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Application of Axiomatic Design principles for concept
evaluation
Josipa Delaš1, Stanko Škec1,*, and Mario Štorga1
1Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, 10000 Zagreb, Croatia
Abstract. The main objective of this paper is to propose a modified methodology for concept evaluation
by applying Axiomatic Design principles. Several drawbacks were recognised during the literature review
and application of established Axiomatic Design principles that limit its use for concept evaluation. These
drawbacks include the lack of analysis of concepts that violate the Independence Axiom, the application to
concepts that are not generated with Axiomatic Design and inclusion of constraints and requirements in
the evaluation process. The proposed methodology consists of four steps of which the first one is to
analyse the compliance of concepts with a set of functional requirements. Afterwards, to determine the
possible violation of the Independence Axiom, non-diagonal elements need to be examined and
reangularity and semiangularity values calculated for each concept. Finally, concepts are evaluated in
terms of Information Axiom to include requirements, criteria and constraints other than functional
requirements. Applying Information Axiom to all concepts regardless of Independence Axiom violation
provides insight into the complexity of concepts. The proposed methodology was applied to mobility
scooter conceptual design conducted in cooperation with an industrial partner. The partner company
provided input and system constraints at the beginning of the project and guidelines for concept
development. Constraints were taken into consideration by applying the Information Axiom in which
constraints are compared with values measured on prototypes.
1 Introduction
A concept is an approximate description of the
technology, working principles, and form of the product
[1]. In a sufficiently developed concept, its aspects (e.g.
ease of use, aesthetic, functionality etc.) can be
evaluated. Concept evaluation is used to determine
which concepts have the highest potential of becoming a
quality product [2]. The evaluation usually occurs at the
end of the conceptual design phase when developing a
new product or when selecting the best concept variant
among existing ones [3]. The evaluation includes a
comparison of concept variants or a comparison of a
concept variant with the defined ideal solution [3].
Along with several existing methods and tools,
Axiomatic Design (AD) theory can also be applied for
concept evaluation [4]. Application of Axiomatic Design
principles usually defines how close the alternative is to
the ideal one as opposed to directly comparing
alternatives to each other. According to [5], ideal
concepts in Axiomatic Design can satisfy the identified
customer needs and are scarcely affected by sensitivity
to possible alterations in later phases. Concepts’ ideality
is achieved by proper implementation of the
Independence Axiom and, subsequently, the Information
Axiom. Along with other AD principles (e.g. domains,
mapping process, decomposition, hierarchy, and
zigzagging [6]), axioms provide the systematic basis for
solving design problems in various design areas.
One of the main advantages of Axiomatic Design, in
terms of concept evaluation, is the timely detection of
internal technical conflicts in generated concepts through
the Independence Axiom [7]. Other advantages include
the ability to evaluate complete and incomplete
information criteria together [8] and visualise
dependencies between design parameters [9]. Further on,
the application of the Information Axiom can be used to
calculate the designs’ complexity [6].
When developing new concepts using AD principles,
evaluation is an integral part of the design process.
Axiomatic Design principles enable continuous
evaluation of concepts that are being generated and
improved since the conformance to axioms can be
checked at every step. However, evaluation is often
applied at the end of the conceptual design phase to
concepts that were not solely generated using AD
principles. Defining the best concept among them is
time-consuming compared to other concept evaluation
methods, such as concept scoring and Pugh’s method
[7]. This is due to the process of finding an independent
set of functional requirements (FRs) and design
parameters (DPs), which is iterative especially for
complex designs.
This paper provides an analysis of existing principles
for concept evaluation with Axiomatic Design and
suggests certain improvements to evaluation
methodology. These improvements are a part of the
proposed modified concept evaluation methodology
which aims to resolve drawbacks observed in literature
as well as in the implementation of AD principles in
concept evaluation. A case study serves as the validation
of the proposed methodology which, combined with the
conducted literature review, provided the basis for the
discussion and the conclusion.
2 Theoretical background
Design using AD principles begins with defining
functional requirements by reformulating customer
needs (CNs) in a way that completely characterises the
functional needs of a product. This first step enables
comparison of different concepts designed to satisfy the
same customer needs. The process of defining or
selecting a DP that satisfies a certain FR is called the
physical mapping [10]. Definition of DPs on higher
decomposition level as specific solutions should be
avoided, due to the risk of constraining the definitions of
lower-level FRs and DPs. Instead, they can represent
conceptual entities whose definition is extracted from the
corresponding FR to prevent making early choices.
