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A selection of material using a novel type decision-making method: Preference selection index method
Materials and Design 31 (2010) 1785–1789
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
A selection of material using a novel type decision-making method: Preference selection index method Kalpesh Maniya a,*, M.G. Bhatt b a b
Department of Mechanical Engineering, C.K. Pithawalla College of Engineering and Technology, Affiliated to Veer Narmad South Gujarat University, Surat 395007, Gujarat, India Department of Production Engineering, Shantilal Shah Engineering College, Bhavnagar, Gujarat, Affiliated to Bhavnagar University, Bhavnagar, Gujarat, India
a r t i c l e
i n f o
Article history: Received 7 October 2009 Accepted 8 November 2009 Available online 12 November 2009 Keywords: Material selection Preference selection index method Validation and consistency test
a b s t r a c t The aim of the current study is to implement a novel tool to help the decision-maker for selection of a proper material that will meet all the requirements of the design engineers. Preference selection index (PSI) method is a novel tool to select best alternative from given alternatives without deciding relative importance between attributes. In the present study, three different types of material selection problems are examined. A validation and consistency test of preference selection index method is performed in present work by comparing results of PSI method with published results of graph theory and matrix approach (GTMA), and technique for order preference by similarity to ideal solution (TOPSIS) method, respectively. The research has concluded that the PSI method is logical and more appropriate for the material selection problems. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Recent developments in design, the selection of materials play an important role for engineers. The material selection should not be solely based on cost but also depends on different properties of material, availability, recycling, production method, disposal method, design life, etc. selection of material depends on number of attributes or factors. Hence, selection of material is a multi attribute decision-making problem. Selection of the appropriate material is an integral part of successfully implementation of an engineer’s design. The ability to select the most appropriate material for a given application is the fundamental challenges faced by the design engineer. A systematic and efficient approach to material selection approach is necessary in order to select the best alternative for a given application [1–5]. The importance of materials selection in engineering design has been well recognized. The design decision-making regarding selecting appropriate materials is dictated by the specific requirements of an application, often the requirements on materials properties [6]. In the past lots of research had been reported for selection of material using classical multi attribute decision-making methods. A multi attribute analysis is a popular tool to select best alternative for given applications and the methods are simple additive weighted (SAW) method, weighted product method (WPM), * Corresponding author. Tel.: +91 0261 2728282. E-mail address: [email protected] (K. Maniya). 0261-3069/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2009.11.020
technique for order preference by similarity to ideal solution (TOPSIS), Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) method, analytical hierarchy process (AHP), graph theory and matrix representation approach (GTMA), etc. [7–10]. Rao [9,10] presented graph theory and matrix representation approach (GTMA) for the material selection. Shanian and Savadogo [11] presented ELimination and Et Choice Translating REality (ELECTRE) outranking method for the material selection. Shanian and Savadogo [12] applied TOPSIS method as multiple-criteria decision support analysis for material selection of metallic bipolar plates for polymer electrolyte fuel cell. Manshadi et al. [13] proposed numerical method for the material selection combining non-linear normalization with modified digital logic method. Chan and Tong [14] used grey relational analysis approach (GRA) for multi-criteria selection method. Rao [15] presented improved compromise ranking method for material selection. Rao and Davim [16] described combined multiple attribute decision-making AHP/TOPSIS methodology. Prasenjit et al. [17] used compromise ranking and outranking methods for material selection. Also material selection is carried out using fuzzy decision-making, material design and selection using multi objective decision-making methods [18–21]. The objectives of current research it to implement a novel method named preference selection index (PSI) method for selection of material for a given application. PSI method is a systematic scientific method or tool for design engineers to select the appropriate material for the given application. To illustrate the PSI method for material selection, one example is considered, which already solved using improved compromise ranking method by Rao [15]. In
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K. Maniya, M.G. Bhatt / Materials and Design 31 (2010) 1785–1789
this research, validation and consistency test of proposed method for material selection are checked by comparing the results of PSI method with published results of GTMA and TOPSIS methods, respectively.
where xij is the j = 1, 2, 3, . . . , M)
2. Preference selection index (PSI) method
In this step, preference variation value (PVj) for each attribute is determined with concept of sample variance analogy using following equation:
The proposed approach is new for selection of material. Mostly material selection is completed using multi attribute decisionmaking methods. A literature review clearly indicates that in all these existing multi attribute decision-making methods it is necessary to assign relative importance between attributes or attributes weight and requires many complex calculations. In the proposed method, it is not necessary to assign relative importance between attributes, but in this method overall preference value of attributes are calculated using concept of statistics. This method is useful when there is conflict in deciding the relative importance between attributes and that is the beauty of PSI method. Using overall preference value, preference selection index (Ii) for each alternative is calculated and alternative with higher value of PSI is selected as best alternative. The detail steps for calculation of PSI are given in the following methodology.
attribute
measures
(i = 1, 2, 3, . . .. , N
Step IV: Compute preference variation value (PVj).
PVj ¼
N X ½Rij Rj 2
where Rj is the mean of normalized value of attribute j and P Rj ¼ N1 Ni¼1 Rij Step V: Determine overall preference value (Wj). In this step, the overall preference value (Wj) is determined for each attribute. To get the overall preference value, it is required to find deviation (Uj) in preference value (PVj) and the deviation in preference value for each attribute is determined using the following equation:
U Wj ¼ PM j
j¼1
The process of transforming attributes value into a range of 0–1 is called normalization and it is required in multi attribute decision-making methods to transform performance rating with different data measurement unit in a decision matrix into a compatible unit. If the expectancy is the-larger-the-better (i.e. profit), then the original attribute performance can be normalized as follows:
xij xmax j
ð1Þ
If the expectancy is the-smaller-the-better (i.e. cost), then the original attribute performance can be normalized as follows:
xmin j
ð2Þ
xij
Alternatives (A i) A1 A2 : : An
C1 x11 x21
Criteria (Cj) C2 …. x12 ….. x22 …..
