clustering is performed using Ward’s linkage  where the
number of clusters is deﬁned to be equal to the quantity of differ-
ent orders of magnitude in the set of component means. Determin-
ing the number of clusters in this way makes the following
assumption: if the environmental impact observations of two com-
ponents differ by an order of magnitude, then, a single normal dis-
tribution created from both is assumed to be a poor approximation
of the population. The clustering step leads to hyperdistributions
where the assumption of unimodality is more appropriate. A sepa-
rate function-level hyperdistribution is created for each compo-
nent cluster, and these cluster distributions can be used to guide
component selection while minimizing environmental impact.
After clustering has been completed, hyperparameters are cal-
culated for each function. A function can have several separate
sets of hyperparameters if the function’s components were
grouped into multiple clusters. First, the sample mean
ple variance r2
jfor each component cluster are calculated as
shown in Eqs. (4) and (5).Nand njare the number of observations
for each component, and yij is a single observation for component
j. The variance for all components r2is assumed to be equal to a
ﬁxed value (In the Case Study section of this article, r2is arbitra-
rily set to 1.5 10
for all components)
Next, the precision-weighted average ^land total precision V1
of each cluster are calculated according to Eqs. (6) and (7).The
weighting factor wjis equal to the number of observations for com-
ponent j.s2is the actual function-level standard deviation, which is
later sampled across a span of evenly spaced values to numerically
calculate the probability of sgiven evidence yto determine pðsjyÞ.
lserves as the function-level mean, further calculation
is needed to determine function-level standard deviation s.
Equation (8) applies Bayes’ theorem with a noninformative uni-
form prior (pðsÞ¼1Þto ﬁnd the posterior distribution pðsjyÞ. The
standard deviation hyperparameter is taken at its expected value:
where its probability density is the highest (Eq. (9)). These equa-
tions are reproduced from O’Halloran’s work , which in turn
sources them from Ref. 
3.3 Step 3: Guidance. The function-level hyperdistributions
developed in Step 2 can provide valuable design guidance, speciﬁ-
cally with respect to making function-to-component design
choices. The approach can also compare alternative functions or
functional models based on the same information. In general,
function-level hyperdistributions with low mean and standard
deviation are preferred. Low mean indicates low environmental
impact, and low standard deviation indicates low variability in
If the goal is to optimize with respect to sustainability, then
each function distribution’s score Scan be calculated by the
inverse of the sum of its standard deviation sand its mean ^
according to Eq. (10). Each of these terms is scaled by a weighting
factor to capture designer priorities about which property to priori-
tize. Ranking importance by low scores prioritizes distributions
with low means and low standard deviations—i.e., function distri-
butions with consistently low environmental impact.
If sustainability is a constraint rather than an optimization vari-
able, then a z-score can be used to rank function distributions
based on the likelihood that they will meet a predeﬁned environ-
mental impact target according to Eq. (11), where lis the mean, r
is the standard deviation, and xis the target value
The raw numbers produced by Eqs. (10) and (11) are not mean-
ingful without context. The Sand zscores are only assessed rela-
tive to one another to produce a rank ordering of priority.
In this section, an focusing on the conceptual design of a
mechanical clock is presented to demonstrate the FDS method’s
mechanics. A Design Repository was populated with 17 common
consumer products such as an orbital sander, a CD player, a vac-
uum cleaner, a camera, and other products. Environmental impact
data were calculated as per Step 1 of the FDS methodology.
An initial conceptual design of a mechanical clock might lead
to the function chain in Fig. 3. This chain may exist as part of a
Fig. 3 Functional model of a manually operated mechanical
Journal of Mechanical Design APRIL 2017, Vol. 139 / 041102-5
larger model that also includes secondary functionality like using
mechanical energy to indicate a signal (e.g., using a clock face) or
protecting sensitive components from undesirable forces (e.g.,
impact) or materials (e.g., water).
The chain in Fig. 3indicates that mechanical energy will be
imported and stored for later use (in this case, moving the clock
hands). Applying the algorithm from the FDS methodology in
Step 2 shown in Eqs. (10) and (11) leads to the function distribu-
tions described by Fig. 4and Table 1. These distributions were
generated with a uniform prior density for the mean and an
assumed sample variance of 1.5 10
for mass normalized ReC-
Guidance is provided by FDS per Step 3 of the methodology in
prioritizing for which subfunctions to perform component selec-
tion and detail design. The scores and priority ranks in Table 1are
given by Eq. (10) using uniform weights of w^
l¼1 and ws¼1.
