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1 POLITECNICO DI TORINO Repostory ISTITUZIONALE Prortzaton of QFD Customer Requrements Based on the Law of Comparatve Judgments Orgnal Prortzaton of QFD Customer Requrements Based on the Law of Comparatve Judgments / Franceschn, Forenzo; Masano, Domenco. - In: QUALITY ENGINEERING. - ISSN STAMPA. - 7:4(015), pp Avalablty: Ths verson s avalable at: 11583/ snce: T15:8:47Z Publsher: Taylor and Francs Publshed DOI: / Terms of use: openaccess Ths artcle s made avalable under terms and condtons as specfed n the correspondng bblographc descrpton n the repostory Publsher copyrght (Artcle begns on next page) 4 December 018

2 Prortzaton of QFD Customer Requrements based on the Law of Comparatve Judgments Forenzo Franceschn 1 and Domenco Masano 1 forenzo.franceschn@polto.t Poltecnco d Torno, DIGEP (Department of Management and Producton Engneerng), Corso Duca degl Abruzz 4, 1019, Torno (Italy) Abstract Qualty Functon Deployment (QFD) s a useful tool to mprove the desgn/development process of products and servces. The ntal phases of the QFD process.e., those concernng the collecton and analyss of the so-called Voce of the Customer are probably the most crtcal, because any dstorton can propagate to the whole process results, makng t neffectve or even msleadng. The focus of ths paper s on the phase of prortzaton of customer requrements (CRs). There are numerous technques for ths task; however () the smplest often ntroduce questonable or unrealstc assumptons, whle () the most sophstcated often requre too much elaborate and repettous nformaton from customers, whch may lead to nconsstences. Ths paper ntroduces a new prortzaton technque based on the Thurstone s Law of Comparatve Judgment. Ths technque makes t possble to aggregate the evaluatons by multple respondents and transform them nto an nterval scale, whch depcts the relatve mportance of CRs. The greatest strength of ths technque s combnng a refned theoretcal model wth a smple and userfrendly data collecton process. The descrpton s supported by a realstc applcaton example concernng the prortzaton of QFD s CRs n the desgn of an arcraft seat. Keywords: QFD, Customer requrements, Prortzaton, Relatve mportance ratngs, Law of Comparatve Judgment, Thurstone scalng, Interval scale. 1. Introducton and lterature revew Qualty Functon Deployment (QFD) s a powerful technque to ncrease the customer satsfacton of product and servces. The mplementaton of QFD may generate sgnfcant mprovements n the desgn/development process, such as fewer and earler desgn changes, mproved cross-functonal communcatons, mproved product/servce qualty, and reduced development tme and cost (Hauser and Clausng, 1988; Grffn and Hauser, 1993; Tran and Sherf, 1995; Franceschn, 00). These mprovements are crtcal success factors to companes n a global marketplace characterzed by ntense nternatonal competton. The great dffuson of QFD s demonstrated by the lterally thousands of scentfc publcatons llustratng a varety of ndustral applcatons, methodologcal mprovements, new varants, and possble ntegraton wth other tools. 1

3 Typcally, QFD utlzes four sets of matrces the so called Houses of Qualty (HoQs). The four HoQs respectvely translate () customer requrements (CRs) nto engneerng characterstcs and, n turn, nto () parts characterstcs, () process plans, and (v) producton requrements (Franceschn, 00). For detaled nformaton, we refer the reader to the vast lterature and extensve revews, e.g., (Chan and Wua, 00; Sharma et al., 008). The customer nput, also defned as Voce of the Customer (VoC), s the key startng pont for QFD process; f t does not accurately reflect what the customer expects from the product/servce of nterest, the process may lead to ncorrect conclusons (Srel et al, 007). Therefore, the frst HoQ, also defned as Product Plannng HoQ, s of fundamental and strategc mportance (Gonzalez et al. 003). The Product Plannng HoQ constructon process can be summarzed nto ten phases, as shown n Fg. 1. Phase 6 Correlatons between the Hows Phase 5 Engneerng Characterstcs (Hows) Phase 1 Phase Phase 7 Phase 3 Phase 4 Customer Requrements (Whats/VoC) Relatve Importance Ratngs Relatonshps between the Whats and the Hows Compettve Prorty Ratngs Fnal Importance Ratngs Phase 8 Engneerng Ratngs Phase 9 Engneerng Compettve Evaluaton Phase 10 Fnal Engneerng Ratngs Fg. 1. Man phases of the Product Plannng HoQ constructon process. Among these phases descrbed n detal n the lterature, e.g., see (Chan and Wua, 00; Franceschn, 00; Franceschn and Rossetto, 00) partcularly sgnfcant are those related to the VoC collecton and analyss. The ntal phase (.e., Phase 1, Customer Requrements, n the scheme n Fg. 1) concerns the VoC collecton through ntervews and questonnares and analyss, n order to determne an exhaustve lst of CRs. For ths task, t s necessary to select a representatve sample of (potental) customers, wth reasonable knowledge of the product/servce to be desgned. It was found emprcally that samples consstng of 0 to 30 respondents are suffcent to cover most CRs; also, for data collected to be reasonable and applcable, respondents have to gan a full understandng of the task requred (Urban and Hauser, 1993). In the second part of ths phase, a cross-functonal team of experts composed of members from

