# Determining Design Characteristics Of Automobile Seats .

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Design Characteristic of Automobile Seatsis equal to the number of FRs, the design can be namedcoupled, decoupled, or uncoupled. If the number of DPsis equal to the number of FRs, the types of designmentioned above are defined according to therelationships between FRs and DPs. If the relationmatrix is diagonal, the design is uncoupled (Eq. 4). Thistype of design is the ideal design. If the design matrix islower triangular, the design is decoupled (Eq. 5).Otherwise, the design is coupled.15Figure 2. Decomposition by zigzaggingAD theory is based on two axioms, independence axiomand information axiom. Formal definitions of axiomsare as follows16:Axiom 1. The Independence Axiom: Maintain theindependence of the functional requirementsAxiom 2. The Information Axiom: Minimize theinformation content of the design.The first axiom, the independence axiom, is aboutmaintaining the independency between functionalrequirements (FRs) and design parameters (DPs). Inother words, the design can be acceptable if and only ifFRs must be satisfied by DPs without affecting anyother FR. FRs are defined as the minimum set ofindependent requirements that characterizes designgoals.16-17 The relationship between FRs and DPs isdefined by Equations (1-3). mxn(1)a1n a 2 n . a mn (2) FR [ R] DP ,R aij a11 aR 21 . a m1a12a 22.am2a m3aij FRi DPj(3)where R is a relation matrix between FR and DP. Therelation matrix consists of “1” and “0” elements “1”represents a relation between any FR and any DP while“0” represents no relation. In AD methodology, thereare three types of design with respect to the number ofFRs and DPs; (1) if the number of DPs is larger than thenumber of FRs, the design is named as coupled. (2) Ifthe number of FRs is larger than the number of DPs, thedesign is named as redundant, (3) if the number of DPs0 0 . . 0 a mn a11 0A . 00a 22 a11 aA 21 . a m10a 22.am2a m3.0.(4)0 0 . a mn (5)The second axiom, information axiom, is aboutminimizing the information content of the design. Inother words, among all proposed solutions that satisfythe independence axiom, the best design is the designthat has the minimum information content. Informationaxiom provides a conventional method to assess thedesigns to select the best one. The selection process isbased on the criterion which states that the design withthe highest probability of FR success is the bestdesign.17 If the probability of success for a given FR isp, the information content is calculated by Eq. (6);I i log 21pi(6)If there are two or more FRs, the total informationcontent is calculated as follows;16-17I system log 2 P( m)(7)mI system log 2 ( Pi )(8)i 1I system i 1 log 2 Pi i 1 log 2 (1 / Pi )Published by Atlantis PressCopyright: the authors45mm(9)