For each function with multiple clusters, it is assumed that the
best (least impactful) one is selected. This is the case for the
“transfer mechanical energy” function. The outcome suggests that
for the available historical impact data in the consumer product
domain, the functions of “store mechanical energy” and “supply
mechanical energy” have the greatest historical risk of causing
high environmental impact.
One notable drawback of ﬁtting a predictive probability distri-
bution to historical data is that a sufﬁcient number of samples is
needed in order to assume that a normal distribution is a good
approximation of the data. In this case study, this assumption only
holds true for the 53 observations in “transfer mechanical energy.”
The other four functions have ﬁve or fewer observations, so these
results should be viewed only as demonstrative of the method,
and not as evidence about the relative environmental impacts of
Rectifying this drawback requires expanding the design reposi-
tory with additional products that contain observations of func-
tions of interest. Assuming that all functional models are created
at the secondary level (their most expressive level ), there are
420 unique functions (21 verbs and 20 objects). Using the com-
mon heuristic that 30 samples enables the normality assumption
according to the central limit theorem  (in the absence of a
priori data to test for normality), 13,600 samples would be
required for such a database to provide predictive power for any
conceivable functional model. Given an average product size of
approximately 37 functions in the Design Repository, as few as
368 products could enable FDS on a full set on any functional
model. Because some function data must be split into multiple
groups when component data violates assumptions of normality
and unimodality, some functions are separated into multiple clus-
ters. The total number of required products in the database scales
linearly with the number of component clusters per function, as
shown in Eq. (12). For example, if every function’s component
data contained two distinct modes, the database would require 736
products. While there are certainly some assumptions built into
this calculation, it informs the feasibility of a database to support
FDS. Further, it highlights the importance of reliable digital prod-
uct data and data mining techniques to gather a variety of well-
formed computable product data.
Size ¼ðverbsÞðobjectsÞðcomponent clusters per functionÞ(12)
Guidance is further provided with respect to component selec-
tion. For functions that have been solved by a wide variety of
components, it is likely that some of the components tend to make
up a much larger proportion of the product’s total impact than
others. The clustering stage of the algorithm groups together with
function–component pairs have similar orders of magnitude in
their mass-normalized environmental impact scores. Table 2
shows ﬁve clusters for the “transfer mechanical energy” function.
The component groupings shown in Table 2provide a starting
point for selecting components to satisfy the “transfer mechanical
energy” function. Cluster 3 is the best-case cluster, possessing the
smallest means and standard deviations of its components’ impact
observations. Alternatively, if only one type of component is
suited to the task, then, the designer has information about which
function level means and standard deviations to select when com-
paring “transfer mechanical energy” to other functions. Notably,
the small quantities for the parameters in Table 2mean that their
impacts manifest as cumulative effects over many units (i.e., mil-
lions of products produced). Their real value in this context is in
enabling relative comparisons between design alternatives rather
than providing absolute measures of sustainability gain—a much
more challenging issue.
Contextual information and human reasoning skills play an
important role in applying the results of the analysis. Using these
results a designer can isolate “store mechanical energy” and
“supply mechanical energy” as key functions that are likely to
inﬂuence environmental impact. The designer may then focus on
designing an environmentally friendly torsional “spring” compo-
nent to serve the role of storing energy, prioritizing design deci-
sions that affect this component ahead of other functions and
The next highest priority function—“transfer mechanical
energy”—has ﬁve clusters. In this case, selecting a cluster is
straightforward. Cluster 3 possesses not only the most favorable S
score, but also contains components that would transmit intention-
ally created low magnitude mechanical energy in a clock. Clusters
Fig. 4 Probability density of each function in a mechanical
clock functional model
Table 1 Mechanical clock design function prioritization
Function Total observations Number of clusters Score Mean StDev Priority
Change mechanical 5 1 2.40 10
Import mechanical 2 1 1.10 10
Store mechanical 4 1 1.00 10
Supply mechanical 4 1 1.00 10
Transfer mechanical 53 5 1.09 10
041102-6 / Vol. 139, APRIL 2017 Transactions of the ASME
1, 2, and 5 are more appropriate for transferring unintentional or
system-wide mechanical energy, such as using a “housing” or a
“bracket” to absorb impacts or vibrations. Cluster 4’s electric
motor transfers mechanical energy as a side effect of converting
electrical energy into mechanical energy—a behavior that is not
desirable in our human-powered clock. After selecting Cluster 3,
a designer may then select a shaft component as in Fig. 5, fol-
lowed by a knob to import mechanical energy and a gear assembly
to change mechanical energy. This shows that the FDS method
can reclaim an expected clock design from sustainability data that
does not contain data for a clock—that aggregated environmental
impact data from other contexts produces reasonable results in a
new design context.