Designs are detailed by decomposing FRs and DPs from
a high level of abstraction to lower levels which contain
detailed modularity elements [9]. The decomposition is
achieved by zigzagging from FRs and DPs on different
levels. From DPs on the higher-level, we define FRs on
the lower level that completely satisfy the highest-level
FR. DPs are then defined for lower-level FRs
accordingly. These relationships between FRs and DPs
are recorded in the design matrix.
The design matrices present the basis for the
concept evaluation in terms of Axiomatic Design
principles. The relationship between a specific FR and a
corresponding DP found in the design matrix is called
coupling. The Independence Axiom says that in an
acceptable design, FRs and DPs are related in such a
way that a specific DP can be adjusted to satisfy its
corresponding FR without affecting other FRs [11].
Designs defined as uncoupled have coupling only in the
main matrix diagonal and completely fulfil the
Independence Axiom. The decoupled design has
couplings on one side of the main matrix diagonal as
well and therefore partially satisfies the Independence
Axiom. Coupled design violates the Independence
Axiom as it has couplings on both sides of the main
matrix diagonal.
Concept evaluation using AD principles is based
on a claim that a good concept completely satisfies the
Independence Axiom. Depending on the number of
couplings and design matrix size, in certain cases, it can
be easy to distinguish which concept satisfies the
Independence Axiom the most (by only looking at the
design matrices). In other cases, independence is
measured by calculating reangularity (R) and
semiangularity (S). Reangularity relates the angles
between the axes of the design parameters, while
semiangularity measures the magnitude of the diagonal
elements [12]:
(1)
(2)
In these equations, A refers to the value inside the design
matrix in the row defined with the first index and the
column defined with the second index.
R value decreases as the degree of coupling increases.
For R=S=1, the design is completely uncoupled, and for
R=S<1 the design is decoupled. This calculation
presents the basis for the coupling analysis which
determines whether the Independence Axiom has been
satisfied, and is implemented as the first part of the
evaluation using AD principles. Procedure found in [11]
is the most common for conceptualisation and analysis
of the generated concepts with Axiomatic Design. It
states that if multiple designs satisfy the Independence
Axiom, the best among them is chosen by utilising the
Information Axiom [Fig. 1]. The Information Axiom
states that the information content in a design should be
minimised. In other words, the design that results in the
highest probability of meeting design specifications is
the best one [11]. The highest probability of success
indicates the lowest amount of information needed to
manufacture (produce) the design [10]. However, the
Independence Axiom is often satisfied, and thereby the
Information Axiom is not utilised as a part of the
evaluation procedure [8].
Fig. 1. Flowchart of the application of Axiomatic Design [11]
Several studies of evaluation with Axiomatic Design
principles have been conducted ([13]–[15]) based on the
aforementioned procedure. For example, AD principles
were used to analyse and improve designs of emergency
core cooling systems by complying to the Independence
Axiom and, afterwards, the best among them was chosen
with the Information Axiom [13]. Further, evaluation of
the suspension systems was conducted by applying the
axioms and analysing coupling to improve ride comfort
[14]. In a case study that evaluated existing friction
devices [15], the Information Axiom is applied even
though none of the designs satisfies the Independence
Axiom. In some studies, the evaluation was conducted as
part of the application of Axiomatic Design principles
for product development [16][17].
Based on these and other formerly conducted studies
three drawbacks of concept evaluation with Axiomatic
Design were recognised. To start with, problems occur
when concepts that weren’t generated with AD
principles are being evaluated since the evaluation
procedure itself doesn’t alternate the relationships
between defined FRs and DPs. To be more precise,
procedure for evaluation is not defined if concepts that
weren’t generated using AD principles violate the
Independence Axiom. However, concepts that are
chosen for detailing can be subsequently modified by
taking into consideration recognised couplings.
Secondly, there is a lack of guidelines for
incorporating different types of requirements and criteria
in concept evaluation. For instance, non-technical
requirements are defined as constraints and, as such, are
not part of the design matrix (and, consequently, not part
of the evaluation) [7]. This exclusion of non-technical
requirements can result in unaesthetic and costly
products that fail to satisfy customer needs [11].
