J. Cent. South Univ. Technol. (2010) 17: 244−256
DOI: 10.1007/s11771−010−0038−y
Material selection of polymeric composite automotive bumper beam using
analytical hierarchy process
A. HAMBALI1, S. M. SAPUAN1, N. ISMAIL1, Y. NUKMAN2
1. Department of Mechanical and Manufacturing Engineering, Universiti Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia;
2. Department of Engineering Design and Manufacture, University of Malaya,
50603 Kuala Lumpur, Malaysia
© Central South University Press and Springer-Verlag Berlin Heidelberg 2010
Abstract: Selection of materials, as an area of design research, has been under considerable interest over the years. Materials
selection is one of the most important activities in the product development process. Inappropriate decision of materials can cause the
product to be reproduced or remanufactured. To avoid this circumstance, one of the useful tools that can be employed in determining
the most appropriate material is analytical hierarchy process (AHP). To illustrate the application of AHP, six different types of
composite materials were considered. The most appropriate one for suitability of use in manufacturing automotive bumper beam was
determined by considering eight main selection factors and 12 sub-factors. The AHP analysis reveals that the glass fibre epoxy is the
most appropriate material because it has the highest value (25.7%, mass fraction) compared with other materials. The final material is
obtained by performing six different scenarios of the sensitivity analysis. It is proved that glass fibre epoxy is the most optimum
decision.
Key words: composite; polymer matrix; bumper beam; analytical hierarchy process
1 Introduction
The importance of materials selection in the product
development process has been well recognized. To
develop a systematic method for selecting the best
material is not an easy task because the best material is
determined by a number of factors that influence the
selection process. There are two main reasons why
materials selection is required: firstly, to design an
existing product for better performance, lower cost,
increasing reliability and reduced weight and secondly,
to select a material for a new product [1−2]. Materials
selection is a main product design consideration because
product’s overall performance is mainly affected and
determined by materials selection process [3].
There are very limited reports on materials selection
for the composite automotive bumper beam. However,
several papers discussed the selection of a material for
automotive bumper beam. For example, SAPUAN et al
[4] employed weighted objective method for the
selection of materials for the bumper system.
HOSSEINZADEH et al [5] studied several composite
materials and conventional materials for automotive
bumper beam and characterized them based on the cost,
production and weight by impact modelling using
LS-DYNA ANSYS 5.7. It is shown that sheet moulding
compound (SMC) is best material for bumper beam.
SUDDIN et al [6] described the development of the
knowledge based system (KBS) for materials selection in
bumper beam design. The KBS is an expert system
approach to selecting the most suitable material by
defining constraint values into the system.
However, the above-mentioned methods do not
provide easy ways to assist material engineers to
determine the most appropriate material. One of the
useful tools that provide a sequence way of materials
selection process is analytical hierarchy process (AHP).
AHP is a basic approach to decision making, which is
designed to cope with both the rational and the intuitive
to select the best from a number of alternatives evaluated
with respect to several criteria [7]. Decision support
system (DSS) resource defines AHP as an approach to
decision making that involves structuring multiple choice
criteria into a hierarchy, assessing the relative importance
of these criteria, comparing alternatives for each criterion,
and determining an overall ranking of the alternatives
[8].
Generally, implementing AHP is based on
experience and knowledge of the experts or users to
determine the factors affecting the decision process
[9−10]. According to Refs.[11−12], AHP is an intuitive
Received date: 2009−03−27; Accepted date: 2009−09−04
Corresponding author: A. HAMBALI, Doctoral candidate; Tel: +60−3−89466318; Fax: +60−3−86567122; E-mail: hambali@utem.edu.my
J. Cent. South Univ. Technol. (2010) 17: 244−256
method for formulating and analyzing decisions. The
advantages of using AHP include achieving higher
quality product and shorter product development process.