5 Comparative Model Case Study
The developing world encompasses between 2.1 and 6.6 billion
people by some estimates and contains an estimated purchasing
power of 5 trillion USD [120,121]. 17% of the world’s population
does not have access to electricity  yet in Africa, 60% of the
population had access to mobile phones in 2010 (up from 11% in
1999). In Kenya in 2011, 93% of households had a mobile phone.
In 1999, less than 3% of Kenyan households had access to a
mobile phone [123–125]. Several different options are available
for people to charge mobile phones when they do not have access
to electricity from the grid, including solar charging , wind
charging , paying a merchant to charge the device , sec-
ondary battery charging , thermal electric charging ,
and mechanical charging . As being connected via a mobile
phone, it becomes more important to people in the developing
world [130,131], and mobile phone adoption is expected to
increase . Thus, a robust market exists for phone chargers
that do not require electrical grid power. One such option that we
analyze here is a mechanically powered phone charger design.
This case study demonstrates FDS as an enabler of environmental
impact-based comparison between two alternative functional con-
cepts of a phone charger for the developing world.
The two alternative functional concepts of the mobile phone
charger both use mechanical energy to provide power, but the
way that each concept stores the energy is different. The ﬁrst
(Fig. 6) stores and supplies energy in mechanical form (e.g.,
springs, ﬂywheels, or gravitational potential energy). The second
(Fig. 7) stores and supplies energy in electrical form (e.g., capaci-
tor). We assume that the remaining functions are identical
between systems, enabling a valid comparison of the differences
Table 2 Transfer mechanical energy component clusters
Function–component pairs Function mean Function StDev
Cluster 1 Transfer mechanical_housing 1.05 10
Cluster 2 Transfer mechanical_bracket 4.99 10
Cluster 3 Transfer mechanical_actuator 5.1510
Transfer mechanical_electric plate
Transfer mechanical_electric switch
Transfer mechanical_friction enhancer
Cluster 4 Transfer mechanical_electric motor 2.10 10
Cluster 5 Transfer mechanical_stabilizer 3.38 10
Fig. 5 Clock energy chain component selection
Fig. 6 Mechanical phone charger functional model 1—store as
Fig. 7 Mechanical phone charger functional model 2—store
Journal of Mechanical Design APRIL 2017, Vol. 139 / 041102-7
between concepts. For a designer prioritizing sustainability, these
two functional models form the basis for comparing two concep-
tual alternatives within the context of the overall system. The key
results of an FDS analysis are shown in Tables 3and 4.
The following measures are taken to ensure sufﬁcient data can
be extracted from the limited data set. The set of 17 products in
the data set contains only one observation each for the functions
“export electrical energy” and “convert mechanical energy to
electrical energy.” To mitigate this issue, export electrical energy
is considered as “transfer electrical energy.” Additionally, the
function convert mechanical energy to electrical energy is instead
represented as “convert electrical energy to mechanical energy”
based on the general principle that an electric motor driven in
reverse is an electric generator.
5.1 Component Level Guidance. As part of the FDS method,
historical data for components within each function are clustered. In
selecting between different clusters, the designer receives component-
level feedback (3-B) about the impact of a speciﬁc choice. For exam-
ple, FDS clusters circuit boards and electric wires into different
groups, where the circuit board group has a much higher historical
impact. This suggests that electric wire or other components in its
cluster should be used where possible. This type of guidance was
shown in greater detail in the mechanical clock example.
5.2 Function Level Guidance. Given the similarity of the
models, many of the best and worst case component selections
produce identical importance rankings. With respect to function-
level guidance (3-A), however, comparing scores for storing
mechanical energy (1.00 10
) against those for storing electrical
energy (2.90 10
) suggests that it will be easier to create a low
environmental impact system by storing energy mechanically.
Additionally, a variety of secondary tests can further inform
design decisions when selecting between replacement functions.