Thirdly, decomposition can include non-essential
functions, which aim to increase attractive qualities of a
product [18]. For instance, primary functions of a mobile
phone are to send and receive phone calls, provide
access to the Internet, take photos etc., but adding
additional features to the camera can make the mobile
phone more desirable. This approach leads to concepts
that have a different set of FRs, even though they satisfy
the same customer needs (CNs). When using AD
principles for evaluation often certain concepts don’t
fulfil all identified FRs. As such, concepts have design
matrices of various sizes what makes a comparison of
concepts difficult. In other words, it is hard to achieve
the ranking of alternatives since AD principles usually
compare concepts to the ideal one.
Building on these premises, the following research
methodology was used to structure and conduct this
study.
3 Research methodology
The literature review was conducted during the
preliminary research phase to analyse existing evaluation
procedures based on Axiomatic Design principles.
Initial concept evaluation was done based on [11],
which, along with the analysis of existing case studies,
revealed its drawbacks. This procedure suggests
applying Axiomatic Design in the same way for different
purposes - concept development, analysis of existing
designs and design improvement [11]. As such, it seems
to be too generic and does not provide sufficient
guidelines for the concept evaluation itself. For instance,
in a case study of evaluating in-pipe robot design [16],
dependencies of FRs and DPs were observed only at
their own level of decomposition. This type of
dependency analysis could lead to unrecognised
couplings that, consequently, cause design issues in later
stages of the design process. Other examples found in
literature usually define a different design matrix for
each concept. In such cases, concepts aren’t compared to
one another but only tested to see if and to what extent
do they satisfy the Independence Axiom.
To address issues identified during the initial
concept evaluation, the proposed methodology suggests
creating a single design matrix equal for all developed
concepts that includes their FRs and corresponding DPs.
Mutual comparison of concepts can provide further
insights into their strengths and weaknesses.
Decomposition of a single concept rarely shows which
FRs are missing, whereas having multiple concepts
defined with the same FRs can indicate which FRs
haven’t been fulfilled by different concepts. Therefore,
the analysis of fulfilment of FRs is set as a first step of
the concept evaluation with the modified procedure. The
second step, the analysis of non-diagonal elements, is
added for similar reasons. An indication of mutual
couplings can also help the designer to recognise
reoccurrence of specific design problems, and imply
potential solutions through comparison with other
matrices. Examples found in the literature mostly aim at
an analysis of concepts that are being generated by
considering the Independence Axiom. Concepts that
were not generated with AD principles often cannot be
altered in such way, and therefore this methodology
proposes an additional application of the Information
Axiom to better inform a designer before deciding on a
potential concept that should be further developed.
In order to illustrate the application of the modified
methodology for concept evaluation, it was applied to
mobility scooter conceptual design conducted in
cooperation with an industrial partner.
4 Proposed modified methodology for
concept evaluation
To tackle the previously mentioned problems in Sections
2 and 3, this paper proposes the modified concept
evaluation methodology [Fig. 2]. The proposed
procedure is primarily intended for evaluation of
concepts that weren’t generated with AD principles. In
such cases, FRs are set after working principles of a
product have already been defined. Such concepts cannot
be changed to satisfy the Independence Axiom since
alterations aren’t a part of the evaluation process.
Unlike the procedure provided in [Fig. 1] where
evaluation begins with the Independence Axiom, in
modified methodology presented in this paper evaluation
starts with an analysis of the number of fulfilled FRs.
Therefore, evaluation applying Independence Axiom is
conducted when there isn’t a single concept that satisfies
the set of FRs. This second part of the evaluation starts
with an analysis of non-diagonal elements in the design
matrix. Non-diagonal elements, i.e. couplings, found in
one concept can perhaps be resolved by taking a partial
solution from another concept which lacks that non-
diagonal element.
Fig. 2. Modified flowchart of the application of Axiomatic
Design
This step is followed by the coupling analysis of the
created design matrices. Design matrices of the highest
level cannot be solely used for evaluation because they
aren’t related to concepts, but present general
decomposition of the design problem. Therefore, lower-
level design matrices are integrated into upper-level
matrices until the single final matrix for all developed
concepts is defined. If a concept does not fulfil a certain
FR or lacks a specific DP, corresponding row or column
needs to be removed from the design matrix creating a
smaller matrix for that concept. Due to possible design
complexity, obtained design matrices can be large,
which is why reangularity and semiangularity should be
calculated to determine the coupling measure for specific
concepts. This calculation enables direct comparison of
concepts based on satisfaction of the Independence
Axiom. However, calculation of semiangularity and
reangularity metrics often requires a substantial amount
of data and is, therefore, more appropriate for later
stages of the design process. This data could be obtained
from computer simulations (e.g. FEM and kinematic
analysis) or analysis of produced prototypes.