4 marketng, desgn, qualty, fnance and producton have to revew, reorganze and nsert the CRs nto the Product Plannng HoQ. The next stage, whch s the focus of ths paper, s that of the prortzaton of CRs (.e., Phase, Relatve Importance Ratngs, n the scheme n Fg. 1), presumng that the man CRs related to the product/servce to be desgned have already been dentfed n Phase 1. The expresson Relatve Importance Ratngs ndcates that ths prortzaton s amed at dscrmnatng a CR based on ts mportance over the others. On the other hand, Phase 4, Fnal Importance Ratngs (n Fg. 1), denotes a prortzaton that also takes nto account the comparson of qualty performance of the products/servces of the company and those of ts compettors. In Phase, a sample of customers generally the same nvolved n Phase 1 have to prortze the QFD s CRs usng several possble approaches. Some of them are pont drect scorng method (Hauser and Clausng, 1988; Grffn and Hauser, 1993), analytc herarchy process (AHP) (L et al., 009; Chuang, P.T., 001), analytc network process (ANP) (Karsak et al., 00; Lee et al., 008), outrankng methods (Franceschn and Rossetto, 1995; Fguera et al., 005), fuzzy varants (Chan et al., 1999; Kwong and Ba, 00; Buyukozkan et al., 004), and technques derved from the Kano model (Matzler and Hnterhuber, 1998; Srel et al., 007; Chaudha et al., 011). Wthout gong nto these technques n detal, we remark that they may use dfferent knds of response data and elaboratons from respondents. Even though all these technques are supposed to reflect the VoC, sometmes they may lead to msleadng results, especally when the data collecton approach s too complex and elaborate. Here are some examples: Technques based on the AHP and ANP method requre CR udgments n the form of pared comparson data, defned on a rato scale; e.g. CR 1 s twce as mportant as CR (Chuang, 001; Franceschn, 00; Kwong and Ba, 00; Lee et al., 008, L te al., 009). These evaluatons are nevtably arbtrary and subectve as respondents may fnd t dffcult to express ther udgments on ths scale. Technques that ntegrate the Kano model n the QFD envronment requre relatvely complex questonnares (Nahm et al., 013) and the defnton of arbtrary weghts for the (qualtatve) Kano categores (.e., basc or must-be (B), one dmensonal (O), attractve (A), ndfferent (I), reverse (R) and questonable (Q) (Tan and Shen, 000)). Other sophstcated technques for the CR prortzaton, such as that proposed by Nahm et al. (013), model the uncertanty n customer requrements, takng nto account the uncertanty of customer s udgment. Unfortunately, they generally nclude complex and structured questonnares and, sometmes, ntroduce questonable assumptons n the response data processng. In the classcal questonnares for prortzng QFD s CRs, respondent udgements are defned on a 5-level ratng response scale (1=Not at all mportant, =Low mportance, 3=Medum 3