S. Cebi, C. KahramanIn Figure 3, system design, design range and systemprobability density function, and common range areillustrated.Figure 3. System design, design range, and common area3.Proposed MethodologyThe proposed methodology is based on the first axiomof the axiomatic design. The framework of the proposedmethodology is given in Figure 4.Step 1: Determine design groups. While determining thedesign group, the potential user population of thedesigned product must be taken into consideration.Step 2: Define FRs in the functional domain. In thisstep, to define design parameters, functionalrequirements are determined to satisfy customer needs.To determine FRs, customer surveyors, interview, andliterature review are utilized.Step 3: Define DPs in the physical domain. Designparameters are defined to satisfy the defined FRs.Step 4: Decompose FRs and DPs. FRs and DPs at thetop level are decomposed until to obtain applicabledesign parameters.Step 5: Construct the design matrix and evaluate therelations between FRs and DPs. In this study, theevaluation of relations is realized by using a linguisticscale with fuzzy membership functions making ourmethod different from the conventional axiomaticdesign methodology. In the axiomatic designmethodology, relations are defined by 0 or 1. If there isa relation between a FR and a DP, it is depicted by 1 inthe relation matrix. Otherwise, the relation is denoted by0 as it is mentioned before. However, in real caseproblems, sometimes, the relations between FRs andDPs can be unknown or uncertain. Moreover, there canbe a little or indirect relationship between a FR and aDP such that this relation can be negligible. Hence, theconventional axiomatic design principles can becomeinsufficient to define the degrees of relations betweenFRs and DPs under uncertainty or fuzziness. When therelationships between FRs and DPs are unknown orwhen they are weak relationships, these relationshipscan be defined by linguistic descriptions. Linguisticdescriptions are the formal representation of systemswhich are made through the fuzzy set theory, fuzzyrelations, and fuzzy operators. Linguistic scales describethe evaluation system of human logic which is used indaily life.18 Expressing preferences in a qualitative wayby using linguistic terms is better than it is in aquantitative way by using precise numbers.19 In thisstudy, the linguistic scale shown in Figure 5 is used todescribe the relations between FRs and DPs when arelation cannot be assessed precisely. Seven linguisticterms are defined in an interval ranging from 0 to 1shown in Figure 5. By the given linguistic scale,relations between FRs and DPs can be assessed by usingthe interval between [0,1] instead of only 0 or 1.The evaluation of the relation matrix is implemented bya group of experts directly (Eq. 10). a 11 aR k 21 a m1a 12 a 22 a m 2a 1n a 2 n , a mn k 1,2,.,K(10)where m and n are the number of FRs and DPs,respectively; k is the number of experts; R k is the fuzzydesign matrix belonging to kth expert.Step 6: Aggregate the experts’ assessments. If theevaluation of a relation matrix is implemented by eachexpert separately, the arithmetic mean method is usedfor aggregation. FRi R c DPj (11)[ R C ] [aij ], i 1,2,3, ,m and j 1,2,3, ,n(12)where FRi, DPj, and Rc are ith functional requirement, jthdesign parameter, and fuzzy co-decision matrix thatshows the relations between FRs and DPs, respectively.Published by Atlantis PressCopyright: the authors46

Design Characteristic of Automobile SeatsFigure 4. Framework of the proposed methodologyFigure 5. Linguistic scale for relationshipsPublished by Atlantis PressCopyright: the authors47

S. Cebi, C. KahramanStep 7: Calculate the functional independency. At first,the sequence of FRs is determined by Equations. 13 and14;nS FRi aijm(13)j 1mS DPj a ijm(14)i 1where aijm is the middle value of a fuzzy triangularnumber, which shows the relation between FRi and DPj.SFRi and SDPj are the sequence scores of FRi and DPj,respectively. FRs are ranked with respect to thesequence score in co-decision matrix from minimum tomaximum considering the proposed design parameters.If there is any equality among the sequence scores ofFRs, the FR which belongs to the biggest SDPj is writtenfirstly. If both SFRi and SDPj of FRs are equal, thesequence can be made in the way whatever the designerwants. It must be noted that if there is a logical sequenceamong the DPs or FRs, this relation must be taken intoconsideration firstly. For example, DPb is created afterDPa. DPb is not written before DPa even if SDPb isbigger than SDPa. Then Equation 15 is used to calculatethe degree of functional independency.m C m a iji 1 j i 1m m(15) 1 where C is the coupled ratio which denotes the degreeof independence and a ij is the fuzzy relationshipbetween the related FR and DP. If C 1 or C , thedesign is coupled and if C 0 or C , the design isuncoupled or decoupled, where is the value whichshows the level of acceptable or tolerable relationdefined by experts. The value larger than 0 or indicates the coupled design (Eq.16).If C 0 or C andm i 1c i 1 j 1m i 1 1i 1 j 1 Ck 1c 21c 12 c 1n1 c 2n cn1 c n 2 1, k 1,2,3, .K(17)where C k is a pairwise comparison matrix whichbelongs to kth expert for FRm. The triangular fuzzynumbers are given by Eq.(18) for pairwise comparisonmatrices. (1,1,3), (1,3,5), (3,5,7), (5,7,9), (7,9,9), if i is moreimportantthan j (1,1,1),c ij if i and j havethesameimportance, (1,1,3) 1 , (1,3,5) 1 , (3,5,7) 1 , (5,7,9) 1 , (7,9,9) 1 if i is lessimportantthan j (18)The linguistic scale for triangular fuzzy numbers in Eq.(18) is given in Table 1.Table 1. Linguistic scale for the weight matrix21i 1 j i 1 a ij a design is uncouple. Otherwise it is decoupled. Here cis the uncoupled ratio.Step 8: Calculate the importance of functionalrequirements. The importance of the functionalrequirements is calculated by pairwise comparisons.Buckley’s method is used to obtain weights20-21: Thepairwise comparison matrix is given by Eq. (17) for anyexpert. 0,(16)Linguistic scales(1,1,3)(1,3,5)(3,5,7)(5,7,9)(7,9,9)Scale of fuzzy numberEqually importantWeakly importantEssentially importantVery strongly importantAbsolutely important(Eq)(Wk)(Es)(Vs)(Ab)Then, the fuzzy weighted design matrix is calculated byBuckley’s Method as follows: ri (c i1 c i 2 . c in )1 / n(19) 1wFRi ri ( r1 r2 . rn )(20)where c in is the fuzzy comparison value of DPi to DPnunder the relevant FR, and ri is the geometric mean offuzzy comparison values of DPi to each DP under FRn. wFRi is the fuzzy weight for FRi. When there are morePublished by Atlantis PressCopyright: the authors48