If a final decision cannot be made based on these
steps, the Information Axiom is applied, because, unlike
the Independence Axiom, it can take into consideration
other requirements that have been set on the product.
Various constraints can be used to calculate the
information content and help choose the best concept.
Values of these constraints can be used as the design
range (DR), and the ability of the system to fulfil these
values is called the system range (SR). The probability
of success or, in other words, the information content, is
the intersection between the design range and system
range. The concept with the smallest information content
is the best one according to the Information Axiom.
5 Application of proposed methodology
Within the scope of a student product development
project course, new mobility scooter concepts were
developed. Mobility scooters are electrically powered
vehicles designed specifically for the people with limited
mobility. The aim of the student development project
was to develop a mobility scooter which can be folded
and adjusted according to the user needs while
considering its aesthetics and ergonomics constraints. At
the end of the project, prototypes of developed concepts
were produced. This enabled measurement of the
fulfilment of the desired requirements set at the
beginning of the project. Proposed evaluation
methodology was afterwards applied to developed
concepts in order to illustrate its application on the
student project.
5.1 Defining requirements
Evaluation criteria for the case study were derived from
customer needs, constraints and non-functional
requirements. Customer needs were defined from
information gathered through market research and
interviews with customers. Most important CNs include
the need for a mobility scooter to be lightweight enough
for a single person to lift and carry, the possibility of
transporting in a car trunk and airport luggage, and the
ability to adjust the vehicle so that it suits various
people, regardless of their height and mobility. In
addition to this, non-functional requirements were
defined, because they contain features essential to the
customer which couldn’t be incorporated into functional
requirements (e.g. easy to clean). Industrial partner
provided input constraints which present target values
for parameters measured on produced prototypes (e.g.
mass needs to be under 10kg). Legal obligations are
translated into system constraints which must be met
(e.g. max speed of 6 km/h).
Functional requirements on the highest level are
defined from customer needs regardless of the partial
solutions provided in concepts. Satisfying the FRs set on
the highest level is a priority because otherwise the basic
product functions aren’t fulfilled. The defined set of FRs
on the highest level is then decomposed to determine
FRs on lower levels.
5.2 Generating design matrices
Design parameters of each level are obtained through the
standard process of zigzagging as explained in Section 2.
This zigzagging procedure results in initial design
matrices that define relationships between FRs and DPs
of each level separately and cannot be used for concept
evaluation. The process of determining initial design
matrices is iterative to ensure that FRs defined by
decomposition are mutually exclusive and collectively
exhaustive (MECE) [19]. In a collectively exhaustive
decomposition, higher-level FR is completely defined
with corresponding lower-level FRs. Mutually exclusive
decomposition results in lower-levels FRs that do not
overlap. As such, this process describes the minimum set
of FRs that entirely characterises the design objective
[4]. However, developed concepts can contain additional
functional requirements that can result in deviations
from the ideal design. Without introducing additional
FRs, it wouldn’t be possible to conduct the detailed
evaluation.
Design matrices are filled with symbols X in case of
an existing relationship between specific FR and a
corresponding DP, and 0, when there is no relationship
between FR and DP. In other words, the designer
determines which FRs and DPs are coupled. The
relationship can be defined with a design equation to
determine the exact value, but it usually assumes the
value of 1 if an FR and a DP are completely coupled.
Design matrix of the highest level is upper triangular
(decoupled) [Table 1]. Design matrices on lower levels
need to be uncoupled or also upper triangular to satisfy
the Independence Axiom. In other words, coupling that
appeared on the highest level of decomposition must be
reflected on lower levels as well. Subsequently, the
coupling is affected by changing the order of fulfilling
functional requirements. The order of rows in the design
matrices indicates the order of fulfilling FRs.
Mobility scooter design was decomposed on 3 levels,
and the total of 30 FRs and DPs was defined. For
conciseness, only 3 out of 9 initial design matrices will
be shown and explained.