Table 3 Mechanical phone charger 1 results
Component cluster Function Priority Score (maximize) Mean StDev Clusters
Best case Convert electrical to mechanical 2 1.08 10
Import mechanical 3 1.10 10
Store mechanical 1 1.00 10
Supply mechanical 1 1.00 10
Transfer electrical 4 1.58 10
User selected Convert electrical to mechanical 2 8.49 10
Import mechanical 4 1.10 10
Store mechanical 3 1.00 10
Supply mechanical 3 1.00 10
Transfer electrical 1 1.55 10
Worst case Convert electrical to mechanical 2 8.49 10
Import mechanical 4 1.10 10
Store mechanical 3 1.00 10
Supply mechanical 3 1.00 10
Transfer electrical 1 1.36 10
Table 4 Mechanical phone charger 2 results
Component cluster Function Priority Score (maximize) Mean StDev Clusters
Best case Convert electrical to mechanical 2 1.08 10
Import mechanical 3 1.10 10
Store electrical 1 2.90 10
Supply electrical 1 2.90 10
Transfer electrical 4 1.58 10
User selected Convert electrical to mechanical 3 1.08 10
Import mechanical 4 1.10 10
Store electrical 2 2.90 10
Supply electrical 2 2.90 10
Transfer electrical 1 1.55 10
Worst case Convert electrical to mechanical 2 8.49 10
Import mechanical 4 1.10 10
Store electrical 3 2.90 10
Supply electrical 3 2.90 10
Transfer electrical 1 1.36 10
These results can be used to facilitate all three types of design guidance shown in Fig. 1—component-level (3-B), function-level (3-A), and functional
model level (3-C). These strategies are summarized in Table 5
Table 5 Design guidance using FDS
Guidance type Strategy
Component-level By inspection, choose components to satisfy function from historical environmental impact scores
Function-level Create a triangle distribution for each function based on the best case, worst case, and most probable component clusters for
given design context. Compare replacement functions by testing for signiﬁcant differences between triangle distributions
Functional model-level Compare two models with Mann Whitney U test on models’ environmental impact scores
041102-8 / Vol. 139, APRIL 2017 Transactions of the ASME
When generating function hyperdistribution parameters, each
functional concept can be analyzed separately according to its best-
case, worst-case, and most likely (human assessed) component clus-
ters. Human input is critical because it injects contextual information
about the model under investigation. For example, one of the clusters
for transferring electrical energy includes an electric wire, an electric
socket, and brushes (as in a brushed motor). A second cluster con-
tains electromagnets and housings. In the context of phone chargers,
the designer is able to specify that electric wires and sockets are
more likely solutions than electromagnets and housings.
These points can then deﬁne a triangular probability density
function (PDF) to support signiﬁcance tests between the impact of
alternative functions . For example, given two triangular
PDFs for the functions “store electrical” versus “store mechani-
cal,” we can test for whether there exists a signiﬁcant difference
in environmental impact of replacing one function with the other.
One simple approach is to uniformly resample points from each
PDF, and then perform a Kolmogorov–Smirnov test to determine
whether the difference between replacement functions is signiﬁ-
cant [134,135]. Performing this test for store electrical versus store
mechanical is trivial in the context of this case study because there
is only one component cluster for each function, but doing so with
100 resamples for each returns a signiﬁcant difference between
functions (p¼1.55 10
). Given a large database with more
samples, this result would be nontrivial to achieve via inspection.
5.3 Model Level Guidance. When comparing two complex
functional models with the same black box function, it may not be
possible to replace functions in a one-to-one manner. For these sit-
uations, a Mann Whitney U test can assess whether the impacts
between models are signiﬁcantly different . For this test, all
alignable (isomorphic) identical functions should be omitted (e.g.,
“import mechanical” in both models). For the two models in this
case study, a Mann Whitney U test does not provide conﬁdence that
the system-level models are signiﬁcantly different (p¼0.33). This
suggests that either (1) a ﬁner grained function-level analysis would
be more appropriate (as is the case here) or (2) there is no signiﬁcant
detectable difference in the models’ predicted environmental impact.
The FDS method is beneﬁcial to product designers wishing to
optimize environmental impacts of a new product still in the con-
ceptual stages of design. Early conceptual designs can be analyzed
for sustainability using functional model representations of the
designs and the FDS method. Existing design repositories are
used to provide clusters of component solutions to functions.
While the preceding case studies use a subset of product data
from the Design Repository, the method is applicable to any set of
product information that is cataloged according to functions, com-
ponents, and environmental impacts. Designers can then choose
between these functions and components to help minimize envi-
ronmental impacts and maximize sustainability of the product
design. Historical data from existing products provide guidance
on the likely outcome of a new product being designed.