: :
: :
xm1
xm2
Fig. 1. Decision matrix.
: : …..
Cm x1n x2n : : xmn
Uj
ð5Þ
The total overall preference value of all the attributes should be P one, i.e. j Wj ¼ 1. Step VI: Obtain preference selection index (Ii). Now, compute the preference selection index (Ii) for each alternative using following equation:
Ii ¼
Rij ¼
ð4Þ
and overall preference value (Wj) is determined using following equation:
Step I: Identify the goal; find out all possible the material alternatives, selection criteria and its measures for the given application. Step II: Formulate decision matrix.The solving each MADM problem begins with constructing decision matrix. Let, A = {Ai for i = 1, 2, 3, . . . , n} be a set of alternative, C = {Cj for j = 1, 2, 3, . . . , m} be a set of decision criteria or attributes, xij is the performance of alternative Ai when it examined with criteria Cj. Then the decision matrix is represented in tabular format as shown in Fig. 1. Step III: The data normalization.
Rij ¼
ð3Þ
i¼1
Uj ¼ 1 PVj 2.1. Methodology of PSI method
and
M X ðRij Wj Þ
ð6Þ
j¼1
Step VII: After calculation of the preference selection index (Ii), alternatives are ranked according to descending or ascending order to facilitate the managerial interpretation of the results, i.e. an alternative is ranked/selected first whose preference selection index (Ii) is highest and an alternative is ranked/selected last whose preference selection index (Ii) is the lowest and so on. 3. Illustration of example In this section, one example of material selection problem is considered to demonstrate the methodology of preference selection index method. This example is earlier illustrated by Rao [15] using improved compromise ranking method. The quantitative and qualitative data of material selection problem is shown in Table 1. The detailed steps involved in the application of PSI method for selecting optimal material for the given application are described below: Step I: Decide the all the possible alternative materials for a given application, its selection criteria, and its values. In present study, five material alternatives with four attributes, and their attribute measures are considered as same of Rao [15] and
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K. Maniya, M.G. Bhatt / Materials and Design 31 (2010) 1785–1789 Table 1 Quantitative data of material selection attributes [15]. Material
1 2 3 4 5
Tensile strength (MPa)
Material selection attributes Young’s modulus (GPa)
Density (gm/cm3)
Corrosion resistance
1650 1000 350 2150 700
58.5 45.4 21.7 64.3 23
2.3 2.1 2.6 2.4 1.71
Average (0.5) Low (0.335) Low (0.335) Average (0.5) Above average (0.59)
the attributes are tensile strength, Young’s modulus, density and corrosion resistance. Step II: In this step, decision matrix is formulated. A decision matrix is nothing but representation of all the data in tabular format and it is shown in Table 1. Step III: In this step, attribute measures are normalized to convert in compatible unit using Eqs. (1) and (2). In present study, density of material is non-beneficial attributes, i.e., lower value is desirable and the remaining three attributes are beneficial, i.e., higher value is desirable. The normalized data of the material selection attributes is shown in Table 2. Step IV: The values of preference variation (PVj) are calculated using Eq. (3) and these are given below: PV1 = 0.4571; PV2 = 0.3755; PV3 = 0.0703; PV4 = 0.1466. Step V: Overall preference values (W) of attributes are calculated using Eq. (5) and these are given below: U1 = 0.5429; U2 = 0.6245; U3 = 0.9297; U4 = 0.8534 and W1 = 0.1840; W2 = 0.2117; W3 = 0.3151; W4 = 0.2894. Step VI: Overall preference selection index (Ii) is calculated for each alternative using Eq. (6) and its values are given below: I1 = 0.8133; I2 = 0.6560; I3 = 0.4730; I4 = 0.8655; I5 = 0.7401. Step VII: Best alternative is ranked by Ii is the one with maximum value of Ii and ranking order is given as 4–1–5–2–3. As per the ranking order, alternative 4 is the first choice, alternative 1 is the second choice for a given application and alternative 3 is the last choice. Rao [15] solved the same problem earlier using improved compromise ranking method. Rao [15] obtained alternative 4 is the best or first choice and alternative 1 is the second choice by applying improved compromise ranking method with use of analytical hierarchy approach (AHP) for determination of attribute’s weight or to assign relative importance between attributes. The results of PSI method are matches with results obtained by Rao [15]. But Rao [15] made a calculation mistake and he explained the improved compromise ranking methods only for four alternative materials. Hence, results comparison table is not shown for this material selection example. If decision makers use AHP method for determination of attribute weight then it necessary to check consistency in judgments taken to assign relative importance between attributes. It is difficult to assign relative importance be-