AHP helps to capture both subjective and objective
evaluation measures, thus providing a useful mechanism
for checking the consistency of the evaluation measures
and alternatives suggested by the team, and reducing bias
in decision-making. AHP allows organizations to
minimize common problems of decision-making process,
such as lack of focus, planning, participation or
ownership, which ultimately are costly distractions that
can prevent teams from making the right choice [8].
AHP has been widely used to solve multi-criteria
decision making in both academic research and in
industrial practice. It has been implemented in almost all
the applications related to decision-making and currently
predominantly used in the theme of selection and
evaluation especially in the area of engineering, personal
and social categories [13]. Although, AHP has been
widely used in solving decision making problems, it is
still very limited in making right decision in field of
materials selection process. HO [9] reviewed
international journals related to application of AHP from
1997 to 2006 and found that AHP can be implemented in
a wide variety of fields. However, there are a few studies
on the application of AHP related to the materials
selection for the composite automotive components.
Only one paper discussed the use of AHP in material
selection process [10].
The literature reviews indicate the above
researchers have not addressed the use of AHP to
determine the most appropriate material for the
composite automotive bumper beam. The aim of this
work is to assist designers to evaluate and determine the
most optimum material by implementing AHP.
2 Selection of materials at conceptual design
stage
The proposed framework for the selection materials
process during concept selection at the conceptual design
245
stage is shown in Fig.1. The selection method helps the
designers to determine the best material in concept
selection at the conceptual design stage. A fundamental
issue in polymeric composite automotive components
particularly related to the selection of materials is a main
focus. Thus, this work is only addressed in terms of
selecting the best material in the context of concurrent
engineering environment. Then, AHP, as a decision
support tool, is linked to the framework in order to
determine the most appropriate material for the
automotive components. After the best material is
determined or called material selected, various scenarios
of the sensitivity analysis are performed to test the
stability of the priority ranking and to increase the
confidence in the choice of material in order to carry out
the final decision.
3 Selection of materials for polymeric
composite bumper beam
The use of composite materials has been rapidly
increased in automotive industry. Automotive industry
faces greater market pressure to develop high quality
products more quickly at lower cost. To determine the
right material is a crucial decision in the automotive
industry. In recent years, the use of composites has been
greatly focused on automotive components such as
automotive bumper system. The bumper system is
generally recognized as being composed of four basic
components of bumper fascia, energy absorber, bumper
beam and bumper stay, as depicted in Fig.2. One of the
most important components of bumper system is the
bumper beam. It plays an important role of absorbing the
bulk of energy and provides protection to the rest of the
vehicle [14−15]. Therefore, it is important to determine
the right material for the automotive bumper beam.
3.1 Various polymeric-based composite automotive
bumper beams
Composite bumper beams become more common
due to the increased number of low volume vehicles and
Fig.1 Framework of selection process at conceptual stage in concurrent engineering environment
246
Fig.2 Diagram of bumper systems [16]
greater emphasis toward weight reduction. As the
function of a bumper beam is to absorb kinetic energy
during a collision, the use of composite materials to
replace steel or aluminium was reported in the literature.
There are many attempts and successful application of
polymeric-based composite in automotive bumper beam.
MOHAN [17] discussed the use of structural reinforced
injection moulding (SRIM) composite in an automobile
bumper beam. The material used was glass fibre
reinforced polypropylene. The tooling cost was lower
than that of metal processes because of the low moulding
pressure used. CLARK et al [18] explained their
extensive work on bumper beams using glass fibre
reinforced plastics to study the stress contour in the
component. Three-dimensional models were developed
and the analysis was performed using ABAQUS software.
The material selected was 40% (mass fraction) glass
fibre reinforced polypropylene. CHEON et al [19]
developed a composite bumper beam for a passenger car
using glass fibre epoxy composite materials with the
exception of the elbow section. The elbow section was
made of carbon fibre epoxy composite materials. From
the static bending test of the prototype composite bumper,
it was found that the mass of the composite bumper
beam was 30% lighter than that of the steel bumper beam
without sacrificing the static bending strength.