5 mportance, 4=Hgh mportance and 5=Very hgh mportance). Ths response scale has two nherent lmtatons: 1. Snce t s an ordnal scale, t only allows comparsons lke CR 1 s more mportant than CR. Unfortunately, a typcal abuse s promotng ths scale to an nterval or even rato scale, so as to make ncorrect comparsons lke the dstance, n terms of mportance, between CR 1 and CR s greater than that between CR 3 and CR 4 or CR 1 s three tmes more mportant than CR (Stevens, 1946; Berko, Kloeber, Deckro, 00; Franceschn, 007).. These scales are used subectvely, as there s no absolute reference shared by all respondents. In general, ndulgent respondents wll tend to assgn hgher levels of mportance, whle severe respondents wll tend to assgn lower ones. For example, let us consder the ratngs about three CRs (.e., CR 1, CR and CR 3 ) by two fcttous respondents (A and B). These ratngs on a 5-level scale are respectvely A: 3,, 1, and B: 5, 4,. Despte the relatve rankngs are dentcal (.e., CR 1 > CR > CR 3 ), udgments by A (severe respondent) are concentrated n the lowest levels of the scale, whle those of B (ndulgent respondent) n the hghest. For ths reason, t s questonable to aggregate udgments by dfferent respondents through ndcators of central tendency, such as the medan or the mean value. The obectve of ths paper s to ntroduce a smple technque for the CR prortzaton, based on the so-called Thurstone s Law of Comparatve Judgement, for aggregatng the udgments by multple respondents and transformng them nto a numercal nterval scale (Thurstone, 197). An mportant beneft of ths technque s combnng a smple and user-frendly data collecton process based on the defnton of respondent udgements on a 5-level ordnal scale wth a refned theoretcal model. The remander of ths paper s structured nto three sectons. Sect. provdes some background nformaton, whch s helpful to grasp the logc of the novel prortzaton technque: () basc concepts concernng the Thurstone model and () descrpton of a process for dervng response data sutable to ths model, keepng data collecton as smple and user-frendly as possble. Sect. 3 shows a realstc applcaton example concernng the prortzaton of the QFD s CRs n the desgn of an arcraft seat for passengers. The concludng secton summarzes the orgnal contrbutons of the paper, focusng on the benefts and lmtatons of the proposed technque, and possble future research.. Background Informaton.1 Bascs of Thurstone s Law of Comparatve Judgement In 197, Thurstone presented hs Law of Comparatve Judgement (LCJ),.e., a mathematcal model 4

6 to estmate scale values based on bnary choces between stmul (Thurstone, 197). The explanaton of ths model wll refer to the problem of the relatve mportance prortzaton of QFD s CRs, on the bass of the VoC. Thurstone postulated that each stmulus (CR n ths case) wll possess some attrbute (mportance level n ths case) n varyng but unknown degrees. For each of the CRs and among all subects, t s assumed that a preference wll exst. These two condtons mply the assumpton of undmensonalty of the scale representng the mportance of CRs (McIver and Carmnes, 1981). It s also assumed that, for each -th CR, the preference wll be dstrbuted normally,.e., CR ~ N(, ), beng and the unknown mean value and varance of that CR. A person s preference for each CR versus every other CR s thereby obtaned. The more persons who select one CR of a par over the other CR, the greater the mportance for that CR, and thus the greater ts scale weght (Edwards, 1957). Thurstone s LCJ s an ndrect form of measurement based on a transformaton of ndvdual preferences (nput data) nto scale values on a psychologcal contnuum. Such ndrect approaches are referred to as scalng processes. There are many scalng models; the most well known are the Rasch model (Rasch, 1966; Jansen, 1984) and conont analyss (Luce and Tukey, 1964). In addton, the LCJ model s based on dervng group scale values from dspersed ndvdual choce data. Therefore, t can be also consdered as a statstc choce model. In Thurstone s termnology, choces are medated by a dscrmnal process. He defnes ths as the process by whch an ndvdual dentfes, dstngushes, or reacts to stmul. Let us consder the theoretcal dstrbutons of the dscrmnal process for any two CRs, CR and CR (see Fg. (a)). In the LCJ model, the dstrbuton assocated wth a gven CR s characterzed by a dsperson (or varance) of that CR, whch reflects the subect-to-subect varablty. Dspersons may be dfferent for dfferent CRs. Let and correspond to the (unknown) scale values of the two CRs and and the (unknown) varances. The dfference (CR = CR CR ) wll follow a normal dstrbuton wth parameters: and. (1) where: and denote the (unknown) mean values of CR and CR ; and denote the (unknown) varances of CR and CR ; denotes the (unknown) correlaton between the pars of dscrmnal processes CR and CR. Consderng the area subtended by the dstrbuton of CR, let us draw a vertcal lne passng through the pont wth CR = CR CR = 0 (see Fg. (b)). The area to the rght of the lne depcts the observed proporton of tmes (p ) that CR 0. Of course, the area to the left depcts the 5