tween attributes when numbers of attributes are larger in selection process. In present work, PSI method gives same results with minimum and simple calculations without support of any other methods like AHP method, Entropy method that are used for determination of attribute’s weight. A PSI method can use for any numbers of attributes. 4. Validation of PSI method To validate proposed method for material selection, an example based on graph theory and matrix approach (GTMA) for material selection problem is considered as the same of Rao [9,10]. In this problem, Rao [9,10] has taken six alternatives and four attributes for material selection as shown in Table 3. In GTMA, there is need to assign a relative importance between material selection attributes. Generally in the GTMA a relative importance between attributes are assigned using 8-scales proposed by Chen and Hawang [7], scale proposed by Saaty [22], and the 11-point scale given by Venkatasamy and Agrawal [23]. Rao [9,10] had assigned the relative importance between attribute by considering the 11-point scale given by Venkatasamy and Agrawal [23] as shown in Fig. 2. This example is solved using PSI method, which is described in Section 2.1 and according to step III of PSI method a normalized value of material selection attributes are calculated by using Eqs. (1) and (2). In this example, cost of material is non-beneficial attributes and the remaining three attributes are beneficial attributes. The normalized data of the material selection attributes are shown in Table 4. Result: By applying step IV to step VII of PSI method, results are obtained and it compared with the published result of GTMA applied by Rao [9,10] as given in Table 5. Discussion: For the given application, Rao [9,10] used GTMA and get the ranking order of material is 5–4–2–3–1–6 where as PSI method suggests the ranking order of material is 5–4–2–3–1–6. Both the method suggests that material 5 is best alternative while material 6 is last alternative. The results of PSI method exactly match with the result of GTMA by Rao [9,10]. A GTMA must require deciding the relative importance between attributes whereas the proposed PSI method does not need to decide any relative importance between attributes or deciding weight of attributes. Let,
Table 3 Quantitative data of material selection attributes [9,10]. Material
1 2 3 4 5 6
Hardness (HB)
Material selection attributes Machinability rating % (MR)
Cost ($/lb) (C)
Corrosion resistance (CR)
420 350 390 250 600 230
25 40 30 35 30 55
5 3 3 1.3 2.2 4
Extremely high (0.865) High (0.665) Very high High (0.665) High (0.665) Average (0.5)
Table 2 Normalized (Rij) data of material selection attributes. Material
1 2 3 4 5
Tensile strength (MPa)
0.7674 0.4651 0.1628 1.0000 0.3256
HB
Material selection attributes
HB
Young’s modulus (GPa)
Density (gm/cm3)
Corrosion resistance
0.9098 0.7061 0.3375 1.0000 0.3577
0.7435 0.8143 0.6577 0.7125 1.0000
0.8475 0.5678 0.5678 0.8475 1.0000
D4×4 =
MR C CR
MR
C
CR
− − 0.335 0.665 0.665 0.665 − − 0.745 0.745 0.335 0.255 − − 0.335 0.335 0.255 0.335 − −
Fig. 2. A relative importance between attributes [9,10].
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Table 4 Normalized data (Rij) of material selection attributes. Material
1 2 3 4 5 6
Table 7 Normalized value of attributes for wind turbine blades material.
Hardness (HB)
Normalized value of material selection attributes Machinability rating % (MR)
Cost ($/ lb) (C)
Corrosion resistance (CR)
0.7000 0.5833 0.6500 0.4167 1.0000 0.3833
0.4545 0.7273 0.5454 0.6364 0.5454 1.0000
0.2600 0.4333 0.4333 1.0000 0.5909 0.3250
1.0000 0.7688 0.8613 0.7688 0.7688 0.5780
Steel Aluminum Glass-E Carbon Aramid
Table 5 Result comparison of PSI method with GTMA. Material
1 2 3 4 5 6
Published results of GTMA [9,10]
Results of PSI method
VPF value
Rank
Index value (I)
Rank
1.2071 1.3358 1.3166 1.6169 1.6353 1.1250
5 3 4 2 1 6
0.6321 0.6436 0.6393 0.6973 0.7294 0.5884
5 3 4 2 1 6
5. Consistency test of PSI method To apply the new methods for material selection problem it is require checking the consistency of the new methods. To check consistency of proposed method, another problem is considered,
Table 6 Objective date of material for wind turbine blade [24].
Steel Aluminum Glass-E Carbon Aramid
Stiffness (GPa)
Material selection attributes Tensile strength (MPa)
Density (g)/cm3
Elongation at break (%)
Maximum temperature
0.0857 0.0285 0.2086 1.0000 0.3428
0.0475 0.0225 0.875 1.0000 0.9000
0.1933 0.5370 0.5709 0.8286 1.0000
1.0000 0.8000 0.2000 0.1200 0.7333
1.0000 0.8000 0.7000 1.0000 0.5000
Table 8 Result comparison of PSI method with TOPSIS method.
there is a decision-making problem for selection of material alternative with M attributes and N alternative and it will be solved by graph theory and matrix approach. Subsequently, it is essential to find determinant of M M relative assignment matrix for N times. It easy to get the determinant of 3 3 and 4 4 matrices but it is difficult to solve determinant of M M matrix. It indicates lots of calculation are required to find best and worst alternative using GTMA, but similarly same best and worst alternative will be obtained using PSI with minimum calculation without considering any kind of relative importance and solving any size of relative assignment matrix. Hence, the application of GTMA becomes intricate when large numbers of alternatives and attributes are involved for selection of material alternative for the given application. In addition, GTMA requires special computer programming to get determinant of matrix larger then 4 4 matrix whereas PSI method is easy to understand, simple in calculations and does not require special computer programming compares to GTMA. A validation for any new approach is not just sufficient but it also requires checking of its consistency by applying the proposed method to other problems. Hence, consistency test is required to approve new methodology.
