Available online at ScienceDirect. Procedia CIRP 53 (2016 ) 21 28

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1 vailable olie at ScieceDirect Procedia CIRP 53 (206 ) 2 28 The 0th Iteratioal Coferece o xiomatic Desig, ICD 206 systematic approach to couplig disposal of product family desig (part ): methodology * Correspodig author. address: rbxiao@63.com Rebi Xiao a, *, Xiafu Cheg b a School of utomatio, Huazhog Uiversity of Sciece ad Techology, Wuha , Chia b School of Mechaical ad Electroical Egieerig, East Chia Jiaotog Uiversity, Nachag 33003, Chia bstract I this paper, o the basis of compariso ad aalysis o the similarities ad differeces of desig couplig betwee product family ad sigle product, a systematic approach to couplig disposal of product family desig is proposed, ad couplig disposal flow of two level icludig strategy level ad operatio level is give. From strategy level of platform pla, axiomatic desig theory is utilized as framework to aalyze ad classify fuctioal requiremets, desig parameters are mapped with zigzaggig mode, ad platform parameters are idetified. I the view of platform operatio level, desig structure matrix (DSM) coverted by desig matrix DSM are clustered ad grouped ito modules, ad couplig correlatio matrix of product family desig is established, which ca realize high cohesio degree i a sigle module ad low couplig degree amog all the modules. The, from the couplig iside platform modules, iside customizatio modules, ad amog desig parameters with differet modules, the correspodig decouplig methods of product family desig are preseted, ad the methods architecture of to couplig disposal of product family desig is established. 206 The uthors. Published by Elsevier by Elsevier B.V. This B.V. is a ope access article uder the CC BY-NC-ND licese ( Peer-review uder resposibility of the scietific committee of The 0th Iteratioal Coferece o xiomatic Desig. Peer-review uder resposibility of the scietific committee of The 0th Iteratioal Coferece o xiomatic Desig Keywords: product family, coupled desig, couplig disposal, decouplig. Itroductio With the users icreasig demads for product customizatio ad the rapid developmet of iformatio techology, Mass Customizatio has recetly received a sigificat amout of attetios withi the busiess commuity []. Product family developmet has bee widely recogized as a effective way to implemet mass customizatio [2]. product family is a group of related products based o the same product platform by providig a variety of products for achievig the ecoomy of scale ad accommodatig the proliferatio of customized product variats across differet market segmets. Platform-based product family desig is a effective meas ot oly to capture total cost savigs ad speed time to market but also to maitai differetiatio ad competitiveess. However, the desig of a product family is typically more challegig tha desigig sigle product. I regard to the desig of product families, may literatures have bee published durig the last decades. variety of methods ad tools have bee extesively developed to support product family desig. Simpso [3] as well as Jose ad Tolleaere [4] provided comprehesive state-of-the-art reviews of modular desig, product family desig ad platform-based product developmet. Kumar et al. [5] proposed a methodology to desig product families itegratig market cosideratios to examie the impact of icreasig the product variety. Barajas ad gard [6] proposed a comprehesive methodology to form product families by takig advatage of the fuzzy logic to tackle ucertaities. Eichstetter et al. [7] preseted a approach to idetify compoets i order to optimize commoality for a product family of arbitrary high-dimesioal oliear systems The uthors. Published by Elsevier B.V. This is a ope access article uder the CC BY-NC-ND licese ( Peer-review uder resposibility of the scietific committee of The 0th Iteratioal Coferece o xiomatic Desig doi:0.06/j.procir

2 22 Rebi Xiao ad Xiafu Cheg / Procedia CIRP 53 ( 206 ) 2 28 There exist geerally relatioships betwee product variats i product family that cause physical couplig betwee product platforms ad it will icrease the difficulty of product desig. Thus the couplig should be avoided to the greatest extet. But i the actual product desig, due to techical or other limitatios, it is very difficult to get ucoupled desig or decoupled desig. Therefore, couplig problem i product desig has become oe of the key problems to be solved urgetly i egieerig ad idustry fields. Che ad Teg [8] itroduced the cocept ad descriptio methods of product desig couplig, elaborated the couplig aalysis method which was commoly used at preset ad its applicatio i product desig, ad discussed the compariso of the studies o direct couplig ad couplig propagatio ad the existig problems. Idepedece axiom i xiomatic Desig (D) theory provided the fudametal