Table 1. Decomposition on the highest level
INDEX
FR
DP
1
Ensure load capacity
Rigidity of basic
structure
2
Allow movement of
parts
Movable subsystem
3
Ensure the flow of
energy required for
movement
System for movement
4
Enable operating of the
vehicle
Operating components
(3)
By further decomposition of the FR1 Ensure load
capacity, another upper triangular matrix was generated
[Table 2]. This design matrix for FR1 includes, in
addition to others, the symbol x, which means that the
FR and DP aren’t coupled at the moment, but could
become in later stages of the design process. We can
define that X>>x, and the relationship containing x as
currently uncoupled, but there is no guarantee of
satisfying the Independence Axiom in case the concept is
changed. For instance, DP12 Dampening front fork can
affect the FR11 Ensure construction rigidity depending
on the design.
Table 2. Decomposition of FR1 Ensure load capacity
INDEX
FR
DP
11
Ensure construction
rigidity
Shock-absorbent frame
12
Reduce the shock
impact on the front part
of the construction
Dampening front fork
13
User positioning
Adjustable seat
14
Secure user against
fallout
Safety supports
15
Enable transportation
of additional cargo
Removable storage
space
(4)
Decomposition of the FR14 Secure user against
fallout resulted in decoupled matrix [Table 3]. The DPs
on this level are parts of the DP13 Adjustable seat what
leads to couplings that potentially have to be resolved.
Yet, FRs on the observed level are independent, and the
couplings can be shown in the final matrix.
Table 3. Decomposition of FR14 Secure user against
fallout
INDEX
FR
DP
141
Support legs
Stable leg support
142
Support arms
Firm seat armrests
143
Support back
Firm seat backrest
(5)
The FR1 Ensure load capacity was decomposed
with two matrices shown above. Decomposition is the
same for each scooter which makes them comparable.
5.3 Evaluation based on achieved matrices
According to the first evaluation step, none of the
mobility scooter concepts entirely fulfils the defined set
of FRs. Moreover, 3 out of 4 concepts do not allow the
transportation of additional cargo (FR15). Other than this
FR, concepts only partially fulfil the FR21 Enable
folding, meaning that the mobility scooter concepts can
be folded but not by satisfying the entire set of FRs on
the lower level. This is due to the implementation of FRs
that are specific to certain concepts. This problem can
occur when evaluating concepts which were not
generated using AD principles since the same higher-
level FR can be achieved through a different set of
lower-level FRs. In such cases, not fulfilling every FR
defined on a lower level doesn’t imply that a higher-
level FR hasn’t been satisfied. Fulfilment of FRs for
each concept is shown in a tabular view, to make
analysis easier [Table 4]. If a particular concept fulfils an
FR, the table contains an X, otherwise it contains 0.
Concept 4 fulfils more FRs in comparison to others
and, therefore, its final design matrix contains the
highest number of FRs and DPs. However, matrix size
doesn't necessarily imply that concept represents a better
solution. For instance, every scooter can fulfil FR21
Enable folding and, multiple FRs on its lower
decomposition level present a complicated folding
procedure for the user. In other words, additional FRs
can be perceived as redundant. Since Concept 2 can
fulfil all the higher-level FRs (Enable transportation of
additional cargo, Enable folding and Adjust vehicle to
the user), it is considered as a better concept, even
though concept 4 fulfils all lower-level FRs for adjusting
the vehicle to the user. Concepts 1 and 3 were identified
as weaker solutions based on this first step of evaluation.
Table 4. Evaluation based on fulfilment of FRs that haven’t
been satisfied in all concepts
Functional requirements (FR)
Concept 1
Concept 2
Concept 3
Concept 4
Enable transportation of
additional cargo (FR15)
0
X
0
0
Enable folding (FR21)
Alter frame
length (FR211)
X
0
0
0
Rotate seat
carrier (FR212)
X
0
X
X
Enable tiller
folding
(FR213)
X
0
0
X
Enable frame
folding
(FR214)
0
X
X
X
Adjust vehicle to the user
(FR23)
Adjust tiller
height (FR231)
0
X
0
X
Adjust tiller
angle (FR232)
0
0
0
X
Adjust seat
height (FR233)
0
X
0
X
Enable seat
rotation
(FR234)
0
X
0
X
The next step in evaluation is the analysis of non-
diagonal elements in the final matrices of each concept.
Table 5 shows how many non-diagonal elements are
shared between different concept solutions. This
comparison may indicate which independencies
designers most often fail to satisfy. In addition, it can
support designers in their search for partial solutions in
other concepts that managed to satisfy Independence
Axiom.