Material
Material
Stiffness (GPa)
Material selection attributes Tensile strength (MPa)
Density (g/cm3)
Elongation at break (%)
Maximum temperature
30 10 73 350 120
190 90 3500 4000 3600
7.5 2.7 2.54 1.75 1.45
15 12 3 1.8 11
550 400 350 550 250
Material
Steel (A1) Aluminum (A2) Glass-E (A3) Carbon (A4) Aramid (A5)
Published results of TOPSIS [24]
Results of PSI method
Performance score (P)
Rank
Index value (I)
Rank
0.5188 0.5217 0.4520 0.5606 0.5908
4 3 5 2 1
0.6058 0.5820 0.4965 0.7990 0.6584
3 4 5 1 2
which is solved using TOPSIS method. Suresh Babu et al. [24] have presented an illustrative problem for the material selection for typical wind turbine blades using TOPSIS method. The problem considering five alternatives and five attributes as shown in Table 6. This problem is solved using PSI methodology, which is described in Section 2.1 and according to step III of PSI method, normalized value of material selection attributes for wind turbine blade are calculated by using Eqs. (1) and (2). In this example, density of material is non-beneficial attributes and the remaining 4 attributes are beneficial attributes. The normalized data of the material selection attributes are shown in Table 7. Result: By applying step IV to step VII of PSI method, results are obtained and it is compared with the published result of TOPSIS considered by Suresh Babu et al. [24] for selection of material for wind turbine blades as given in Table 8. Discussion: Suresh Babu et al. [24] used the TOPSIS method and had considered attributes weight according to an importance and capability of materials as Wj = [1,2,2,3,4]. Suresh Babu et al. [24] obtained the ranking an order of ideal solution is A5 > A4 > A2 > A1 > A3 whereas PSI method suggests the ranking an order of ideal solution is A4 > A5 > A1 > A2 > A3. Suresh Babu et al. [24] recommend that material alternative A5, i.e. aramid fiber is the first choice, and carbon fiber, aluminum, and steel are placed in the second, third, and fourth choices, respectively. Whereas, PSI method suggests material alternative A4, i.e. carbon fiber the first choice, and aramid fiber, steel, and aluminum are placed in the second, third, and fourth choice, respectively. Both the method suggest that material alternative A3, i.e. Glass-E is the last choice. According to the TOPSIS method aramid fiber is the best alternative but due to poor compressive strength, poor machinability and poor environmental stability and poor temperature strength, Suresh Babu et al. [24] have revised the results and selected the best alternative as carbon fiber material (i.e. A4) for wind turbine blades analysis and worst material is A3. While PSI method already suggests carbon fiber material (i.e. A4) is the best alternative and worst material is Glass-E (i.e. A3). 6. Concluding remarks In present study, PSI method is applied on three different types of material selection problems without considering any relative importance between attributes. The results obtained by PSI method
K. Maniya, M.G. Bhatt / Materials and Design 31 (2010) 1785–1789
are compared with published results of improved compromise ranking method, graph theory and matrix approach and TOPSIS method. These three methods are very different in functioning, and assignment of relative importance between attributes or in determination of weight of attributes compared to PSI method even though PSI method gives the same result for selection of material i.e. appropriate or best material for the given application. Finally, it is concluded that preference selection index method is most appropriate and competent for selection of the best material for any given application when large numbers of attribute are involved in selection process. This method can be applied successfully to any number of alternatives. The PSI method gives directly optimal solution without assigning the relative importance between materials selection attributes and it is the beauty of PSI method. In addition, calculations are uncomplicated, easy to understand, systematic and logical approach due to use of concept of statistics compare to GTMA, VIKOR, TOPSIS, etc. preference selection index method can be considered as a novel tool for selection of materials by design engineers. References [1] Fisher PE, Lawrence W. Selection of engineering materials and adhesives. Taylor & Francis Group: CRC Press; 2005. [2] Ashby MF, Johnson K. Materials and design: the art and science of materials selection in product design. Oxford: Butterworth Heinemann; 2002. [3] Farag M. Materials selection for engineering design. New York: Prentice-Hall; 1997. [4] Edwards KL. Selecting materials for optimum use in engineering components. Mater Des 2005;26:469–73. [5] Deng YM, Edwards KL. The role of materials identification and selection in engineering design. Mater Des 2007;28:131–9. [6] Edwards KL, Deng YM. Supporting design decision-making when applying materials in combination. Mater Des 2007;28:1288–97. [7] Chen SJ, Hwang CL. Fuzzy multiple attribute decision-making methods and applications. Lecture notes in economics and mathematical systems. Berlin: Springer-Verlag; 1992.