criterio to judge whether the desig is success or ot ad its improvemet directios [9]. For example, Johaesso [0] defied couplig fuctio as mutual egative effect betwee two subsystems while implemetig a fuctioal requiremet. Kag [] proposed usig TRIZ coflict matrix ito axiomatic desig, choosig appropriate ivetio priciple to decouple the couplig i axiomatic desig. Choi ad Hwag [2] proposed to represet the system structure usig the flow chart, takig axiomatic desig matrix as oliear, ad the aalysis the couplig relatioship betwee the various modules. Su et al [3] used the split algorithm to rearrage the desig matrix, measured the fuctio couplig through aalytic hierarchy process, ad searched the optimum ad iitial iteratio sequece of couplig fuctio through optimizatio algorithm. Lee [4] comprehesive cosidered the costs ad beefits of removig odiagoal elemets i the desig matrix ad achieved decouplig by determiig the miimum sequece odiagoal elemets. Based o the desig associatio, redesig divisio ad mode selectio, Che et al. [5] aalyzed the product iteral couplig relatioship ad put forward the decompositio couplig desig methods so as to realize the rapid redesig to support the product agile maufacturig. Cao et al. [6] proposed the structured couplig desig method based o the idepedece axiom, usig decompositio operatio to idetify the idepedet fuctio ad the couplig fuctio sets, applyig the pairwise compariso method ad triagular fuzzy umber to measure couplig fuctio. Yu et al. [7] based o the etwork aalysis method to study the iteractios betwee fuctioal requiremets i axiomatic desig, ad put forward the evaluatio algorithm i iteractio ad discrimiated method to determie whether the iteractio could be igored. Cai et al. [8] used the axiomatic desig theory to idetify the couplig fuctio while plaig the desig matrix, adopted systematic iovative thikig mode to describe the couplig problems, selected ad applied iovative thikig motivatio techiques to completely decouple the associated fuctioal requiremets. They also defied the cocept of fuzzy idepedet rage, put forward a decouplig method based o satisfactio, decouplig desig those couplig desig that violatio the idepedece axiom accordig to the satisfactio degree ad the fuzzy idepedet rage [9]. The above researches maily focus o the couplig desig problems of sigle product ad used the explicit way of product desig decouplig. This paper aims at the problem that the product family desig is uable to complete decouplig, ad discusses how to deal with physical couplig desig problem. This paper maily studies the couplig disposal strategy ad decouplig methods i product family desig. 2. Couplig aalysis ad processig i product family desig For sigle product desig, from the perspective of product fuctioality - parameter, the couplig problem ca be divided ito two categories: fuctioal couplig ad physical couplig. For fuctioal couplig, we ca use the idepedece axiom, guided by the zigzaggig mappig process i the adjacet domai of D framework, to decompose FRs ad adjust the desig matrix, ad reveal the iteractio betwee FRs ad DPs to idetify idepedet desig tasks ad couplig desig tasks. The fuctioal couplig is disposed by this way. For physical couplig that is also called parameter associatio, we ca use the Directed Graph, CMP (Critical Path Method), PERT (Program Evaluatio ad Review Techique), IDEF (Itegrated Defiitio Methods), Petri ets, DSM (Desig Structure Matrix) or other methods for couplig aalysis ad decouplig. Especially DSM method is widely used, ad it may make the desig task achieve the sequece optimizatio of desig tasks [20]. I product desig, there are two ways to deal with couplig problems: oe is the split method, ad the other is iteral iteratio method [2]. Therefore, desig couplig problem of sigle product maily determie the parameters or the properties of the task or iterative sequece from micro level, ad ca be used i customize desig as well as iovatio desig, to improve the desig efficiecy ad reduce the desig complexity. Product family refers to a group or a series of products. It is suitable to adaptability desig of the product, ad maily cosists of modular desig ad parametric desig. The purpose is to improve ad modify the existig products. Product family desig is based o commo platform ad derives series of products. Commo platform parameters reflect the uiversalities of product platform, ad idividual parameters reflect the differeces of product platform. Geerality ad differece of product platform is a pair of cotradictios. The more commo platform parameters, the better platform geerality, the lower desig cost, but the customizatio ability will become poorer ad ca t fully meet customers diverse demads. The less commo platform parameters, the lager platform diversity, the easier to satisfy the customized eeds, but the geerality will become less ad desig costs will icrease. I both modular ad parametric product family, the desig couplig ot oly has the characteristics of sigle product desig, but also takes the relatioship betwee product variats i product family ito cosideratio. Overall, there may be couplig relatioship betwee parameters i product family desig, ad there exist associatio relatioship ad