7 complementary proporton (1 p ). (a) CR, CR ~ N, ~ N undmensonal scale (psychologcal contnuum) (b) z Φ 1 1 p 1 p CR ~ N, 0 CR CR CR Fg.. (a) Theoretcal dstrbutons of the dscrmnal process for two CRs (.e., CR and CR ). (b) Lnk between CR = CR CR, and z,.e., the unt normal devate correspondng to the probablty 1 p, beng p = Pr(CR 0). In the standard method of Thurstone scalng, the pared comparson approach s used to collect response data. Under the protocol, respondents are forced to express a preference for one CR over another (.e., by askng them to rank order CRs two at a tme rather than all at once). All possble n n ( n ) pars are assessed, n beng the number of CRs of nterest. Pared comparson data of each respondent are reported nto a bnary matrx (B). For the purpose of example, Fg. 3(a) shows three matrces (B 1, B and B 3 ) related to three fcttous respondents. The element of the sngle respondent s matrx s 1 when the CR n the -th row s preferred to that n the -th column. If two CRs have dentcal level of mportance (e.g., CR 3 and CR 4 n matrx B 1 ), ther mutual pared comparsons are conventonally 0.5. After the total pars of CRs have been determned for a large number of respondents (N), respondents matrces can be summed nto a sngle frequency matrx (F), whose general element f represents the number of tmes that CR was preferred to CR. Fg. 3(b) reports the matrx F aggregatng the udgment matrces B 1, B and B 3. The general element f, whch appears n the -th row and -th column, denotes the observed number of tmes that CR was udged better or worse than CR. f Matrx P (Fg. 3(c)) s constructed from matrx F ( p ). The element p s the observed N proporton of tmes that CR was chosen over CR. Symmetrc cells now sum to unty. Interpretng p n probablstc terms, t can be stated that p = Pr(CR 0). Snce CR follows a normal dstrbuton, a standardzed varable can be defned: 6

8 z CR, () where the element z s the unt normal devate. For CR = 0 the unt normal devate s determned by the theoretcal proporton (1 p ),.e., z = -1 (1 p ), beng the cumulatve dstrbuton functon of the standard normal dstrbuton (see Fg. (b)). The element z wll be postve for all values of (1 p ) over 0.50 and negatve for all values of (1 p ) under (a) Respondent pared comparson matrces Respondent 1 B 1 = CR CR CR CR CR CR CR CR (b) matrx F f denotes the number of tmes that CR s preferred to CR CR * 0.00* Respondent B = CR CR CR CR CR * CR3 1.00* CR4 1.00* 1.00* (c) matrx P p denotes the proporton of tmes that CR s preferred to CR CR Respondent 3 B 3 = CR CR CR CR CR CR CR / n (d) matrx Z z = -1 (1 p ) (e) Thurstone scale (arbtrary zero) Fg. 3. Man steps of Thurstone scalng. In detal, for CR = 0, Eq. becomes: z 0 z, wth z = -1 (1 p ). (3) Combnng the second formula n Eq. 3 wth the expresson of n Eq.1, we obtan: z, (4) Matrx P s used to construct matrx Z (see Fg. 3(d)), the basc transformaton matrx. Zeros are entered n the dagonal cells n matrx Z because we can ordnarly assume that here = 0. Apart from the aforementoned assumptons, the Thurstone model consdered here s based on the 7

9 followng further hypotheses: CRs are udged dfferently by subects; f all subects would express the same preference for each outcome, the model would not be vable (proportons of 1.00 and 0.00 n the matrx P cannot be used because the z values correspondng to these proportons are ). Ths s the case for the par-wse comparsons CR 1 and CR 3, CR 1 and CR 4, and CR and CR 4 n the matrx P n Fg. 3(c): n every comparson the second CR s unanmously preferred to the frst. A smplfed approach for tacklng ths problem s assocatng values of p wth z = -1 ( ) = 3.09 and values of p wth z = -1 ( ) = (see the tems marked wth * n the matrx P n Fg. 3(c)). More sophstcated solutons to deal wth ths ssue have been proposed (Edwards, 1957; Krus and Kennedy, 1977). As a further practcal assumpton, t s assumed that the CRs standard devatons are all equal ( = = = ). Therefore Eq. 4 turns nto: z 1, (5) It s further assumed that the ntercorrelatons are all equal to one another (, Eq. 5 turns nto:, ), so that z 1, (6) More precsely, Thurstone (197) states that n a pared udgment n whch the evaluaton of one of the stmul has no nfluence on the evaluaton of the other stmulus, the correlaton s lkely to be very low and possbly even zero. Also, the assumpton that the ntercorrelatons are all equal to zero s relatvely safe when () the set of stmul s rather varegated 1 and () the group of respondents s not too small. Snce, n the case of the QFD s CR prortzaton, both these condtons are generally satsfed, t does not seem unreasonable to assume that 0,,. Then, under the assumptons we have made, 1 (or n the case s assumed to be zero) wll be a constant and s the common scale factor of the varous arthmetc mean pars of CRs. Wthout any loss of generalty, ths common scale factor s set to 1, so that: z. (7) Eq. 7, wth the assumptons nvolved n ts dervaton, s commonly referred to as Case V of the LCJ (Thurstone, 197). Now we can show that Thurstone scale values for each CR can be obtaned from the elements of the matrx Z. Actually, f we sum the entres n the -th column of the matrx Z, we obtan: 1 The adectve varegated ndcates that the stmul of nterest represent dfferent basc concepts, not the same one, ust stated n dfferent ways. 8