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[8] Hwang CL, Yoon KP. Multiple attribute decision-making: methods and applications. New York: Springer; 1991. [9] Rao RV. Decision making in the manufacturing environment using graph theory and fuzzy multiple attribute decision-making methods. London: SpringerVerlag; 2007. [10] Roa RV. A material selection model using graph theory and matrix approach. Mater Sci Eng A 2006;431:248–55. [11] Shanian A, Savadogo O. A material selection model based on the concept of multiple attribute decision making. Mater Des 2006;27:329–37. [12] Shanian A, Savadogo O. TOPSIS multiple-criteria decision support analysis for material selection of metallic bipolar plates for polymer electrolyte fuel cell. J Power Sources 2006;159:1095–104. [13] Manshadi BD, Mahmudi H, Abedian A, Mahmudi R. A novel method for materials selection in mechanical design: combination of non-linear normalization and a modified digital logic method. Mater Des 2007;28:8–15. [14] Chan JWK, Tong TKL. Multi-criteria material selections and end-of-life product strategy: grey relational analysis approach. Mater Des 2007;28:1539–46. [15] Rao RV. A decision-making methodology for material selection using an improved compromise ranking method. Mater Des 2008;29(10):1949–54. [16] Rao RV, Davim JP. A decision-making framework model for material selection using a combined multiple attribute decision-making method. Int J Adv Manuf Technol 2008;35:751–60. [17] Chatterjee Prasenjit, Athawale Vijay Manikrao, Chakraborty Shankar. Selection of materials using compromise ranking and outranking methods. Mater Des 2009;30(10):4043–53. [18] Liao TW. A fuzzy multi-criteria decision-making method for material selection. J Manuf Syst 1996;15:1–12. [19] Ashby MF. Multi-objective optimization in material design and selection. Mater Des 2000;48:359–69. [20] Khabbaz SR, Manshadi BD, Abedian A, Mahmudi R. A simplified fuzzy logic approach for materials selection in mechanical engineering design. Mater Des 2009;30:687–97. [21] Fayazbakhsh K, Abedian A, Manshadi BD, Khabbaz SR. Introducing a novel method for materials selection in mechanical design using Z-transformation in statistics for normalization of material properties. Mater Des 2009;30: 4396–404. [22] Saaty TL. Fundamentals of decision-making and priority theory with the AHP. Pittsburg: RWS Publications; 2001. [23] Venkatasamy R, Agrawal VP. A digraph approach to quality evaluation of an automotive vehicle. Qual Eng 1997;9:405–17. [24] Suresh Babu K, Subba Raju NV, Srinivas Reddy M, Nageswara Rao D. The material selection for typical wind turbine blades using a MADM approach & analysis of blades. In: Proceeding of MCDM, Chania, Greece: June 19–23; 2006.
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
A selection of material using a novel type decision-making method: Preference selection index method Kalpesh Maniya a,*, M.G. Bhatt b a b
Department of Mechanical Engineering, C.K. Pithawalla College of Engineering and Technology, Affiliated to Veer Narmad South Gujarat University, Surat 395007, Gujarat, India Department of Production Engineering, Shantilal Shah Engineering College, Bhavnagar, Gujarat, Affiliated to Bhavnagar University, Bhavnagar, Gujarat, India
a r t i c l e
i n f o
Article history: Received 7 October 2009 Accepted 8 November 2009 Available online 12 November 2009 Keywords: Material selection Preference selection index method Validation and consistency test
a b s t r a c t The aim of the current study is to implement a novel tool to help the decision-maker for selection of a proper material that will meet all the requirements of the design engineers. Preference selection index (PSI) method is a novel tool to select best alternative from given alternatives without deciding relative importance between attributes. In the present study, three different types of material selection problems are examined. A validation and consistency test of preference selection index method is performed in present work by comparing results of PSI method with published results of graph theory and matrix approach (GTMA), and technique for order preference by similarity to ideal solution (TOPSIS) method, respectively. The research has concluded that the PSI method is logical and more appropriate for the material selection problems. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Recent developments in design, the selection of materials play an important role for engineers. The material selection should not be solely based on cost but also depends on different properties of material, availability, recycling, production method, disposal method, design life, etc. selection of material depends on number of attributes or factors. Hence, selection of material is a multi attribute decision-making problem. Selection of the appropriate material is an integral part of successfully implementation of an engineer’s design. The ability to select the most appropriate material for a given application is the fundamental challenges faced by the design engineer. A systematic and efficient approach to material selection approach is necessary in order to select the best alternative for a given application [1–5]. The importance of materials selection in engineering design has been well recognized. The design decision-making regarding selecting appropriate materials is dictated by the specific requirements of an application, often the requirements on materials properties [6]. In the past lots of research had been reported for selection of material using classical multi attribute decision-making methods. A multi attribute analysis is a popular tool to select best alternative for given applications and the methods are simple additive weighted (SAW) method, weighted product method (WPM), * Corresponding author. Tel.: +91 0261 2728282. E-mail address: [email protected] (K. Maniya). 0261-3069/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2009.11.020
technique for order preference by similarity to ideal solution (TOPSIS), Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) method, analytical hierarchy process (AHP), graph theory and matrix representation approach (GTMA), etc. [7–10]. Rao [9,10] presented graph theory and matrix representation approach (GTMA) for the material selection. Shanian and Savadogo [11] presented ELimination and Et Choice Translating REality (ELECTRE) outranking method for the material selection. Shanian and Savadogo [12] applied TOPSIS method as multiple-criteria decision support analysis for material selection of metallic bipolar plates for polymer electrolyte fuel cell. Manshadi et al. [13] proposed numerical method for the material selection combining non-linear normalization with modified digital logic method. Chan and Tong [14] used grey relational analysis approach (GRA) for multi-criteria selection method. Rao [15] presented improved compromise ranking method for material selection. Rao and Davim [16] described combined multiple attribute decision-making AHP/TOPSIS methodology. Prasenjit et al. [17] used compromise ranking and outranking methods for material selection. Also material selection is carried out using fuzzy decision-making, material design and selection using multi objective decision-making methods [18–21]. The objectives of current research it to implement a novel method named preference selection index (PSI) method for selection of material for a given application. PSI method is a systematic scientific method or tool for design engineers to select the appropriate material for the given application. To illustrate the PSI method for material selection, one example is considered, which already solved using improved compromise ranking method by Rao [15]. In
1786
K. Maniya, M.G. Bhatt / Materials and Design 31 (2010) 1785–1789
this research, validation and consistency test of proposed method for material selection are checked by comparing the results of PSI method with published results of GTMA and TOPSIS methods, respectively.
where xij is the j = 1, 2, 3, . . . , M)
2. Preference selection index (PSI) method
In this step, preference variation value (PVj) for each attribute is determined with concept of sample variance analogy using following equation:
The proposed approach is new for selection of material. Mostly material selection is completed using multi attribute decisionmaking methods. A literature review clearly indicates that in all these existing multi attribute decision-making methods it is necessary to assign relative importance between attributes or attributes weight and requires many complex calculations. In the proposed method, it is not necessary to assign relative importance between attributes, but in this method overall preference value of attributes are calculated using concept of statistics. This method is useful when there is conflict in deciding the relative importance between attributes and that is the beauty of PSI method. Using overall preference value, preference selection index (Ii) for each alternative is calculated and alternative with higher value of PSI is selected as best alternative. The detail steps for calculation of PSI are given in the following methodology.
attribute
measures
(i = 1, 2, 3, . . .. , N
Step IV: Compute preference variation value (PVj).