KUMAR and JOHNSTON [20] studied and
compared the performance of C- and I-section of bumper
beam using a variety of compression-moldables, and the
material employed was glass-mat thermoplastic (GMT)
composite. GILLIARD et al [21] developed the I-section
beam with 40% (mass fraction) chopped fibre glass GMT.
They found that the I-section bumper design has
improved static load and dynamic impact performance
by using lower cost mineral filled/chopped fibre glass
GMT. According to Ref.[22], front and rear bumper
beams of some general motors models are generally
made of 60% (mass fraction) glass fibre vinylester SMC,
reinforced with a newly developed chopped and
continuous strand glass fibre, giving strength in all
directions. MOINAR [23] employed a composite
J. Cent. South Univ. Technol. (2010) 17: 244−256
material, namely glass fibre embedded with a
thermosetting isopolyester resin matrix, to produce the
composite bumper beam. KELMAN and NELSON [24]
used composite materials consisting of fibre glass
perform and two-component urethane based resin polyol
and isocyanate to manufacture the composite bumper
beam.
HOSSEINZADEH et al [5] investigated and
compared various polymeric-based composites such as
SMC and GMT, and conventional materials such as steel
and aluminium in terms of deflection, stress distribution
and kinetic energy transfer when subjected to lowvelocity impacts for automotive bumper beam. The
results show that SMC composite is the best material for
automotive bumper beam due to good impact behaviour,
easier production and lower cost. ROBIAH et al [25]
investigated the best condition of compounding
parameter and mechanical properties of discontinuous
carbon fibre reinforced polypropylene for the application
of car bumper beam. It was found that, the additional
10% (mass fraction) of chopped carbon fibre gives a
significant increase in the tensile strength properties.
ANONYMOUS [26] used polyester fiber weave
reinforced GMT materials for bumper beams due to its
low stiffness and excellent energy absorption properties.
3.2 Factors consideration in materials selection for
polymeric composite automotive bumper beam
The selection of the best material for the polymeric
composite automotive bumper beam depends upon the
following factors.
3.2.1 Energy absorption (EA)
The most important consideration in selecting the
most appropriate material for polymeric composite
automotive bumper beam is the ability of the material to
absorb enough kinetic energy. Bumper beam is a main
structure for absorbing the energy of collisions. The
property of material that shows the ability of the material
to absorb energy is impact toughness (ITH) [27]. ITH is
defined as a measure of the ability of material to absorb
energy during impact.
3.2.2 Performance (PR)
Performance is defined as the ability of a bumper
beam to stay intact or rigid at high-speed impact and
prevent damage to the bodywork in minor impacts. Two
factors of material properties should be considered,
namely, flexural strength (FS) and flexural modulus
(FM). FS is defined as the ability of materials to
withstand failure due to bending. FM is also known as
stiffness. It is defined as the capability of materials to
resist against bending or deflection.
3.2.3 Cost (CS)
Cost plays a very significant role in determining the
J. Cent. South Univ. Technol. (2010) 17: 244−256
best material at the early stage of product development
process. In this work, raw material cost (RMC) is
considered as a main factor for determining the most
appropriate material. RMC is defined as the cost of raw
material that will be used in fabricating the product.
3.2.4 Weight (W)
One of the primary reasons for material engineers to
investigate composite materials for a specific vehicle
application is weight reduction. Thus, selecting a
material that enables to reduce the weight of vehicle is
very important. The density of a material (DS) is defined
as its mass per unit volume. Low density of material can
contribute to weight reduction.
3.2.5 Service condition (SC)
As bumper beam is exposed to weather, the
candidate materials under consideration are expected to
satisfy the resistance to weather conditions. Thus, service
conditions during use are also important and should also
be taken into account in materials selection. Two
material properties that need to be considered are
resistance to corrosion (RC) and water absorption (WA).
RC is defined as the ability of a material to resist
corrosion, and WA is defined as the amount of water
absorbed by a material.