10 n 1 where n z n, (8) n z 1 1 n 1 means that the -th column s held constant and the summaton s over the n rows of the table. The frst term on the rght s the sum of the scale value of the -th CR and the second term s the sum of the scale values of all n CRs on the psychologcal contnuum. Dvdng both sdes of Eq. 8 by n, we have: n n z 1 1 z n n, (9) beng: z the arthmetc mean of the entres n the -th column of the matrx Z; the arthmetc mean of the (n) values; the mean value of the -th CR. Thus we see that the mean of the z values n the -th column of the matrx Z expresses the mean value of -th CR n terms of ts devaton from the mean of all the values (.e., ). Ths procedure can be appled to every column of matrx Z, n order to obtan the scale values of every CR. These values are shown n the second row at the bottom of matrx Z (Fg. 3(d)) and graphcally represented n Fg. 3(e). As a check upon calculatons, we observe that the sum of the scale values n devaton form s equal n to zero ( z n n 0 ). CRs wth negatve scale values are thus udged to be 1 n 1 n 1 less favourable than the average of the scale values of all CRs and those wth postve scale values are udged to be more favourable than the average. Snce the scale orgn taken as the mean of the scale values of the CRs on the psychologcal contnuum s arbtrary, we can apply a permssble scale transformaton (.e., monotoncally ncreasng lnear functon (Stevens, 1946)), so as to obtan numercal values easer to handle. Ths wll not change the relatve poston of the scale values on the psychologcal contnuum.. Practcal response mode As shown n Sect..1, n the standard method of Thurstone scalng, the pared comparson approach s used to collect response data. A drawback of ths approach s that t can be tedous and complex to manage for n greater than 4 or 5, snce t requres so much repettous nformaton from respondents. An alternatve response mode, whch also yelds data sutable for Thurstone scalng, s based on two steps: 9

11 1. Turnng each respondent s udgments, typcally expressed on a 5-level ratng scale (see Fg. 4(a)), nto rank order data (see Fg. 4(b)).. For each respondent, rank order data can be transformed nto pared comparson data and reported nto a matrx (see Fg. 4(c)). The element of the sngle respondent s matrx s 1 when the CR n the -th row s preferred to that n the -th column. If two CRs have dentcal level of mportance, ther mutual pared comparsons are conventonally 0.5. The response mode based on a 5-level ratng scale as well as beng less tedous and tme consumng than the pared comparson approach forces the respondent to be transtve (e.g., f CR 1 > CR and CR > CR 3, then CR 1 > CR 3 ). Also, t s generally famlar to respondents and therefore less subect to msnterpretaton. (a) Respondent udgments Importance level (b) Rank order data (c) Respondent s matrx wth pared comparson data Respondent 1 CR1 CR CR3 Not at all Low Medum Hgh Very hgh (CR 3 ~ CR 4) > CR 1 > CR B 1 = CR CR CR CR CR4 Importance level Respondent CR1 CR CR3 Not at all Low Medum Hgh Very hgh CR 4 > (CR ~ CR 3) > CR 1 B = CR CR CR CR CR4 Importance level Respondent 3 CR1 CR CR3 Not at all Low Medum Hgh Very hgh CR 3 > CR 4 > CR 1 > CR B 3 = CR CR CR CR CR4 Fg. 4. Process for dervng pared comparson data based on respondents udgments, defned on a 5-level ratng scale. The bnary matrces (B 1, B and B 3 ) n (c) are derved from the results of the questonnares n (a). The same three fcttous respondents ntroduced n Fg. 3 are consdered. In (b), symbols ~ and > respectvely mean ndfferent to and preferred to. 3. Applcaton example To exemplfy the performance of the proposed approach, ths secton llustrates an example about the CR prortzaton for a cvlan arcraft seat, from the perspectve of passengers. 10