PVj ¼
N X ½Rij Rj 2
where Rj is the mean of normalized value of attribute j and P Rj ¼ N1 Ni¼1 Rij Step V: Determine overall preference value (Wj). In this step, the overall preference value (Wj) is determined for each attribute. To get the overall preference value, it is required to find deviation (Uj) in preference value (PVj) and the deviation in preference value for each attribute is determined using the following equation:
U Wj ¼ PM j
j¼1
The process of transforming attributes value into a range of 0–1 is called normalization and it is required in multi attribute decision-making methods to transform performance rating with different data measurement unit in a decision matrix into a compatible unit. If the expectancy is the-larger-the-better (i.e. profit), then the original attribute performance can be normalized as follows:
xij xmax j
ð1Þ
If the expectancy is the-smaller-the-better (i.e. cost), then the original attribute performance can be normalized as follows:
xmin j
ð2Þ
xij
Alternatives (A i) A1 A2 : : An
C1 x11 x21
Criteria (Cj) C2 …. x12 ….. x22 …..
: :
: :
xm1
xm2
Fig. 1. Decision matrix.
: : …..
Cm x1n x2n : : xmn
Uj
ð5Þ
The total overall preference value of all the attributes should be P one, i.e. j Wj ¼ 1. Step VI: Obtain preference selection index (Ii). Now, compute the preference selection index (Ii) for each alternative using following equation:
Ii ¼
Rij ¼
ð4Þ
and overall preference value (Wj) is determined using following equation:
Step I: Identify the goal; find out all possible the material alternatives, selection criteria and its measures for the given application. Step II: Formulate decision matrix.The solving each MADM problem begins with constructing decision matrix. Let, A = {Ai for i = 1, 2, 3, . . . , n} be a set of alternative, C = {Cj for j = 1, 2, 3, . . . , m} be a set of decision criteria or attributes, xij is the performance of alternative Ai when it examined with criteria Cj. Then the decision matrix is represented in tabular format as shown in Fig. 1. Step III: The data normalization.
Rij ¼
ð3Þ
i¼1
Uj ¼ 1 PVj 2.1. Methodology of PSI method
and
M X ðRij Wj Þ
ð6Þ
j¼1
Step VII: After calculation of the preference selection index (Ii), alternatives are ranked according to descending or ascending order to facilitate the managerial interpretation of the results, i.e. an alternative is ranked/selected first whose preference selection index (Ii) is highest and an alternative is ranked/selected last whose preference selection index (Ii) is the lowest and so on. 3. Illustration of example In this section, one example of material selection problem is considered to demonstrate the methodology of preference selection index method. This example is earlier illustrated by Rao [15] using improved compromise ranking method. The quantitative and qualitative data of material selection problem is shown in Table 1. The detailed steps involved in the application of PSI method for selecting optimal material for the given application are described below: Step I: Decide the all the possible alternative materials for a given application, its selection criteria, and its values. In present study, five material alternatives with four attributes, and their attribute measures are considered as same of Rao [15] and
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K. Maniya, M.G. Bhatt / Materials and Design 31 (2010) 1785–1789 Table 1 Quantitative data of material selection attributes [15]. Material
1 2 3 4 5
Tensile strength (MPa)
Material selection attributes Young’s modulus (GPa)
Density (gm/cm3)
Corrosion resistance
1650 1000 350 2150 700
58.5 45.4 21.7 64.3 23
2.3 2.1 2.6 2.4 1.71
Average (0.5) Low (0.335) Low (0.335) Average (0.5) Above average (0.59)
the attributes are tensile strength, Young’s modulus, density and corrosion resistance. Step II: In this step, decision matrix is formulated. A decision matrix is nothing but representation of all the data in tabular format and it is shown in Table 1. Step III: In this step, attribute measures are normalized to convert in compatible unit using Eqs. (1) and (2). In present study, density of material is non-beneficial attributes, i.e., lower value is desirable and the remaining three attributes are beneficial, i.e., higher value is desirable. The normalized data of the material selection attributes is shown in Table 2. Step IV: The values of preference variation (PVj) are calculated using Eq. (3) and these are given below: PV1 = 0.4571; PV2 = 0.3755; PV3 = 0.0703; PV4 = 0.1466. Step V: Overall preference values (W) of attributes are calculated using Eq. (5) and these are given below: U1 = 0.5429; U2 = 0.6245; U3 = 0.9297; U4 = 0.8534 and W1 = 0.1840; W2 = 0.2117; W3 = 0.3151; W4 = 0.2894. Step VI: Overall preference selection index (Ii) is calculated for each alternative using Eq. (6) and its values are given below: I1 = 0.8133; I2 = 0.6560; I3 = 0.4730; I4 = 0.8655; I5 = 0.7401. Step VII: Best alternative is ranked by Ii is the one with maximum value of Ii and ranking order is given as 4–1–5–2–3. As per the ranking order, alternative 4 is the first choice, alternative 1 is the second choice for a given application and