3 Rebi Xiao ad Xiafu Cheg / Procedia CIRP 53 ( 206 ) master-slave relatioship betwee commo platform parameters ad idividual parameter. Sice commo platform parameters caot deped o the idividual parameters, ad the idividual parameters caot affect the basic fuctioal requiremets, this is a oe-way relatioship. If the masterslave ad correlatio relatioships betwee idividual parameters ad commo platform parameters are igore, it is difficult to accurately describe the ature of product family couplig problems. Product platform plaig is desig for product family ad also follows the geeral laws of product desig. ccordig to the D priciple [9], ucouplig desig is the most satisfied i ay product desig. However, i actual product desig, completely ucouplig desig is rare. Most product desig is more or less couplig, just differet i the couplig degree. Product family desig is o exceptio, but accordig to the meas ad characteristics, the couplig betwee platform parameters ad o-platform parameters should be avoided. Strog associatio parameters are ot suitable to be platform parameters. Platform parameters ca have a weak effect o the o-platform parameters but o-platform parameters caot have a feedback effect o platform parameters, that s to say the ifluece is oe-way. Product family desig icludes both product platform desig ad member s desig of product family. Product platform desig measures the product family optimality from a macro level, while a sigle product desig is a special desig case i product family uder the costraits ad overall goal. It maily cosiders the techical optimizatio with "desig parameter". The couplig processig of product family desig icludes strategy level ad operatio level. Based o the viewpoit of platform strategy level, we maily cosider the user demad respose, fuctio demad aalysis ad modelig ad the platform flexible plaig uder the market segmetatio framework. Based o the viewpoit of platform operatio level, we maily trade off the geerality ad differece of product platform, cluster desig parameters ad determie the optimal values of desig parameters, so as to improve the robustess of product family desig ad reduce the couplig i desig. The couplig process of product family desig stated above is show i Fig.. 3. Couplig disposal of product family desig o strategy level Fuctioal requiremet aalysis is very importat i early product family desig. Suitable requiremets modelig ca reduce the desig couplig, shorte the product developmet cycle, ehace the robustess ad improve the adaptability of product family desig. Therefore, we should early pla related desig activities ad orgaizatios, aalysis the relatioship betwee product desig parameters ad the type of fuctioal requiremets, to set up fuctioal requiremets model reasoably. Fig.. The couplig disposal flowchart of product family desig. ccordig to Xiao et al. [22], we may divide fuctioal requiremets of the product ito basic fuctioal requiremets, expectable fuctioal requiremets ad additioal fuctioal requiremets. The divisio of fuctioal requiremet types ca help to aalyze the couplig relatio of product family better. Each product variat should meet the basic fuctio requiremets of product family ad the satisfy expectable fuctioal requiremets ad additioal fuctioal requiremets. Such a classificatio way of fuctioal requiremets ca better determie the structure of product platform, the compositio of product family ad the relatioship betwee family members. But it may lead to too little customizatio parameters ad too may platform parameters, ad ca oly use as prelimiary couplig aalysis of product family desig. ssumig the umber of fuctioal requiremets is. The basic fuctioal requiremets, expectable fuctioal requiremets ad additioal fuctioal requiremets are expressed i FR b FR e FR a respectively. The fuctioal requiremets FR = {FR b, FR e, FR a } T ={FR, FR 2,, FR } T. ccordigly, the desig parameter DP ={DP, DP 2, DP } T, DP decide the mai characteristic parameters ad structure desig parameters set of fuctioal requiremets characteristics i product family. The relatioship betwee desig parameters ad fuctio requiremets ca be writte as FR... DP FR FR FR b e a FR FRu FR u FRu FR u v v u u u u v, v,,... u, u, uv, uv, DP u DPu DPu DPu v DP v ()