3.2.6 Manufacturing process (MP)
MP is also needed to be considered when
determining the best material at the early stage of the
product development process. Shape (SH) is defined as
the ability of a material to be shaped into the finished
product. As the bumper beam is in a very complex shape,
whether the materials to be formed or shaped according
Fig.3 AHP principle and its steps
247
to design requirements need to be considered.
3.2.7 Environment consideration (EC)
Due to increasing environmental demands,
especially on dealing with products end of life phase, it is
important to select the materials easily to be recycled and
treated for a better environment. Recycling (RY) is
defined as the ability of a material to be recycled at the
end of life phase. Disposal (DP) is defined as the ability
of a material to be disposed of in an environmental way
such as landfill and incineration.
3.2.8 Availability of material (AVM)
AVM can be categorized into two factors, namely
availability of raw material (AM) and availability of
materials information (AI). The availability of AM
means an existence of the raw material in the place of
manufacturing; and the availability of AI is defined as
the material information readily available to designers
during the design process.
3.3 AHP steps at concept selection stage
The AHP developed by SAATY [28] is a powerful
and flexible weighted scoring decision making process
that helps people to set priorities and make the best
decision when both qualitative and quantitative aspects
of a decision need to be considered. Generally, AHP is
based on the following three principles: decomposition,
comparative judgment, and synthesis of priorities
[28−30]. These principles can be elaborated by
structuring them in a more encompassing nine-step
process, as shown in Fig.3.
J. Cent. South Univ. Technol. (2010) 17: 244−256
248
Step 1: Define problem. The first step in using AHP
is to identify the problem and determine its goal. The
problem should be clearly stated and decision makers
have to identify factors or criteria affecting the selection
process. According to Ref.[31], the most creative and
crucial part of the method is the determination of factors
influencing the selection process.
Step 2: Develop hierarchical structure. The most
influential part of decision making is to construct the
decision as a hierarchy. Thus, after determining the
problem, goal, criteria, sub-criteria and decision options,
it is required for decision makers to form a complicated
problem in a hierarchical structure or a model viewing
the relationships among the overall goal, criteria,
sub-criteria and alternatives, as shown in Fig.4.
Fig.4 Four-level of hierarchy model
Generally, the structure of the hierarchy comprises
four basic levels as follows.
(1) Level 1: Goal. The objective or the overall goal
of the decision is presented at the top level of the
hierarchy (level 1). The goal represents the problem to be
solved, for instance, to select the best material for the
composite automotive bumper beam.
(2) Level 2: Criteria. The second level (level 2)
represents the main criteria or major factors that affect
the selection process. The criteria identified by decision
makers rely on the type of problems that contribute to the
objective.
(3) Levels 3: Sub-criteria. The sub-criteria are
placed at the third level (level 3) of the hierarchy, which
allows more detailed in the AHP model. By adding
sub-criteria or more specific criteria of the problem, the
process of selection can be performed more accurately
for determining the best option.
(4) Level 4: Decision alternatives. Finally, the
decision alternatives or options are presented at the
lowest level (level 4) of the hierarchy.
Step 3: Construct pairwise comparison matrix. One
of the major strengths of AHP is the use of pairwise
comparison to derive accurate ratio scale priorities.
Pairwise comparisons are fundamental to the AHP
methodology [32]. Then, a pairwise comparison matrix
(size n×n) is constructed for the lower levels with one
matrix in the level immediately above. The pairwise
comparisons generate a matrix of relative rankings for
each level of the hierarchy. The number of matrices
depends on the number of elements at each level. The
order of the matrix at each level depends on the number
of elements at the lower level that it links to.
Step 4: Perform judgement of pairwise comparison.
Pairwise comparison begins with comparing the relative
importance of two selected items. There are n×(n−1)
judgments required to develop the set of matrices in step
3. The decision makers have to compare or judge each
element by using the relative scale pairwise comparison
as shown in Table 1. The judgements are decided based
on the decision makers’ or users’ experience and
knowledge. The scale used for comparisons in AHP
enables the decision maker to incorporate experience and
knowledge intuitively.