12 Through market survey, a sample of 30 respondents.e., regular ar passengers are selected to dentfy the CRs by ndvdual ntervew, focus groups and exstng nformaton. Fnally, 1 maor CRs (reported n Tab. 1) are dentfed to represent the maor concerns of customers. Then, a questonnare for assessng the level of mportance of each of the 1 CRs s submtted to each of the respondents. Results, defned on a 5-level ratng scale, are reported n Tab. A.1 (n the appendx). Abbr. Descrpton CR 1 Comfortable (does not gve you back ache) CR Enough leg room CR 3 Comfortable when you reclne CR 4 Does not ht person behnd when you reclne CR 5 Comfortable seat belt CR 6 Seat belt feels safe CR 7 Arm rests not too narrow CR 8 Arm rest folds rght away CR 9 Does not make you sweat CR 10 Does not soak up a splt drnk CR 11 Hole n tray for coffee cup CR 1 Magaznes can be easly removed from rack Tab. 1. Lst of the maor CRs related to an arcraft seat, from the perspectve of passengers. For each respondent, udgements are then transformed nto ranked order data and, n turn, nto pared comparson data, accordng to the procedure descrbed n Sect... For example, as regards the respondent 1, rank order data are (CR 5 ~ CR 7 ) > (CR 1 ~ CR 3 ~ CR 6 ) > (CR ~ CR 8 ~ CR 9 ) > CR 10 > (CR 4 ~ CR 11 ~ CR 1 ), whch are transformed nto the matrx n Fg. A.1 (n the appendx). We remark that, consstently wth the conventon ntroduced n Sect..1, the mutual pared comparsons of two CRs wth dentcal mportance are both 0.5 (e.g., see CR 1 and CR 8 or CR 1 and CR 1 n the matrx n Fg. A.1 (n the appendx). Next, the pared comparson data matrces relatng to the 30 respondents are summed nto a sngle frequency matrx (F), n Fg. A. (n the appendx). The matrx F s transformed nto the matrx P (n Fg. A.3, n the appendx) and subsequently nto the matrx Z (n Fg. A.4, n the appendx). Accordng to the conventon llustrated n Sect..1, for p and p 0.999, z values have been set to and respectvely (see the p values marked wth *, n the matrx P (Fg. A.3, n the appendx). Thurstone scale values for each CR are fnally calculated through the mean value of the column elements of the matrx Z (see the second row at the bottom of matrx Z, n Fg. A.4 n the appendx). Snce the unt and the orgn of the resultng nterval scale are both arbtrary, we can transform the scale values so that they are ncluded n the nterval [1; 5], accordng to the transformaton: ' max mn mn, (10) beng: 11

13 the scale value related to the -th CR, resultng from Thurstone scalng; the transformed scale value related to the -th CR n the nterval scale [1, 5]. Fg. 5 provdes a graphcal representaton of the Thurstone scale values, before and after the transformaton n Eq. 10. Ths transformaton s nothng else than a monotoncally ncreasng lnear functon of the type: = a + b, (11) beng: max( ) 5 mn( ) 4 a and b 0. max( ) mn( ) max( ) mn( ) Ths transformaton eases Phases 4 and 8 of the Product Plannng HoQ constructon process (n Fg. 1), snce they are tradtonally based on CR mportance levels defned on a 1 to 5 scale. (a) CR 10 CR 1 CR 11 CR 8 CR 4 CR 3 CR 9 CR 6 CR 7 CR CR 5 CR (b) CR 10 CR 1 CR 11 CR 8 CR 4 CR 3 CR 9 CR 6 CR 7 CR CR 5 CR Fg. 5. Resultng Thurstone scale values (a) before and (b) after the scale transformaton n Eq Concludng remarks The followng three subsectons respectvely dscuss () the benefts of the proposed procedure, () ts lmtatons and () some deas for future research. 4.1 Benefts The proposed procedure allows aggregaton of the typcal CR udgments generally expressed on ordnal response scales nto a contnuous nterval scale, avodng the typcal abuses (e.g., arbtrary promoton of the scale propertes) of the classcal approaches (Franceschn et al., 007). Unlke other methods, such as the AHP, ANP or Kano model, the proposed procedure does not requre complcated elaboratons by respondents. Partcularly n populatons n whch educatonal attanment and numeracy are lmted, a smple measurement strategy may have consderable practcal advantages over more complex technques, such as ease of comprehenson and greater relablty due to reduced measurement error. However, the fact remans that the Thurstone model can be extended to more complex response modes, such as questonnares n 1