4 24 Rebi Xiao ad Xiafu Cheg / Procedia CIRP 53 ( 206 ) 2 28 From the view of satisfyig customers demads, each DP correspods to oe FR of the product. Desig parameters that realize the basic or expectable fuctios of product family are defied as commo parameters ad platform parameters. Those realize additioal fuctioal requiremets are defied as custom parameters. D c, D p ad D r represet u commo parameters, v platform parameters ad w custom parameters respectively (u+v+w), DP ={D c, D p, D r } T. We ca get series of products depeds o differet values of desig parameters, i which the first p+q have the commo topology structure ad have less or eve igored effect o product fuctio. Their values are similar or withi a certai scope betwee differet product variats withi a give product family, they are commo platform parameters ad make up the matrix of product family. Sice the basic fuctioal requiremets of each product variat i the product family are the same, accordig to relatioship betwee FRs ad DPs ad characteristics aalysis of the product family platform, basic fuctioal requiremets are just affected by commo parameters ad should ot be affected by other desig parameters, ad commo parameters do ot deped o other desig parameters. That is b FRi 0, i, 2,, u; ju+, u+2,, (2) vw DPj Dci 0, i, 2,, u; ju+, u+2,, (3) vw DPj Similarly, platform parameters are shared by product family members ad should avoid couplig with custom parameters, its correspodig fuctioal requiremets would ot be affected by custom parameters. That is e FRi 0, i, 2,,v; ju+v+, p+2,, (4) w DP j D pi 0, i, 2,,v; ju+v +, u+v +2,, (5) w DPj Whe a fuctioal requiremet FR i has chaged due to customers idividual requiremet, the correspodig desig parameter DP i should adjust to satisfy this fuctioal requiremets. t the same time, the o-correspodig desig parameters DP j jimay also chage to elimiate the ifluece of DP i chaged. The greater ratio of DP i chaged with DP chaged, the smaller affect of this parameter o the other desig parameters, product variat is relatively easier, the desig parameters adaptability is better. Obviously, i the product family desig, o-couplig desig parameters are more flexibility, ad are more suitable for mass customizatio. Whe product family desig has satisfied idepedece axiom, it is effective ad easy to be implemeted to use formula (2) ~ formula (5) to idetify the commo platform parameters. But i geeral, there is the couplig i desig which makes it difficult to meet all the equatios above, thus lead to too less commo platform parameters. We ca cosider the differece betwee product variats at this time. I product family desig, whether product variats have i commo with a certai product desig parameter ca be cosidered i terms of diversity. ssumig i a product family, the desig parameters DP i of two product variats ad B is similar, their values are U(DP i ) ad U(DP B i ) respectively. The, the differece degree of these two desig parameter values ca be calculated by the followig formula B U ) U ) d B ) (6) B maxu ), U ) Differece degree matrix of m products sets up by the differece degree of desig parameter DP i ca be expressed as 0 d2 ) dm ) d2( DPi ) 0 d2m ) D ( DP ) i (7) dm( DPi ) dm2 ) 0 Differece degree matrix D(DP i ) shows the differece degree of product variats i oe product family about a desig parameter. The smaller differece degree about oe desig parameter, the less sesitive of this desig parameter, ad is more suitable to be a platform parameter. Through the above discussio o fuctioal requiremets, we ca pla platform desig activities reasoably based o the couplig relatioship aalysis betwee three types of fuctioal requiremets, thus support for the choice of platform parameters, ad reduce the couplig of product family desig from strategy aspect. 4. Product family decouplig desig based o couplig correlatio matrix 4.. Couplig correlatio parameters aalysis i product family Oce platform parameters of product family are determied, desig matrix obtaied by D ca be coverted to DSM. The we ca recostruct desig structure matrix. Firstly DSM is divided ito two parts, oe is desig parameters about commo platform, ad aother is idividual parameters orieted to idividual demads of the customers. Secodly clusterig algorithm is used to cluster ad geerate the clusterig modules so as to make the cohesive degree withi the modules as high as possible ad the couplig betwee modules as low as possible. Fially, the couplig betwee modules is aalyzed to fid a kid of desig with least couplig associatio betwee desig parameters. I this way, the product structure is divided ito several couplig modules with smaller depedece. The resultig matrix is called the couplig correlatio matrix of product family desig, as show i Fig. 2. The objective of clusterig modules i DSM is high cohesio degree i a sigle module ad low couplig degree amog all the modules. The relatioship betwee desig parameters relies o the desig team's experiece ad kowledge. Through the aalysis of desig parameters o fuctioal relevace, coectio relevace, physical relevace ad so o, we ca calculate the comprehesive relevace degree betwee desig parameters.