To do pairwise comparison, for instance (Table 2), if
C−1 is strongly more important than C−3, then a=5.
Reciprocals are automatically assigned to each pairwise
comparison.
Step 5: Synthesize pairwise comparison.
Hierarchical synthesis is used to weight the eigenvector
entries by the weights of the criteria and the sum is taken
as overall weighted eigenvector entries corresponding to
Table 1 Scale for pairwise comparisons [33]
Relative
intensity
Definition
Explanation
1
Equal value
Two requirements are of equal value
3
Slightly more value
Experience slightly favours one requirement over another
5
Essential or strong value
Experience strongly favours one requirement over another
7
Very strong value
Requirement is strongly favoured and its dominance is demonstrated in practice
9
Extreme value
Evidence favouring one over another is of the highest possible order of affirmation
2, 4, 6, 8
Intermediate values between
two adjacent judgments
When compromise is needed
Reciprocals
Reciprocals for inverse comparison
J. Cent. South Univ. Technol. (2010) 17: 244−256
249
Table 2 Performing judgement of pairwise comparison of
criteria with respect to goal
a
Goal
C−1
C−1
C−2
1
C−2
C−3
C−4
5
1
C−3
1/5
1
C−4
Table 3 Random index (RI) of analytic hierarchy process (AHP)
[33]
n
1
2
3
4
5
6
RI
0
0
0.58
0.90
1.12
1.24
n
7
8
9
10
11
12
RI
1.32
1.41
1.45
1.49
1.51
1.58
1
those in the next lower level of the hierarchy. There are a
number of methods that can be used to calculate
eigenvector or vectors of priorities, and one of them is
the average of normalized column (ANC) method [34].
ANC is to divide the elements or scale points of each
column by the sum of the columns, to add the element in
each resulting row and divide this sum by the number of
elements in the row (n). This is a process of averaging
over the normalized columns. In mathematical form, the
eigenvector or vector of priorities can be calculated as
1 n aij
Wi = ∑ n
, i, j=1, 2, …, n
(1)
n j =1
a
∑ ij
i =1
where W is the eigenvector (priority vector); aij is the
relative scale, i.e., 1, 3, 5, …; and n is the number of
criteria.
Step 6: Perform consistency analysis. As the
comparisons are carried out through personal or
subjective judgments, some degree of inconsistency may
occur. To guarantee that the judgments are consistent, a
process called consistency verification, which is regarded
as one of the most advantages of the AHP, is
incorporated in order to measure the degree of
consistency among the pairwise comparisons by
computing the consistency ratio [15]. The consistency is
determined by the consistency ratio (CR), the ratio of
consistency index (CI) to random index (RI) for the same
order matrices. To calculate CR, three steps have to be
implemented as follows.
(1) Calculate eigenvalue λmax
n
n
∑ aij × w j
i =1
wi
λmax = ∑
j −1
(2)
(3)
where n is the matrix size or criterion.
(3) Calculate CR
CR can be calculated using the formula
CR=CI/RI
3.4 Determination of the best material during concept
selection
In order to determine the most suitable material,
AHP steps have to be employed by utilizing expert
choice software. The software developed by FORMAN
et al [35] is a multi-attribute decision support software
tool based on the AHP methodology, and is also easy to
use and understand, thus providing visual representations
of overall ranking on a computer screen. The steps of
using AHP through utilizing expert choice 11 software
are as follows.
Step 1: Define problem. A case study used in this
work is concerned with the problem to determine the best
material for the automotive bumper beam. After
implementing several design steps in product development process, six materials are considered (Table 4).
Step 2: Develop hierarchy model for material
Table 4 Materials used in automotive bumper beam design
(2) Calculate CI
CI=(λmax−n)/(n−1)
CR is acceptable if it does not exceed 0.10. If it is
more, the judgment matrix is inconsistent. To obtain a
consistent matrix, judgments should be reviewed and
improved by repeating step 4 through step 6.