Table 5. Number of common and total number of non-diagonal
elements in concepts
Concept
1
Concept
2
Concept
3
Concept
4
Concept
1
20
21
22
Concept
2
20
21
29
Concept
3
21
21
22
Concept
4
22
29
22
Total no.
of non-
diagonal
elements
24
36
22
40
The total number of non-diagonal elements
represents how many couplings appear in the final
design matrix of each concept. Concept 4 has the highest
total number of non-diagonal elements. This is partially
due to the many FRs defined for folding of the scooter
and adjusting it to the user. Concept 3 has the lowest
number of FRs for folding and adjusting the vehicle, and
the smallest number of non-diagonal elements.
Comparison of the total number of non-diagonal
elements and the common number of elements can
sometimes indicate a common issue among different
designs. In this case study, there are 19 non-diagonal
elements common to all four concepts. Due to such a
high number of non-diagonal elements, it can be
concluded that maintaining the independence of FR21
Enable folding and FR23 Adjust vehicle to the user was a
difficult task for designers. Beside these two FRs, by
analysing the location of non-diagonal elements, partial
solutions for couplings can be found and applied to other
concepts. For instance, DP311 Li-ion battery is dependent
on the FR46 Usable in darkness. This coupling can be
resolved by providing an independent power source for
the light that every scooter must have due to legal
obligations.
Afterwards, concept comparison was done by
calculating reangularity and semiangularity with
equations given in Section 2 of this paper. At this stage
of the design process, there was not enough information
to determine the exact coupling values. Therefore,
design matrices were populated with values based on
designers’ perception of coupling severity in the
following way: X equals 1, x equals 0,1 due to the
condition X>>x, and 0 remained 0. Calculated values are
shown in [Table 6].
Table 6. Concept comparison by reangularity and
semiangularity values
Reangularity
Semiangularity
Concept 1
0,3266
0,001889
Concept 2
0,3952
0,000564
Concept 3
0,3462
0,003646
Concept 4
0,2933
0,000344
These values imply that none of the concepts satisfies
the Independence Axiom. To our knowledge, literature
doesn’t provide guidelines whether the concept for
further development should be the one with the highest
value of reangularity (R=1 for uncoupled designs) or the
one with the smallest difference between reangularity
and semiangularity (R=S for a decoupled design).
Concept 2 and Concept 4 are closer to satisfying the
desired design matrix than concepts 1 and 3, but are still
far away from fulfilling the Independence Axiom.
Therefore, a final decision wasn’t made and, the
Information Axiom had to be applied for further
evaluation.
In this final step, input constraints provided by the
industrial partner were compared to the values measured
on the prototypes [Table 7]. In addition to this, folding
time was added as an important aspect for the users. The
information content is calculated with equations
provided in [10] where the SR is achieved value on a
concept, and the CR is input constraint value.
Information content is defined as zero if the achieved
value is smaller or the same as required.
Table 7. Concept comparison based on Information Axiom
Criteria
Constraint
value
Concept 1
Concept 2
Concept 3
Concept 4
Mass [kg]
≤10
26,1
23,1
26,3
24,5
Folding
time [s]
min=
13
20
13
27
40
Length
[mm]
≤900
950
810
950
780
Height
[mm]
≤700
770
598
700
650
Width [mm]
≤400
620
670
550
870
Total
information
content
-
2,853
1,952
2,987
4,035
Since the ideal information content is 0, it can be
concluded that Concept 2 is the best solution according
to the Information Axiom. It has the smallest mass and
the least folding time which are two aspects of the
utmost importance for the user. On the other hand,
Concept 4 which fulfils more FRs has proven to be more
complicated compared to other scooters and particularly,
Concept 2.
This application represents four steps explained in
the proposed modified methodology for the concept
evaluation with AD principles. Each step provided
different insights into the strengths and weaknesses of
the analysed concepts. The application also showed that
results are inconsistent by using different AD evaluation
criteria. Using the Independence Axiom, Concept 4 is
perceived as the best solution due to the least amount of
changes that are required for satisfaction and fulfilment
of FRs. However, other steps in the evaluation, like
calculation of reangularity and semiangularity values,
non-diagonal elements and the Information Axiom,
raised serious concerns about Concept 4 due to
additional FRs. These results may be a consequence of
working with concepts that weren’t generated using AD
principles since it can be hard to retroactively achieve
the minimum set of FRs like AD principles demand. If
the evaluation was based solely on the Independence
Axiom, as is usually the case, Concept 4 could’ve been
chosen as the best one. This application shows that a
more extensive validation of various concept evaluation
steps should be taken in further studies to embrace
different criteria and aspects of the proposed solutions.