5 Rebi Xiao ad Xiafu Cheg / Procedia CIRP 53 ( 206 ) Dc+Dp Dr D DP c +D p D r B C 4 D 5 E Fig. 2. Couplig correlatio matrix of product family desig. I couplig correlatio matrix of product family desig, each elemet out of modules meas modules are related, as show i Fig. 2 with rig sig, makes various modules ca't be completely idepedet, which is couplig, ad affects the adaptability of product family desig. ccordig to the couplig correlatio matrix, we ca determie all associatio elemets, B, C, D ad E betwee modules ad coduct a test with them. They ca be cosidered as cotrollable factors i parameter desig, ad their impact o the target are aalyzed to implemet cotrol ad adjustmet, thus improve the robustess of product family desig ad reduce the couplig. I experimetal desig of couplig correlatio parameters, firstly we cosider the ifluece of the upper-left parameters, which is associatio elemets i the commo platform module (such as ad B). Especially whe there are commo parameters which are associatio parameters at the same time (such as ), we should determie their impact o the other modules, sice commo parameters are shared i product family ad ca oly chage withi a certai rage, their chage might cause the architecture chage i product family. Secodly we aalyze the iformatio commuicate relatioships of correlatio parameters i lower-left desig parameters (such as C ad D) to idividual parameters, to make idividual parameters be adapted to the chages of commo platform parameters. Fially we cosider the associatio parameters withi idividual parameters (such as E), sice idividual parameters ca't feedback to the commo platform, which is the primary differece betwee a sigle product desig ad product family desig Processig method for product family desig couplig Product family couplig ot oly affect a sigle product, but might also affect all the desigs of family members. Sice the platform is shared, products topology should remai the same, ad fuctio structure, orgaizatio behavior ad parameters specificatio are allowed to vary withi a certai rage. The platform structure should have certai adaptability ad have o or weak couplig relatio with o-platform structure ad oe-way ifluece it. Couplig relatio desig of product family icludes three parts, oe is iteral couplig of commo platform modules (hereiafter referred as platform module), the secod is iteral couplig of customizatio modules, ad the third is the couplig associatio of desig parameters betwee modules. For these three couplig relatios, we aalyze respectively ad propose correspodig methods to deal with couplig below The couplig iside platform module The couplig iside platform module should be give priority to, sice it would affect the two couplig coditios behid. Commo platform is equal to basic product i product family, its topology structure has bee fixed (regardless of the platform upgradig ad extesio) ad fuctioal domais remai the same, but the itesity or size of fuctioal requiremets may chage withi a certai specificatios by adjustig the correspodig parameter. Processig methods of couplig iside platform module is similar to that of the geeral couplig relatio of product desig, so we ca referece to the related decouplig method which ca be specific stated as follows. Reselect desig parameters or itegrate multiple desig parameters ito a physical part to reduce the ifluece betwee desig parameters, thus reduce the possibility of geeratig couplig relatios i the desig. This is the most effective ad preferred method to reduce the couplig. We cosider other decouplig method oly whe this method is difficult to achieve. Choose the correspodig key DP correspodig to FR. No-correspodig DP has small effect o FR. That s to say, FR should t be sesitive to desig parameters except the key desig parameter. For a couplig module, key desig parameter DP ic chose by fuctioal requiremet FR i should satisfy the followig coditios FRi FRi DPic DPj DP i =, 2,, (8) DP ic j j i j The module is weak couplig if it meets formula (8), otherwise it is a strog couplig. Weak couplig coditios ca be cosidered to be essece decoupled ad make it possible to desig i the case of less iteractio, which ca simplified the problem so as to reduce the iteratio ad shorte the desig cycle. For strog couplig, sice the commo platform is just the substrate of product family, desig target