Step 7: Repeat steps 3−6. Steps 3−6 are performed
for all levels in the hierarchy.
Step 8: Develop overall priority ranking. The
purpose of developing overall priority is to determine the
best alternative arrangement. After the consistency
calculation for all levels is completed, further calculation
of the overall priority vector to select the best design
concept must be performed.
Step 9: Select the best decision. Select the best
decision option according to the results carried out in
step 8.
(4)
where RI is the random index of the same order matrix
(Table 3).
No.
Composite material
1
Glass fibre reinforced epoxy (M−1)
2
Carbon fibre reinforced epoxy (M−2)
3
Carbon fibre reinforced polypropylene (10%) (M−3)
4
Glass fiber reinforced polypropylene (40%) (M−4)
5
Glass fibre reinforced polyester (30%) (M−5)
6
Glass fibre vinylester SMC (60%) (M−6)
J. Cent. South Univ. Technol. (2010) 17: 244−256
250
bumper beam are identified, which are decision options.
Step 3: Perform judgements of pairwise comparison
matrix. Pairwise comparison begins with comparing the
relative importance of the two selected items by using
pairwise numerical comparisons provided by expert
choice 11 software or relative scale pairwise comparison,
as shown in Table 1. Table 5 shows the data used to do
pairwise comparison, which are taken from various
sources [36−42]. The judgements or assigned values (see
Fig.6) are based on the authors’ experience and
knowledge.
Step 4: Synthesize pairwise comparison. After
pairwise comparison process is finished, the priority
vectors and the consistency ratio must be analyzed. The
results of priority vectors and consistency test for the
main criteria with respect to the goal are shown in Fig.7.
EA contributes the highest to the goal with a priority
vector of 0.363 while the availability (AV) contributes
the lowest with a priority vector of 0.022 only. As the
value of consistency ratio (CR=0.05) is less than 0.1, the
judgements are acceptable. If CR＞0.1, the judgment
matrix is inconsistent. To obtain a consistent matrix,
judgements should be reviewed and improved.
Step 5: Perform steps 3−4 for all levels in the
hierarchy for all pairwise comparisons. The results
shown in Fig.8 represent the priority vectors for criteria
selection. In this step, a hierarchy model for structuring
material decisions is developed. The factors that
influence the selection process are translated to the
hierarchy structure, as shown in Fig.5. A four-level
hierarchy decision process (see Fig.5) is described as
follows.
(1) Level 1. Initially, the objective or the overall
goal of the decision is presented at the top level of
hierarchy. Specifically, the overall goal of this case study
is to select the best material for the polymeric composite
automotive bumper beam.
(2) Level 2. The second level represents the main
criteria that can be classified into eight aspects: EA, PR,
CS, WE, SC, MP, environment consideration (EC) and
availability (AV).
(3) Level 3. The sub-criteria are represented at the
third level of hierarchy. Impact toughness (ITH) is a
sub-criterion that affects the energy absorption. There are
two sub-criteria that affect the performance criterion: FS
and FMF. RMC, low density (LD), RC and WA, SH,
recycle (RY) and disposal (DP), and AM and AI, are
sub-criteria that affect the cost, weight, service condition,
manufacturing process, environment considerations and
availability, respectively.
(4) Level 4. Finally, at the lowest level of the
hierarchy, the alternative materials of the automotive
Fig.5 Hierarchical structure of decision problem in selecting the best material for polymeric composite automotive bumper beam
Table 5 Data used for determining the most appropriate material for polymeric based automotive bumper beam
Material
ITH/
(J·cm−1)
FS/
MPa
FM/
GPa
RMC/
DS/
(USD·kg−1) (kg·m−3)
M−1
21.20
483.0
20.7
4
M−2
10.60
656.0
34.5
M−3
3.20
75.8
M−4
7.52
M−5
M−6
CR
WA/%
SH
RY
DP
1 400
Excellent
0.10
High
No
High
Available Available
6
1 600
Excellent
0.10
High
No
High
Available Available
13.8
5
1 110
Excellent
0.01
High
Possible
High
Available Available
294.0
11.4
1
1 560
Excellent
0.07
High
Possible
High
Available Available
8.54
179.0
11.0
2
1 850
Excellent
0.25
High
Possible
High
Available Available
12.80
427.0
17.9
3
1 900
Excellent
0.05
High
No
High
Available Available
Note: Cost of raw materials is estimated in range between high cost (6) and low cost (1).