Design Characteristic of Automobile Seatsthan one expert, geometric mean method is used toaggregate the experts’ preferences before applying Eqs.19-20.Step 9: Calculate the importance of design parameters.The importance of design parameters is calculated inorder to define most important parameters in the design.Sometimes, all functional requirements cannot be fullysatisfied. Hence, the most important item that satisfiesthe functional requirements at most is determined inorder to give it the design priority. Eq. 21 is used tocalculate the weights of design parameters via a relationmatrix.m wDPj wFRi a iji 1,2, ,m and j 1,2, n, (21)i 1 and w are the fuzzy weights of designwhere wDPFRparameters and functional requirements, respectively.Then, the obtained fuzzy numbers are defuzzified intocrisp values. Then, the normalization procedure isapplied. Eqs. 22-23 are used to obtain crisp values forimportance of functional requirements. Eq. 23 presentboth defuzzification and normalization procedures inone formula.lmu TwDPj wDPj wDPj wDPjwDPj (22) TwDPj(23)n Tw DPjj 1lmuwhere wDPj , wDPj , and wDPj are the lower, middle,and upper values of triangular fuzzy numbers whichdepends on the importance of design parameters,respectively.It is also possible to rank the design parameters by afuzzy ranking approach without converting them tocrisp numbers. Many ranking algorithms have beenproposed in the literature. For instance, see a very recentapproach to rank fuzzy numbers in 22.4.AutomobileConsumersSeatDesignforTurkishIn this section, characteristic features of an automobileseat are taken in to consideration based on themethodology given above.Step 1. Determine the design team. The design teamconsists of a project manager, a product designer, andtwo mechanical engineers. The product designers andengineers are familiar with ergonomics and automotiveseat design. The responsibility of the project manager isto lead this design process and supply financial support.Step 2: Define FRs in the functional domain. Todetermine the customers’ expectations a survey isperformed. Eighteen volunteers of taxi drivers areselected as the participant group of the survey withrespect to two criteria. The first one is that drivers musthave at least five years taxi-driver experiences. Thesecond criterion is that drivers must not have anymusculosketal disorders. The main reason to select taxidrivers as an experimental set is that they morefrequently spend longer hours in their vehicles bysitting. The overall expectations of the taxi drivers froman automobile seat are summarized in Table 2. Thefactors listed in Table 2 are the expectations ofparticipants and they are related to seat characteristics.Some factors such as reachability (to glove box, togearshift stick, to hand brake) and good visibilitythrough side window are not taken

based on automobile seat design or seat comfort. 4-15. In the literature, there are two common features of the studies: i) occupant anthropometry, seat geometry, and amount of the sitting time are the most citied factors that affect automobile seat comfort, ii) a subjective evaluation proc

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