ad costraits ca't fully describe clearly, related cotet of desig also ca't completely decided. Therefore, it s a good way to deal with this kid of ucertaity kowledge through probability theory ad fuzzy logic. Decouplig method based o satisfactio, by defiig a miimum value satisfactio for fuctio requiremet, uder a certai approximatio or assumed coditios, elargig or decreasig the fuctioal requiremets scope to get a decouplig desig [9] The couplig iside customizatio module Similar to the couplig iside platform module, the couplig iside customizatio module is also divided ito weak couplig ad strog couplig. Idividual parameters aim at product family members, which is equivalet to the geeral sigle product. But their correspodig desig

6 26 Rebi Xiao ad Xiafu Cheg / Procedia CIRP 53 ( 206 ) 2 28 parameters ca ot affect product platform whe satisfy the product idividuatio demads, sice the platform structure has bee fixed. The decouplig method of weak couplig is the same as " () The couplig iside platform module". But strog couplig is differet, the desig goal ad costrait as well as the desig capacity have bee clear, structured couplig desig ad aalysis method could be take. Through decouplig, refactorig, split ad so o, we ca pla the couplig modules to determie the realizatio sequece of each fuctio. For the strog couplig, accordig to the size of couplig module, we decouple it i differet ways. If there were oly two FRs-DPs couplig desigs, we split the parameters ad aalyze the depedecies ad trasitive relatios betwee them to idetify the operatig parameters ad cotrolled parameters. Operatig parameters are cotrollable parameters, which affect the cotrolled parameters more tha deped o them, so the iterative sequece is from the cotrollable parameters to the cotrolled parameters. s the lower-right module of Fig. 2, there are 2 FRs-DPs, 2 associatio parameters DP 4 ad DP 5. ssumig they are strog couplig. ccordig to correlatio depedece of desig parameter ad trasfer aalysis, we idetify the cotrollable parameters DP 4 ad cotrolled parameters DP 5. Therefore, we should implemet the correspodig fuctioal requiremets of DP 4, ad the implemet the correspodig fuctioal requiremets of DP 5. Whe there are couplig desigs with may FRs - DPs, we ca use two-way compariso ad itelliget optimizatio methods such as immue optimizatio method to solve the problem [6]. The judgmet matrix is costructed by judgmet criterio o each FR ad DP, to get quatitative judgmet about DPs cotributes to FRs ad FRs depedece o DPs. The we comprehesively cosider the quatitative results of FRs-DPs couplig degree to get the possible sortig vectors. I desig parameters of all couplig modules, the first cotrollable parameter, secod cotrollable parameter,, ad cotrolled parameters ca be idetified, thus the best order of all couplig fuctios is determied The couplig associatio of desig parameters betwee modules The couplig associatio of desig parameters betwee modules is due to the associatio elemets ot belogig to the modules i couplig correlatio matrix of product family desig, icludig the couplig associatio of desig parameters betwee platform modules, the couplig associatio betwee platform module ad customizatio platform module, ad the couplig associatio of desig parameters betwee customizatio platform modules. The iteral couplig aalysis of modules is to achieve the iterative sequece of the desig, ad the couplig aalysis betwee modules is to evaluate correlatio degree betwee the modules ad to cotrol ad adjust desig parameters. () The couplig betwee platform modules The couplig betwee platform modules is divided ito oe-way associatio ad mutual associatio. The oe-way associatio betwee modules meas that oe module iflueces but does ot rely o aother module, ad the parameters ca be adjusted by certai sequece to avoid the iformatio feedback of the cotrolled parameters. It s also possible to avoid the associatio of desig parameters by choosig the desig parameters agai. The mutual associatio betwee platform modules meas that two modules are associated with each other. I order to ivestigate the processig method of couplig associatio of desig parameters betwee platform modules, we take the correlatio descriptio ad aalysis of two associatio modules as the example to illustrate (see Fig. 3 ad Fig. 4). The desig parameters DP -DP 4 ad DP 5 -DP 6 are cosidered as the iputs of modules ad 2, while the FR ad FR 2 as correspodig output of the two modules; the arrows i Fig. 4 represet iformatio flows, which are used to describe the commuicatio betwee modules ad 2; C ad C 2 are cotrol factors, which respectively represets the related desig costrait, (specificatio ad criteria, etc, C ad C 2 respectively restricts the rage of solutios for modules ad 2; M ad M 2 are mechaisms, which are the priciples to achieve the FRs. s show i Fig. 3, there are 2 associatio elemets F ad G outside the modules, specifically, the module iflueces the DP 5 of module 2 through the desig parameters DP 2, ad the module 2 iflueces the DP 3 of module through the desig parameters DP 6. The chage of module will cause the chage of module 2, similarly, the chage of module 2 will also affect module. The relatioship betwee the two modules is ot close, because oe of the goals of the couplig module clusterig is to require the couplig degree of the modules as low as possible. t this poit, accordig to the test desig of couplig relatio parameters, aalyzig the impact of the two related parameters o the modules, judgig the degree of mutual depedece betwee the modules, ad determiig the sequece of the modules. DP Module 3 G F 8 Module 2 Fig. 3. Couplig relatioship betwee platform modules for product family. Fig. 4. Schematic diagram of couplig relatio betwee platform modules. (2) The couplig betwee platform module ad customizatio module Whe there exist associatio parameters betwee platform module ad customizatio module i the couplig correlatio matrix, there is couplig relatio betwee them, as show i

7 Rebi Xiao ad Xiafu Cheg / Procedia CIRP 53 ( 206 ) Fig. 5. Ispired by the match method of cotrolled variables ad cotrollable variables i decouplig cotrol system, it s possible to miimize the correlatio betwee modules through selectig the reasoable match of the cotrollable parameters ad cotrolled parameters of associatio parameters, which is also a effective method to weake the couplig relatio. s show i Fig. 2, for the associatio elemet C, the cotrollable parameters is DP 8, the cotrolled parameter is DP 3. Through the reasoable match of DP 8 ad DP 3, it ca reduce the couplig relatio betwee the modules cotaiig the two parameters. Sometimes, the cotrollable parameters or cotrolled parameters have certai associatios with other parameters or certai restrait mechaism leads to the iability to fid direct parameter matchig. t this time, it s also possible to achieve a better match by the appropriate combiatio of cotrollable parameters or cotrolled parameters with their correlative parameters. For the associatio elemet D i Fig. 2, the cotrollable parameter DP 6 affects the cotrolled parameter DP 4, which is coupled with DP 5. So it s possible to combie DP 4 with DP 5 ad the reasoably match with DP 6. (3) The couplig betwee customizatio modules Oly after aalyzig the two kids of the above couplig relatio, should it be possible to cosider the couplig relatio of desig parameters betwee customizatio modules. Compared with the commo platform module, it is i a subordiate positio, because the customizatio parameters of product family oly affect the differece of variat products. Each product variat has differet customizatio parameters, of which some customizatio parameters oly belog to certai product, while some customizatio parameters ca vary i a larger rage (which meas they belog to a umber of variat products). The couplig relatio of desig parameters betwee customizatio modules ca also be oe-way correlatio ad mutual couplig, ad the processig method ca also refer to the method used i ). While the differece is, for mutual couplig of customizatio modules, we should first cosider their associatio with commo platform parameters, ad the aalyze the modules ow iterdepedece, so as to determie the optimal sequece to achieve the fuctio. s show i Fig. 6, assumig there are 2 customizatio modules ad B, desig parameters DP ad DP B respectively represets the iput of the module ad module B, FR ad FR B are the outputs of the two module, DP c ad DP c2 are the commo platform parameters. t this time, there are three possibilities: (a) 2 modules are ot affected by the platform parameters; (b) oly module is depedet o the platform parameters; (c) 2 modules are depedet o differet platform