While the FDS method assumes that a design repository will be
populated with similar products to the new product under develop-
ment, there may be beneﬁts to populating a design repository with
existing products that are unrelated to the new product. For
instance, populating a design repository with children’s toys while
designing a new product for an automotive application could pro-
vide new component solutions that are sustainable and satisfy
functional requirements. In this case, the potential of ﬁnding a
novel solution increases, while the risk of making an inaccurate
prediction also increases. Care should be exercised to use a dataset
of products that are not so completely unrelated to the new prod-
uct that most component solutions are completely untenable, such
as with attempting to use children’s toys while designing a satel-
lite. While we make no attempt in this work to address the larger
issue of assessing conceptual distance between problems and data-
sets in a sustainability context, a rich database and a metric for
computing pairwise conceptual distance between products would
enable analyses on different database subsets with different inter-
nal similarity cutoffs. The appropriate similarity cutoff between
products in a dataset will likely always depend on the speciﬁc
context and application of the sustainability analysis.
Some potential drawbacks to FDS exist, such as the assumption
that the environmental impact of a component is dominated by its
mass (independent of the quantity of components). An extension
of FDS could investigate mitigating this potential limitation using
techniques such as component-speciﬁc penalty functions that rep-
resent the increased environmental costs associated with produc-
ing and shipping multiple components. Further, material
sustainability does not always vary linearly with mass, as in the
case of lightweight composites. Another extension of FDS may
add additional layers of hierarchy to the model for the most criti-
cal drivers of sustainability. Given sufﬁcient data, such an exten-
sion may model information at the function–component–process
level instead of the function–component level.
Another issue that practitioners should be aware of with FDS is
that abstracting real world observations into the fuzzy front end of
design introduces error into the FDS methodology. High variation
in a single function–component pair may violate the normality
assumption, and thus, potentially damage the validity of FDS pre-
dictions. The component clustering step is intended to mitigate
this risk such that each cluster can be approximated as a normal
distribution. High variation of this type (and that within a single
function–component pair) would also have the general effect of
increasing the uncertainty within that function, increasing its pri-
ority in the FDS results—a generally desirable behavior. A limited
amount of this type of variation would still produce an actionable
ranking of functions. However, systemic variation of this type
within a given dataset would yield predictions of questionable
validity. In this case, other types of clustering, models, or abstrac-
tions may produce better results.
7 Future Work
Several areas of potential future expansion of the FDS exist
including extensions to the decision support provided by FDS,
applying Bayesian priors to speciﬁc important functions, and
applying Bayesian inference to functional or component environ-
mental impact data.
Extensions to the decision support of FDS could include auto-
mated individual function assessment, full functional model com-
parisons, and automated functional model evolution process based
upon sustainability criteria. While FDS currently connects func-
tions to potential component solutions, product designers must
select which component solutions are appropriate for the product.
An automated method of component solution selection may save
designers time and accelerate the new product design process.
Applying Bayesian priors based on the expected mass correspond-
ing to various functions may be useful to skew FDS results toward
the least environmentally impactful component solutions to func-
tional requirements. For instance, if a designer knows that the func-
tion “change mechanical energy” will encapsulate many different
control mechanisms (as in a clock), then, it would be informative to
capture this expectation as a Bayesian prior. Similarly, providing
Bayesian inference to update datasets with information from products
as they are being designed may be useful to help steer development
of other portions of a product or to aid in the development of the
next new product. The method could be further improved by intro-
ducing a method to estimate the data variance of the observed com-
ponents, which in this study was arbitrarily selected.
The FDS method presented in this paper helps to address the
growing demand for sustainable consumer products by providing
Journal of Mechanical Design APRIL 2017, Vol. 139 / 041102-9
product designers with a tool to assess environmental impact of
functional selections in functional models created during the con-
ceptual phase of product design. Automated guidance on choosing
the most sustainable component solutions for functions is pro-
vided by FDS through a process of clustering and hierarchical
Bayesian modeling. Environmental impact data comes from ReC-
iPe scoring found in SimaPRO, and product decomposition infor-
mation comes from the Design Repository. Existing LCA and
environmental impact assessment methods calculate environmen-
tal impact after a product has been developed to the component
level. FDS assesses environmental impact during the conceptual
phase of design by providing insights into which functional solu-
tions historically have the greatest risk of causing high environ-
mental impact via mean and standard deviation statistics. The
conceptual design of a clock was presented to illustrate the
mechanics of FDS, while the case study of phone charger concept
variants demonstrates the breadth of guidance provided by the
method. Although the dataset used in both case studies is insufﬁ-
cient to validate FDS, it is sufﬁcient to demonstrate signiﬁcant
promise of the technique. Given a set of historical data, FDS may
enable a designer to make early functional modeling design deci-
sions speciﬁcally based on environmental impact of the product.
This material was based upon the work supported by the
National Science Foundation under Grant Nos. CMMI 0965746
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