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1 ( RSM Abstract In ths paper response surface method (RSM s explaned ntall as one of the most mportant tools of qualt mprovement, then a revew of the lterature s presented n relaton wth the optmzaton of the mult-responses wthn RSM framewor. Attempts are classfed n three groups: loss functon, desrablt functon, and classc methods. Then each tem wll be dscussed usefull. Snce the method of the utlt functon consders the decson-maer's opnons obectvel, t s qute mportant. It should be noted that the functon of common utltes beng used n RSM s n fact L-P metrc formula. The relatonshp between qualt attrbutes and ther respectve effects are not taen nto account b t. Snce t s mportant to provde ad crcumstances and gudelnes for decson-maers n the dscover of the soluton, Raffa and Keene's method s effectve n ths respect. Thus, ths method s used to obtan utlt functon and fnall to determne a satsfactor soluton. The effcenc of the mentoned method s llustrated b an example. Kewords: Response Surface Method (RSM, decson-maers (DM, mult-responses, utlt functon, loss functon...[] (RSM... L-P.. : - - -
2 ٤٢ ( DM.[7].. RSM RSM. DM....[8] RSM. RSM. (Pgnatello,993,6 RSM.( RSM. RSM...[] [] RSM.. -. x mn or (X (X g : ( max Z = ( X r r =,..., K s.t x g ( X =,...,m x x* r (١
3 ٤٣ ( RSM T (X [4].. [5]..... ( L(, X, t = 4 ( X T USL LSL = ( (Ibd.... (٣ - -. ( [5].. [6].[6] ( ( loss( ( X = K( ( X T (٢ ٣ - Qualt Loss Coeffcent ١ - Bunded Obectve - Methods ٢ - Lexcograph - Methods
4 ٤٤ L(, t = [ δ + ( µ T ] + [ δ + ( µ T ( µ T ] = = = + (٤ d ( ( X = d ( ( X = r mn max mn max mn T s mn mn r T f f If f If mn ( X (x mn (x (x T mn (٧ max T (x max max T. S r (. D [ d (. d (... d ( ] ( = -. r L-P s. (٨ در ساير نقاط (٩ RSM (Ibd..(Derrnger, Such,98,7. RSM... (. ( d ( ( X = e d ( ( X = e ( X ( X (٥ (٦ ( ( Del.(castllo,Montgomer,996, Value Functon
5 ٤٥ ( RSM.. RSM -.[3]... x. x x x. A B x C X. X C B B A. RSM....[3].. : [9] (MCDM []...
6 ٤٦ + α U ( A = π + a a a = U ( r. U [. U ( r ] : : ( r... U ( r - - U ( A = a U ( r + a U ( r. U ( r =... n = < > U ( r <. U ( r.. - DM.( - : - (X - (X 3 - (X (X 4 - ( -. ( (١١ (١٢. DM-. X ( B. DM- X X ( A ( C. ( A DM A.. DM A.. (,(,( ( : - U ( A = a U = ( r (١٠
7 ٤٧ ( RSM.. ( ( (١٨ U (, = U(, + U(, + au(,. U(,. ( Y = x +43.9x -.55x x x -.97 x -.84 x 3 3. x x x x x x 3x4 (١٣ (١٩ U(, = 75.4( e ( e ( e ( e (. ( Max S.t z = U(, - < x < Y = x +43.9x -.55x x x -.97 x.84 x 3 3. x x x x x x 3x4 Y = x +3.6x +.59x x x -3.9 x -.94 x x xx x x x 3x4 (٢٠. ( ( Y = x +3.6x +.59x x x -3.9 x -.94 x x xx x x x 3x4 Max Max S. t - x (X ( X. ( =,...,4 DM ( (. U U = 333( e = 987.9( e.44y.47y U(8,5=U(59,98 DM U (59,98 β U (8,5= β. β =.49 β (١٤ (١٦ (١٧ (١٥ (
8 ٤٨ Keene DM. Raffa Raffa Keene... DM DM.. d( d( 6 = ( = ( Raffa Keene. Lngo (٢١ (٢٢ : ( Artles- Leon N.(996 A pragmatc Approach to Multple Response problems usng Loss Functons Qualt Engneerng - * * * * * x x x 3 x 4 Keene & Raffa Derrnger & Such Raffa Keene. Such Derrnger Raffa Keene.8 Keene..54 DM
9 ٤٩ ( RSM Mnmzaton Qualt Engneerng, Vol 4, pp Stewart T.J.(99 A Crtcal Surve on the Status of Multple Crtera Decson Mang Theor and Practce OMEGA, Vol 3, pp W.M.Carlle, D.C.Montgomer and G.C.Runger,( optmzaton problems and Methods n Qualt control and Improvement ournal of Qualt Technolog, Vol, pp-3.,vol, pp 3-6- Bles W.(975, A Response surface Methods for Expermental optmzaton of Mult Response Processes Industral and Engneerng chemstr,vol,pp C.T. Chao, M.Tamede, ( Analzng Experments wth Corrolated Multple Responses Journal of Qualt Technolog,Vol 4, pp Derrnger G. and Such R., (98 Smultaneous optmzaton of several response varables Journal of Qualt Technolog,Vol, pp Del Castllo E.,Montgomer D.C.&Mc Crvlle D.R.(996 Desrablt Functons for Multple Response optmzaton Journal of Qualt Technolog,Vol 3, pp French S. (984 Interactve Mult obectve programmng : ts Ams Applcatons and Demands Journal of the operatonal Research Socet, Vol 4, pp G.Gar Wang, ( Adaptve Response surface Method usng Inherted Latn Hpercube Desgn ponts Journal of Mechancal Desgn, Vol, pp Hafta R.,Scott E.P. and Cruz J.R,(998 Optmzaton and Experments : A Surve Appled Mechancs Revew,Vol 3, pp Keene R.L. and H. Raffa(976 Decsons wth Multple obectves : preferences and value Tradeoffs John wle, Newor. 4- Khur A. and Conlon M., (98 Smultaneous optmzaton of Multple Responses Represented b Polnomal regresson functons Technometrcs,Vol, pp Mers R.and Carter W.J, (973. Response surface Technques for Dual Response Sstems Technometrcs, Vol, pp Mers. R, Khur A and Vnng.G,(99 Response Surface Alternatves to the Taguch Robust parameter Desgn Approach the Amercan statstcan,vol, pp Pgnatello J.J,(993 Strateges for Robust Multresponse Qualt Engneerng,Vol, pp Rchard Suhr and Robert G. Batson, ( Constranged Multvarate Loss Functon
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