14 whch CRs are ordered or compared n pars by each respondent. The Thurstone model s relatvely robust to ncomplete data, lke the omsson of a porton of udgments by respondents. When the ncdence of ncomplete data s hgh, the model presented can be replaced by more refned ones, and t s also possble to check the nternal consstency of the results obtaned (Thurstone, 197; Edwards, 1957). However, f CRs were dentfed correctly, the amount of omtted udgments should not be too large. The opposte could mean that the CRs n use do not reflect the real needs of the customer. 4. Lmtatons Lke any model, that of Thurstone s based on several assumptons, such as, () the phenomena to be scaled must le on a latent undmensonal scale, () the model s based on the normal dstrbuton of stmul, and ( ) dsperson and correlaton of the stmul are assumed to be equal. Some of these assumptons can be relaxed when usng more sophstcated but also complex varants of the proposed model (Maydeu-Olvares and Böckenholt, 008). The 5-level ratng scale for CR udgments s smple and ntutve for the respondent but has a relatvely lmted resoluton. In some cases, ths can make the analyss uncertan, snce t may generate a sgnfcant number of tes (.e., CRs wth dentcal levels of mportance), when udgments are transformed nto pared comparson data. The problem can be solved by usng alternatve response scales wth a larger number of levels, or questonnares n whch the CRs are ranked or compared n pars by each respondent. As for most of the statstcal models, the larger the sample of respondents, the more reasonable and robust results wll be. Thurstone (197) recommends that there be at least a few tens of respondents. Ths seems to be n lne wth the typcal amount of customers nvolved n the ntal phases of QFD process. 4.3 Ideas for future research Further research should nvestgate the relatonshp between results acqured from dfferent technques for CR prortzaton. Moreover, the use of Thurstone LCJ could be extended to other prortzaton processes wthn QFD, such as Phases 3 and 9 n Fg. 1. References Buyukozkan, G., Ertay, T., Kahraman, C., Ruan, D. (004) Determnng the mportance weghts for the desgn requrements n the house of qualty usng the fuzzy analytc network approach. Internatonal Journal of Intellgent Systems, 19(5): Burke E., Kloeber Jr J.M., Deckro R.F. (00) Usng and Abusng QFD Scores. Qualty Engneerng, 15(1):9-1. Chan, L.K., Wua, M.L. (00) Qualty Functon Deployment: A Comprehensve Revew of Its Concepts and Methods. Qualty Engneerng, 15(1): Chan, L.K., Kao, H.P., Wu, M.L. (1999) Ratng the mportance of customer needs n qualty functon 13

15 deployment by fuzzy and entropy methods. Internatonal Journal of Producton Research, 37(11): Chaudha, A., Jan, R., Sngh, A.R., Mshra, P.K. (011) Integraton of Kano s model nto qualty functon deployment (QFD). Internatonal Journal of Advanced Manufacturng Technology, 53(5-8): Chuang, P.T. (001) Combnng the analytc herarchy process and qualty functon deployment for a locaton decson from a requrement perspectve. Internatonal Journal of Advanced Manufacturng Technology, 18(11): Edwards, A.L. (1957) Technques of Atttude Scale Constructon. Irvngton Publshers, New York. Fguera, J., Greco, S., Ehrgott, M. (005) Multple crtera decson analyss: state of the art surveys. Sprnger, New York. Franceschn, F. (00) Advanced Qualty Functon Deployment, St. Luce Press/CRC Press LLC, Boca Raton, FL. Franceschn, F., Rossetto, S. (1995) QFD: the problem of comparng techncal/engneerng desgn requrements. Research n Engneerng Desgn, 7(4): Franceschn, F., Rossetto, S. (00) QFD: an nteractve algorthm for the prortzaton of product s techncal desgn characterstcs. Integrated Manufacturng Systems, 13(1): Franceschn, F., Galetto, M., Masano, D. (007) Management by Measurement: Desgnng Key Indcators and Performance Measurement Systems. Sprnger, Berln Gonzalez, M.E., Quesada, G., Bahll, A.T. (003) Improvng product desgn usng qualty functon deployment: the school furnture case n developng countres. Qualty Engneerng, 16(1): Grffn, A., Hauser, J.R. (1993) The voce of customer. Marketng Scence, 1(1): 1-7. Hauser, J.R., Clausng, D. (1988) The house of qualty. Harvard Busness Revew, 66(3): Karsak, E.E., Sozer, S., Alptekn, S.E. (00) Product plannng n qualty functon deployment usng a combned analytc network process and goal programmng approach. Computers & Industral Engneerng, 44: Krus, D.J., Kennedy, P.H. (1977) Normal scalng of domnance matrces: The doman-referenced model. Educatonal and Psychologcal Measurement, 37: Kwong, C.K., Ba, H. (00) A fuzzy AHP approach to the determnaton of mportance weghts of customer requrements n qualty functon deployment. Journal of Intellgent Manufacturng, 13(5): Jansen, P.G.W. (1984) Relatonshps between the Thurstone, Coombs, and Rasch approaches to tem scalng. Appled Psychologcal Measurement, 8: Lee, Y.T., Wu, W.W., Tzeng, G.H. (008) An effectve decson-makng method usng a combned QFD and ANP approach. WSEAS Transactons on Busness and Economcs, 1(5): L, Y., Tang, J., Luo, X., Xu, J. (009) An ntegrated method of rough set, Kano s model and AHP for ratng customer requrements fnal mportance. Expert Systems wth Applcatons, 36(3): Luce, R.D., Tukey, J.W., (1964) Smultaneous conont measurement: a new type of fundamental measurement. Journal of Mathematcal Psychology, 1(1):1-7. Maydeu-Olvares, A., Böckenholt, U. (008) Modelng subect health outcomes. Top 10 reasons to use Thurstone s method. Medcal Care, 46(4): Matzler, K., Hnterhuber, H.H. (1998) How to make product development proects more successful by ntegratng Kano s model of customer satsfacton nto qualty functon deployment. Technovaton 18(1): McIver, J.P., Carmnes, E.G. (1981) Undmensonal Scalng. Beverly Hlls, CA: Sage Publcatons; Nahm, Y.E., Ishkawa, H., Inoue, M. (013) New ratng methods to prortze customer requrements n QFD wth ncomplete customer preferences. Internatonal Journal of Advanced Manufacturng Technology, 65(9-1): Rasch, G. (1966) An tem analyss whch takes ndvdual dfferences nto account. Brtsh Journal of Mathematcal and Statstcal Psychology, 19(1): Srel, Y., Kauffmann, P., Ozan, E. (007) Integraton of Kano s model nto QFD for multple product desgn. IEEE Transactons on Engneerng Management, 54(): Sharma, J.R., Rawan, A.M., Barahate, M. (008) Qualty functon deployment: a comprehensve lterature revew. Internatonal Journal of Data Analyss Technques and Strateges, 1(1): Stevens, S.S. (1946) On the Theory of Scales of Measurement. Scence, 103(684): Tan, K.C., Shen, X.X. (000) Integratng Kano s model n the plannng matrx of qualty functon deployment. Total Qualty Management, 11(8): Thurstone, L.L. (197) A law of comparatve udgments. Psychologcal Revew, 34: Tran, T.L., Sherf, J.S. (1995) Qualty functon deployment (QFD): an effectve technque for requrements 14