6 Discussion
Application of AD principles to concept evaluation relies
more on technical knowledge, compared to other
methods used for evaluation, since the designer
reformulates the needs perceived by the customer into
the functional requirements [12]. Therefore, this results
in an evaluation process based on the fulfilment and
independence of functional requirements and may reduce
biased personal judgments [7]. However, Axiomatic
Design doesn’t provide a way to check whether the CNs
have been adequately reformulated to FRs. In addition,
there is still no detailed procedure for defining FRs.
Other than defining FRs, it is crucial to specify non-
technical requirements and constraints properly. Until
now, these other types of information usually haven’t
been incorporated into the evaluation process.
In addition, literature doesn’t acknowledge the
difference of evaluating concepts generated with or
without AD principles. Concepts that weren’t generated
with AD principles aren’t improved to satisfy the
Independence Axiom within the scope of the evaluation.
However, conducted evaluation suggests improvements
which can be applied in the later stages of the design
process.
The proposed methodology suggests an
implementation of constraints for the design range as a
part of the Information Axiom. The implementation can
be hard to conduct if there is not enough information
about target values for concepts. However, implemented
constraints can show to what extent the customer needs
are satisfied. Examples found in literature mostly
compared a single concept to its ideal solution [10]-[15].
Previously, concepts were often not compared to one
another due to their different decompositions on lower
levels. The proposed methodology aims to avoid this
problem by generating a general common matrix for
each concept that includes FRs found in all of them. If
the concepts aren’t comparable in such way, evaluation
cannot be done based on fulfilment of FRs and number
of total and shared non-diagonal elements. On the other
hand, if the evaluation based on fulfilment of FRs isn’t
conducted, an incomplete solution could be chosen.
One of the advantages of applying the proposed
methodology is the ability to combine different solutions
from various concepts to solve certain couplings.
Analysis of non-diagonal elements provides insight
about couplings that are the most difficult for the
designer to resolve. It also enables easy comparison of
different solutions which can be beneficial when
combining different concepts. These first two steps, the
fulfilment of FRs and analysis of non-diagonal elements,
are suitable for application in the earlier phases of
conceptualisation. In addition, they are easy to
implement.
In this case study, application of Independence
Axiom in terms of calculating coupling measures
(reangularity and semiangularity) hasn’t provided
sufficient information for concept selection. This may be
due to the small differences between the obtained
concept values and inadequate definition of the coupling
values. Therefore, the Information Axiom was applied to
the concepts that didn’t satisfy the Independence Axiom,
even though Axiomatic Design theory advises against it.
Unlike the first two steps, calculating the coupling
measures and the Information Axiom usually requires
more data and is often more appropriate to implement in
later stages of the design process. More case studies will
be conducted to provide additional validation and testing
of the proposed methodology.
7 Conclusion
The modified methodology proposed in this paper
aims to solve reoccurring issues found in the literature
about various aspects of concept evaluation using AD
principles. The underlying logic of the proposed
methodology suggests a definition of the common
matrices for developed concepts and includes four
subsequent steps to enable proper concept evaluation.
Each of the evaluation steps showed its advantages and
potential issues as pointed out in the previous section.
The validation of the proposed methodology was
carried out by analysing concepts generated during
mobile scooter development. After initial matrices were
defined, couplings were affected by reformulating FRs
and DPs and changing their order in the design matrix.
The proposed evaluation methodology showed that none
of the concepts fulfils the whole set of FRs and the
Independence Axiom. Therefore, the evaluation at this
stage was inconclusive, indicating the need for the
Information Axiom.
Further research should examine the problem of
carrying out different FRs throughout the different
phases of the product lifecycle. For instance, the user
either adjusts the mobility scooter or unfolds/folds it, but
never simultaneously. Currently, such cases are usually
presented as coupling even though it is preferable to
have the same product fulfil different functions at
different times. Coupling measures, R and S, should be
also further studied to ensure the proper analysis and
interpretation of obtained values. Although there are
many ways to apply the Information Axiom, further
research should be conducted to enable implementation
of different types of requirements and criteria.
The case project was a part of the Erasmus+ Strategic
Partnership programme and funded with support from the
European Commission. This communication reflects the views
of the authors, and the Commission cannot be held responsible
for any use which may be made of the information contained
therein.
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