AM
AI
J. Cent. South Univ. Technol. (2010) 17: 244−256
251
Fig.6 Pairwise comparisons of main criteria with respect to goal
Fig.7 Priority vectors and consistency test for main criteria
with respect to goal (CR=0.05 with 0 missing judgment)
and sub-criteria. The judgements for all levels are
acceptable due to the fact that CR is less than 0.1.
Step 6: Select the best material. AHP reveals that
the glass fibre epoxy (M−1) will be the most appropriate
material for the polymeric composite automotive bumper
beam if all criteria and sub-criteria are considered. Fig.9
shows the glass fibre epoxy (M−1) with a weight of
0.257 as the first choice, the second choice is the carbon
fibre epoxy (M−2) with a weight of 0.184, and the last
choice is the glass fibre reinforced polyester (M−5) with
a weight of only 0.112.
4 Verification of decisions through sensitivity
analysis
The power of using AHP through utilizing expert
choice is a sensitivity analysis. The purpose of
performing the sensitivity analysis is to study the effect
of different factors on deciding the best decision option.
The final selection of the design concept is highly
dependent on the priority vectors attached to the main
criteria. Small changes in the priority vectors can
therefore cause major changes of the final ranking [43].
Since these priority vectors are usually based on highly
subjective judgements, the stability of the ranking under
varying criteria weights has to be tested. The sensitivity
analysis can be performed by increasing or decreasing
the priority vector of individual criteria. Then the
resulting changes of the priorities and the ranking of the
alternatives can be observed. Sensitivity analysis
therefore provides information on the stability of the
ranking [31]. Fig.10 shows the sensitivity graph of the
main criteria with respect to the goal. It not only
demonstrates that the glass fibre epoxy (M−1) is the best
choice, but also shows how sensitive the decision is. For
this purpose, the priority vectors of the main criteria are
separately altered, simulating priority vectors between
0% and 100% (note that the priority vectors of the other
criteria change accordingly, reflecting the relative nature
of the priority vectors).
For instance, if the priority vector of CS is increased
by 25% (from 12.2% to 37.2%), consequently, the
ranking of the priorities is changed. The glass fibre
reinforced polypropylene (M−4) with a weight of 0.224
is the first choice, the second choice is the glass fibre
epoxy (M−1) with a weight of 0.209, and the last choice
is the carbon fibre reinforced polypropylene (M−3) with
a weight of only 0.103, as shown in Fig.11.
The final decision was verified by simulating
various scenarios and increasing or decreasing the values
of the priorities vector of the main criteria (EA, PR, WE
and CS). These include the following results.
(1) Priority vector of EA is increased and reduced
by 20% (Figs.12(a) and (b)).
(2) Priority vector of PR is increased and reduced
by 20% (Figs.13(a) and (b)).
(3) Priority vector of WE is increased by 25%
(Fig.14).
(4) Priority vector of CS is increased by 25%
(Fig.15).
252
J. Cent. South Univ. Technol. (2010) 17: 244−256
Fig.8 All priority vectors for criteria and sub-criteria
epoxy after various scenarios of sensitivity analysis are
conducted.
5 Conclusions
Fig.9 Results of selection with overall CR of 0.06
The ranking of the early decisions (Fig.9) was
compared with that obtained after performing six
simulated scenarios, as depicted in Table 6.