parameters. Fig. 5. Schematic diagram of associatio relatio betwee platform module ad customizatio module. Fig. 6. (a) couplig relatio without iformatio iput platform parameter; (b) Couplig relatio with iformatio iput of platform parameters to oe module; (c) Couplig relatio with iformatio iput of platform parameters to 2 modules. For the couplig relatio without platform parameter iput, as show i Fig. 6(a), the 2 customizatio modules have iteractios, but they are ot subject to the impact of platform parameters, ad the processig method is as the same as the processig method to the couplig relatioship betwee 2 platform modules show i Fig. 4. s show i Fig. 6(b), the two customizatio modules have iteractios ad oe of them is depedet o platform parameters. Because the platform parameters prior to customizatio parameters are determied, we should achieve the match associatio of DP c ad module (or its iteral customizatio parameters), ad the aalyze the couplig relatioship betwee modules ad focus o improvig the adaptability of module B, to cotrol the variatio i the associatio parameter of module 2. s show i Fig. 6(c), the two customizatio modules are coupled ad are affected by differet platform parameters. We should fid the reasoable match accordig to the platform parameters ad the correspodig relatioship of the modules (or its iteral customizatio parameters), ad the cosider the reasoable match of the correlatio parameters betwee the 2 modules, to cotrol the variatio i the associatio parameter.

8 28 Rebi Xiao ad Xiafu Cheg / Procedia CIRP 53 ( 206 ) Cocludig remarks To solve the couplig problem of product family desig (or product platform plaig), it ca be achieved from the strategy level ad operatio level. I the view of platform strategy level, from the view of the customers demads, it s easy to divide fuctioal requiremets of the product ito basic fuctioal requiremets, expectable fuctioal requiremets ad additioal fuctioal requiremets. xiomatic desig theory is take as a guide framework, the fuctioal requiremets are zigzaggig mappig to desig parameters, ad the desig matrix is created. The sesitivity amog the desig parameters ad the sesitivity betwee desig parameters ad fuctioal requiremets are aalyzed, ad the differece degree of desig parameters of product variats is calculated. Thus the platform parameters ad customizatio parameters is reasoably idetified. Based o the perspective of the platform operatio level, the desig matrix is coverted ito DSM, ad DSM is recofigured ad clustered ad grouped ito modules with less depedet degree. The couplig correlatio matrix of product family desig is established, which ca realize high cohesio degree i a sigle module ad low couplig degree amog all the modules. The the iterface amog modules ca be idetified, ad the associatio parameters are cosidered as cotrollable factors ad experimetal desig techiques are utilized to aalyze the ifluece of associatio parameters o the desig objectives, so as to ehace the robustess of product family desig ad weake the couplig of product family desig. Fially, the couplig aalysis is carried out from three aspects, which are the couplig iside the platform modules, the couplig iside the customizatio modules ad the couplig associatio of desig parameters betwee the modules, ad the the correspodig desig couplig process method is proposed. Through the system research, this paper establishes the decouplig methodology of product family desig. The methodology ca overcome the lack i axiomatic desig about disposig the couplig desig, which better distributes the desig resources, improves product desig efficiecy ad the level of customizatio. Sice the proposed method focus o the associatio of desig parameters iside module ad betwee modules, it is suitable for coceptual desig ad parameter desig of modular series products, such as vehicle, uiversal crae, agricultural machiery, etc. I the future, we will evaluate the couplig degree betwee modules by couplig associatio path ad associatio ifluece degree, ad validate the effectiveess of this work through the case study of product family desig. ckowledgemets This work was supported by the Natioal Natural Sciece Foudatio of Chia uder the Grat Nos , ad Refereces [] Tseg MM, Jiao J, Merchat ME. Desig for mass customizatio. 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