alternative 3 is the last choice. Rao [15] solved the same problem earlier using improved compromise ranking method. Rao [15] obtained alternative 4 is the best or first choice and alternative 1 is the second choice by applying improved compromise ranking method with use of analytical hierarchy approach (AHP) for determination of attribute’s weight or to assign relative importance between attributes. The results of PSI method are matches with results obtained by Rao [15]. But Rao [15] made a calculation mistake and he explained the improved compromise ranking methods only for four alternative materials. Hence, results comparison table is not shown for this material selection example. If decision makers use AHP method for determination of attribute weight then it necessary to check consistency in judgments taken to assign relative importance between attributes. It is difficult to assign relative importance be-
tween attributes when numbers of attributes are larger in selection process. In present work, PSI method gives same results with minimum and simple calculations without support of any other methods like AHP method, Entropy method that are used for determination of attribute’s weight. A PSI method can use for any numbers of attributes. 4. Validation of PSI method To validate proposed method for material selection, an example based on graph theory and matrix approach (GTMA) for material selection problem is considered as the same of Rao [9,10]. In this problem, Rao [9,10] has taken six alternatives and four attributes for material selection as shown in Table 3. In GTMA, there is need to assign a relative importance between material selection attributes. Generally in the GTMA a relative importance between attributes are assigned using 8-scales proposed by Chen and Hawang [7], scale proposed by Saaty [22], and the 11-point scale given by Venkatasamy and Agrawal [23]. Rao [9,10] had assigned the relative importance between attribute by considering the 11-point scale given by Venkatasamy and Agrawal [23] as shown in Fig. 2. This example is solved using PSI method, which is described in Section 2.1 and according to step III of PSI method a normalized value of material selection attributes are calculated by using Eqs. (1) and (2). In this example, cost of material is non-beneficial attributes and the remaining three attributes are beneficial attributes. The normalized data of the material selection attributes are shown in Table 4. Result: By applying step IV to step VII of PSI method, results are obtained and it compared with the published result of GTMA applied by Rao [9,10] as given in Table 5. Discussion: For the given application, Rao [9,10] used GTMA and get the ranking order of material is 5–4–2–3–1–6 where as PSI method suggests the ranking order of material is 5–4–2–3–1–6. Both the method suggests that material 5 is best alternative while material 6 is last alternative. The results of PSI method exactly match with the result of GTMA by Rao [9,10]. A GTMA must require deciding the relative importance between attributes whereas the proposed PSI method does not need to decide any relative importance between attributes or deciding weight of attributes. Let,
Table 3 Quantitative data of material selection attributes [9,10]. Material
1 2 3 4 5 6
Hardness (HB)
Material selection attributes Machinability rating % (MR)
Cost ($/lb) (C)
Corrosion resistance (CR)
420 350 390 250 600 230
25 40 30 35 30 55
5 3 3 1.3 2.2 4
Extremely high (0.865) High (0.665) Very high High (0.665) High (0.665) Average (0.5)
Table 2 Normalized (Rij) data of material selection attributes. Material
1 2 3 4 5
Tensile strength (MPa)
0.7674 0.4651 0.1628 1.0000 0.3256
HB
Material selection attributes
HB
Young’s modulus (GPa)
Density (gm/cm3)
Corrosion resistance
0.9098 0.7061 0.3375 1.0000 0.3577
0.7435 0.8143 0.6577 0.7125 1.0000
0.8475 0.5678 0.5678 0.8475 1.0000
D4×4 =
MR C CR
MR
C
CR
− − 0.335 0.665 0.665 0.665 − − 0.745 0.745 0.335 0.255 − − 0.335 0.335 0.255 0.335 − −
Fig. 2. A relative importance between attributes [9,10].
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Table 4 Normalized data (Rij) of material selection attributes. Material
1 2 3 4 5 6
Table 7 Normalized value of attributes for wind turbine blades material.
Hardness (HB)
Normalized value of material selection attributes Machinability rating % (MR)
Cost ($/ lb) (C)
Corrosion resistance (CR)
0.7000 0.5833 0.6500 0.4167 1.0000 0.3833
0.4545 0.7273 0.5454 0.6364 0.5454 1.0000
0.2600 0.4333 0.4333 1.0000 0.5909 0.3250
1.0000 0.7688 0.8613 0.7688 0.7688 0.5780
Steel Aluminum Glass-E Carbon Aramid
Table 5 Result comparison of PSI method with GTMA. Material
1 2 3 4 5 6
Published results of GTMA [9,10]
Results of PSI method
VPF value
Rank
Index value (I)
Rank
1.2071 1.3358 1.3166 1.6169 1.6353 1.1250
5 3 4 2 1 6
0.6321 0.6436 0.6393 0.6973 0.7294 0.5884
5 3 4 2 1 6
5. Consistency test of PSI method To apply the new methods for material selection problem it is require checking the consistency of the new methods. To check consistency of proposed method, another problem is considered,
Table 6 Objective date of material for wind turbine blade [24].