16 acquston and reuse. Proceedngs of the nd IEEE Software Engneerng Standards Symposum, Montreal, Canada, Urban, G.L., Hauser, J.R. (1993) Desgn and marketng of new products (Vol. ). Englewood Clffs, NJ: Prentce Hall. Appendx See the followng Fgures and Tables. Respondent No. CR 1 CR CR 3 CR 4 CR 5 CR 6 CR 7 CR 8 CR 9 CR 10 CR 11 CR Tab. A.1. Levels of mportance assgned by 30 respondents to the CRs, through a 5-level ratng scale (1=Not at all mportant, 5=Very hgh mportance). 15

17 CR 1 CR CR 3 CR 4 CR 5 CR 6 CR 7 CR 8 CR 9 CR 10 CR 11 CR 1 CR CR CR CR CR B 1 = CR CR CR CR CR CR CR Fg. A.1. Pared comparson data relatng to the udgments by respondent 1, n Tab. A.1. CR 1 CR CR 3 CR 4 CR 5 CR 6 CR 7 CR 8 CR 9 CR 10 CR 11 CR 1 CR CR CR CR CR F = CR CR CR CR CR CR CR Fg. A.. Matrx F, obtaned from the pared comparson data orgnated from the respondents udgments (n Tab. A.1). 16

18 CR 1 CR CR 3 CR 4 CR 5 CR 6 CR 7 CR 8 CR 9 CR 10 CR 11 CR 1 CR * * * 1.000* 1.000* CR * 1.000* 1.000* CR CR * CR * * 1.000* 1.000* P = CR * CR * 1.000* 1.000* CR * * CR CR * 0.000* * 0.000* 0.000* CR * 0.000* * * CR * 0.000* * * Fg. A.3. Matrx P, obtaned from the matrx F (n Fg. A.). CR 1 CR CR 3 CR 4 CR 5 CR 6 CR 7 CR 8 CR 9 CR 10 CR 11 CR 1 CR CR CR CR CR Z = CR CR CR CR CR CR CR = / n Fg. A.4. Matrx Z contanng the unt normal devates (z ) correspondng to the complementary probabltes (1 p ) to those n matrx P (p ). Values of p and (marked wth * n Fg. A.3) have been conventonally assocated wth z = and respectvely. 17