If the priority vector of EA is increased and reduced
by 20%, priority vector of PR is increased and reduced
by 20% and priority vector of WE is increased by 25%,
the results show that glass fibre epoxy (M−1) is the most
appropriate material. But if the priority vector of CS is
increased by 25%, as a result, the ranking of the
priorities will change, and the glass fibre reinforced
polypropylene (M−4) is the first choice. It can be
concluded from the sensitivity analysis that the final
result of the proposed AHP model is mainly based on
increasing or decreasing the values of the priorities
vector of the main criteria. In this work, the final
decision of the most appropriate material is glass fibre
(1) Determining the right selection of material
during concept selection at the conceptual design stage is
very important. The selection of a material for the
automotive composite bumper is investigated. The
proposed selection framework provides a systematic step
to material engineers to perform material selection
process in concept selection stage.
(2) The use of AHP in solving material selection at
early stage of product development process is explored.
The AHP methodology for determining the most
appropriate material for the automotive bumper beam is
also described. Several sensitivity analysis scenarios are
conducted to verify the final decision. The AHP and
sensitivity analysis reveals that the glass fibre epoxy is
the most suitable material for automotive bumper beam
as it has the highest value (25.7%) compared with other
materials.
(3) Sensitivity analysis of various scenarios is
conducted to verify the selection process. It is proved
that glass fibre epoxy is the most appropriate composite
material to be used in manufacturing automotive bumper
beam. It is indicated that the AHP approach through
utilizing expert choice software is a useful method to
solve decision problem in selection of material in
concept selection stage.
J. Cent. South Univ. Technol. (2010) 17: 244−256
Fig.10 Sensitivity graph of main criteria with respect to goal
Fig.11 Sensitivity graph of main criteria with respect to goal when cost (CS) is increased by 25% (from 12.2% to 37.2%)
Fig.12 Sensitivity graph of main criteria with respect to goal when priority vector of EA is increased (a) and reduced (b) by 20%
253
254
J. Cent. South Univ. Technol. (2010) 17: 244−256
Fig.13 Sensitivity graph of main criteria with respect to goal when priority vector of PR is increased (a) and reduced (b) by 20%
Fig.14 Sensitivity graph of main criteria with respect to goal when priority vector of WE is increased by 25%
Fig.15 Sensitivity graph of main criteria with respect to goal when priority vector of CS is increased by 25%
J. Cent. South Univ. Technol. (2010) 17: 244−256
255
Table 6 Rank of priorities obtained by simulating six scenarios of sensitivity analysis
EA
Rank
PR
Increased
by 20%
Reduced
by 20%
Increased
by 20%
Reduced
by 25%
Increased
by 25%
1
M−1(31.1%)
M−1(20.3%)
M−1(25.7%)
M−1(25.8%)
M−1(25.6%)
M−4(22.4%)
2
M−6 (20.2%)
M−2(19.5%)
M−2(24.8%)
M−6(18.7%)
M−3(21.0%)
M−1(20.9%)
3
M−2 (17.3%)
M−4(17.3%)
M−6(17.1%)
M−4 (16.1%)
M−2(15.6%)
M−6(19.2%)
4
M−4 (11.5%)
M−6(15.5%)
M−4 (12.6%)
M−3(14.5%)
M−4(14.5%)
M−2(14.0%)
5
M−5 (10.5%)
M−3(15.4%)
M−3(10.4%)
M−5(13.0%)
M−6(13.7%)
M−5(13.1%)
6
M−3 (9.5%)
M−5(12.0%)
M−5 (9.5%)
M−2(11.9%)
M−5(9.5%)
M−3(10.3%)
The authors would like to thank Universiti Teknikal
Malaysia Melaka (UTeM) for the scholarship award to
the principal author to carry out his PhD studies at
Universiti Putra Malaysia. Special thank will give
Universiti Putra Malaysia (UPM) for the financial
support through Research University Grant Scheme 2007
(RUG 2007) with vote number 91045.
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CS
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by 20%
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