Steel Aluminum Glass-E Carbon Aramid
Stiffness (GPa)
Material selection attributes Tensile strength (MPa)
Density (g)/cm3
Elongation at break (%)
Maximum temperature
0.0857 0.0285 0.2086 1.0000 0.3428
0.0475 0.0225 0.875 1.0000 0.9000
0.1933 0.5370 0.5709 0.8286 1.0000
1.0000 0.8000 0.2000 0.1200 0.7333
1.0000 0.8000 0.7000 1.0000 0.5000
Table 8 Result comparison of PSI method with TOPSIS method.
there is a decision-making problem for selection of material alternative with M attributes and N alternative and it will be solved by graph theory and matrix approach. Subsequently, it is essential to find determinant of M M relative assignment matrix for N times. It easy to get the determinant of 3 3 and 4 4 matrices but it is difficult to solve determinant of M M matrix. It indicates lots of calculation are required to find best and worst alternative using GTMA, but similarly same best and worst alternative will be obtained using PSI with minimum calculation without considering any kind of relative importance and solving any size of relative assignment matrix. Hence, the application of GTMA becomes intricate when large numbers of alternatives and attributes are involved for selection of material alternative for the given application. In addition, GTMA requires special computer programming to get determinant of matrix larger then 4 4 matrix whereas PSI method is easy to understand, simple in calculations and does not require special computer programming compares to GTMA. A validation for any new approach is not just sufficient but it also requires checking of its consistency by applying the proposed method to other problems. Hence, consistency test is required to approve new methodology.
Material
Material
Stiffness (GPa)
Material selection attributes Tensile strength (MPa)
Density (g/cm3)
Elongation at break (%)
Maximum temperature
30 10 73 350 120
190 90 3500 4000 3600
7.5 2.7 2.54 1.75 1.45
15 12 3 1.8 11
550 400 350 550 250
Material
Steel (A1) Aluminum (A2) Glass-E (A3) Carbon (A4) Aramid (A5)
Published results of TOPSIS [24]
Results of PSI method
Performance score (P)
Rank
Index value (I)
Rank
0.5188 0.5217 0.4520 0.5606 0.5908
4 3 5 2 1
0.6058 0.5820 0.4965 0.7990 0.6584
3 4 5 1 2
which is solved using TOPSIS method. Suresh Babu et al. [24] have presented an illustrative problem for the material selection for typical wind turbine blades using TOPSIS method. The problem considering five alternatives and five attributes as shown in Table 6. This problem is solved using PSI methodology, which is described in Section 2.1 and according to step III of PSI method, normalized value of material selection attributes for wind turbine blade are calculated by using Eqs. (1) and (2). In this example, density of material is non-beneficial attributes and the remaining 4 attributes are beneficial attributes. The normalized data of the material selection attributes are shown in Table 7. Result: By applying step IV to step VII of PSI method, results are obtained and it is compared with the published result of TOPSIS considered by Suresh Babu et al. [24] for selection of material for wind turbine blades as given in Table 8. Discussion: Suresh Babu et al. [24] used the TOPSIS method and had considered attributes weight according to an importance and capability of materials as Wj = [1,2,2,3,4]. Suresh Babu et al. [24] obtained the ranking an order of ideal solution is A5 > A4 > A2 > A1 > A3 whereas PSI method suggests the ranking an order of ideal solution is A4 > A5 > A1 > A2 > A3. Suresh Babu et al. [24] recommend that material alternative A5, i.e. aramid fiber is the first choice, and carbon fiber, aluminum, and steel are placed in the second, third, and fourth choices, respectively. Whereas, PSI method suggests material alternative A4, i.e. carbon fiber the first choice, and aramid fiber, steel, and aluminum are placed in the second, third, and fourth choice, respectively. Both the method suggest that material alternative A3, i.e. Glass-E is the last choice. According to the TOPSIS method aramid fiber is the best alternative but due to poor compressive strength, poor machinability and poor environmental stability and poor temperature strength, Suresh Babu et al. [24] have revised the results and selected the best alternative as carbon fiber material (i.e. A4) for wind turbine blades analysis and worst material is A3. While PSI method already suggests carbon fiber material (i.e. A4) is the best alternative and worst material is Glass-E (i.e. A3). 6. Concluding remarks In present study, PSI method is applied on three different types of material selection problems without considering any relative importance between attributes. The results obtained by PSI method
K. Maniya, M.G. Bhatt / Materials and Design 31 (2010) 1785–1789
are compared with published results of improved compromise ranking method, graph theory and matrix approach and TOPSIS method. These three methods are very different in functioning, and assignment of relative importance between attributes or in determination of weight of attributes compared to PSI method even though PSI method gives the same result for selection of material i.e. appropriate or best material for the given application. Finally, it is concluded that preference selection index method is most appropriate and competent for selection of the best material for any given application when large numbers of attribute are involved in selection process. This method can be applied successfully to any number of alternatives. The PSI method gives directly optimal solution without assigning the relative importance between materials selection attributes and it is the beauty of PSI method. In addition, calculations are uncomplicated, easy to understand, systematic and logical approach due to use of concept of statistics compare to GTMA, VIKOR, TOPSIS, etc. preference selection index method can be considered as a novel tool for selection of materials by design engineers. References [1] Fisher PE, Lawrence W. Selection of engineering materials and adhesives. Taylor & Francis Group: CRC Press; 2005. [2] Ashby MF, Johnson K. Materials and design: the art and science of materials selection in product design. Oxford: Butterworth Heinemann; 2002. [3] Farag M. Materials selection for engineering design. New York: Prentice-Hall; 1997. [4] Edwards KL. Selecting materials for optimum use in engineering components. Mater Des 2005;26:469–73. [5] Deng YM, Edwards KL. The role of materials identification and selection in engineering design. Mater Des 2007;28:131–9. [6] Edwards KL, Deng YM. Supporting design decision-making when applying materials in combination. Mater Des 2007;28:1288–97. [7] Chen SJ, Hwang CL. Fuzzy multiple attribute decision-making methods and applications. Lecture notes in economics and mathematical systems. Berlin: Springer-Verlag; 1992.
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