A Multvrte Aroch for Assessment nd Imrovement of Chemcl Mnufcturng Systems Bsed on Mchne Productvty Onlne number: 094 ALI AZADEH nd VAHID EBRAHIMIPOUR Dertment of Industrl Engneerng, Fculty of Engneerng, Unversty of Tehrn, Irn, P.O.Box:365-4563, Tel: +98-80-067 Fx: +98-80-30 E-ml Address: l@zdeh.com or zdeh@ut.c.r System Anlyss Lbortory, Dertment of Systems Engneerng, Okym Unversty, 700-8530, 3-- Tsushm Nk, Okym, Jn, Tel: +8-86-5-8058 Fx: +8-86-5-8059 E-ml Address: vhd@syslb.sys.okym-u.c. ABSTRACT Ths er resents frmework for ssessment nd rnkng of chemcl mnufcturng systems bsed on mchne roductvty ndctors. The ntegrted roch dscussed n ths er s bsed on Prncle Comonent Anlyss (PCA. The vldty of the model s verfed nd vldted by Numercl Txonomy (NT roch. Furthermore, non-rmetrc correlton method, nmely, Sermn correlton exerment shows hgh level of correlton between the fndngs of PCA nd NT. To cheve the obectves of ths study, comrehensve study ws conducted to locte ll economc nd techncl ndctors (ndexes whch nfluence mchne erformnce. These ndctors re relted to mchne roductvty, effcency, effectveness nd roftblty. 0 ndctors were dentfed s mor ndexes mctng mchnery condtons n mnufcturng systems. Stndrd fctors such s down tme, tme to rer, men tme between flure, oertng tme, vlue dded nd roducton vlue were consdered s shng fctors. The ndustrl sectors re selected ccordng to the formt of Interntonl Stndrd for Industrl Clssfcton of ll economc ctvtes (ISIC. Furthermore, Irnn ndustres re clssfed s 4-dgt ISIC chemcl sectors. Then, comrtve study s conducted through PCA mong the 4-dgt chemcl sectors by consderng the selected 0 ndctors. PCA rnked the chemcl sectors bsed on 0 ndexes dscussed n ths er. Ths n turn shows the wek nd strong onts of chemcl mnufcturng sector wth resect to mchne roductvty. Furthermore, PCA dentfed whch mchne ndctors hve the mor mcts on the erformnce of chemcl sectors.
Keywords: Mchne Indctors, Productvty, Prncle Comonent Anlyss, Numercl Txonomy, ISIC INTRODUCTION Mchne lys n mortnt role n the overll erformnce of mnufcturng systems. In fct, mchne roductvty s correlted wth the overll erformnce of mnufcturng system. Mor fctors nfluencng the overll roductvty of n ndustrl orgnzton re dentfed s technology, mchnery, mngement, ersonnel nd rules nd rocedures (Azdeh, 000. The mchne fctor s mnly concerned wth mchne condton or sttus n secfed erod. Preventve mntennce, rer, mchne lyout nd clbrton nfluence mchne condton. Mchne condton s mesured through smle roductvty models nd ndctors. Moreover, most roductvty ndctors bout mchne re defned n terms of vlblty; oertng tme, rer tme, down tme, etc. Ths study hs dentfed mor roductvty ndctors, whch mct mchne erformnce n chemcl mnufcturng systems. The chemcl mnufcturng systems re ctegorzed ccordng to Interntonl Stndrd for Industrl Clssfcton for ll economc ctvtes (ISIC four-dgt formt. Only ndustrl unts wth more thn 50 ersonnel re consdered for ths study. An ntegrted study must consder not only the trdtonl roductvty vew but lso t must consder other vews such s effcency, effectveness nd roftblty. Effectveness s defned s ctul outut to lnned outut, effcency s defned s ctul outut to ctul nut nd roftblty s defned s totl revenue to totl cost. Furthermore, ths study consders the four vews of mchne roductvty, whch re: trdtonl roductvty, effcency, 3 effectveness nd 4 roftblty. In ths study, ll of the four vews re referred to s mchne roductvty. By referrng to selected number of roductvty ndexes, the ndustrl orgnztons re rnked nd nlyzed by Prncl Comonent Anlyss (PCA. The vldty of the model s verfed nd vldted by Numercl Txonomy (NT roch. It should be mentoned tht Dt Envelo Anlyss (DEA ws frst selected s the verfcton tool, but severl ndexes could not be consdered due to the unque structure of DEA. The four-dgt ISICs of chemcl mnufcturng systems re lsted s follows (U.N, 993; UNIDO, 997; UNIDO, 999; World Bnk, 995; World Bnk, 998; Azdeh &Jl, 00:
ISIC Industry 4 Mnufcture of bsc chemcl, excet fertlzers nd ntrogen comounds 4 Mnufcture of fertlzers nd ntrogen comounds 43 Mnufcture of lstcs n rmry forms nd of synthetc rubber 4 Mnufcture of estcdes nd other gro-chemcl roducts 4 Mnufcture of nts, vrnshes nd smlr cotngs, rntng nk nd mstcs 43 Mnufcture of hrmceutcls, medcl chemcls nd botncl roducts 44 Mnufcture of so nd detergents, clenng nd olshng rertons, erfumes nd tolet rertons 49 Mnufcture of other chemcl roducts n.e.c. 430 Mnufcture of mn-mde fbers PCA Prncl Comonent Anlyss (PCA s wdely used n multvrte sttstcs such s fctor nlyss. It s used to reduce the number of vrbles under study nd consequently rnkng nd nlyss of decson-mkng unts (DMUs, such s ndustres, unverstes, hostls, ctes, etc (Azdeh, 000; Zhu, 998. The obectve of PCA s to dentfy new set of vrbles such tht ech new vrble, clled rncl comonent, s lner combnton of orgnl vrbles. PCA s erformed by dentfyng egnestructure of the covrnce or sngulr vlue decomoston of the orgnl dt. Here, the former roch wll be dscussed. It s ssumed there re vrbles (ndexes nd k DMUs nd suose X = ( x...x k s kx mtrx comosed by x ' s defned s the vlue of th ndex for th DMU nd T therefore Xm = (xm...xkm (m =.... Furthermore, suose X ˆ = ( xˆ...ˆ x k s the stndrdzed mtrx of = ( x... wth xˆ ' s defned s the vlue of th X x k stndrdzed ndex for th DMU nd therefore T X m = ( xˆ m... xˆ km. PCA s erformed to dentfy new ndeendent vrbles or rncl comonents (defned s Y for, =... whch re resectvely dfferent lner combnton of x xˆ ˆ.... As mentoned, ths s cheved by dentfyng egnestructure of the covrnce of the orgnl dt. The rncl comonents re defned by k mtrx Y = ( y... y k comosed by y ' s (Zhu, 998; Ng&Cheng, 997; Agrwl, 999: Ste : Clculte the smle men vector x nd covrnce mtrx S: ^ 3
x = x... x ( ( n whch, x = k x k = for =,..., ( T S = ( s q = ( X x ( X x. for q =,..., k (3 Ste : Clculte the smle correlton mtrx. R = C / s. S. C / s where C / s s dgonl mtrx whose th dognl element s / s for =,,. Ste 3: Slove the followng equton. R λ I = 0 where I s dentty mtrx. The comonents n egenvectors re resectvely the coeffcents n ech coresondng Y: Y m = = l ˆ x m for m =... nd =,..., k (4 Ste 4: clculte the weghts ( w of the rncl comonents nd PCA scores ( z of ech DMU ( =,..., k. Furthermore, the z vector ( z... z k where z shows the score of th DMUs s gven by: w = λ / λ = λ / = z = w Y = =,..., (5 =,...,k (6 Numercl Txonomy Numercl Txonomy roch s cble of dentfyng homogeneous from nonhomogeneous cses. Furthermore, grou of DMUs by gven ndexes s dvded to homogeneous sub-grous (Zhu, 998. It lso rnks the DMUs n rtculr grou. The Numercl Txonomy roch s s follows (Cohen&Frnch, 999: Ste : Suose we hve k DMUs wth vrbles (ndexes whch cn be shown by k by mtrx X = [x] where x s the vlue of th ndex for the th DMU ( =,..., k nd =,...,. 4
Ste : The k by mtrx s stndrdzed such tht ll ndexes hve men of 0 nd vrnceof. The new mtrx s Xˆ = [ xˆ ] kx where xˆ = x x x nd s re s men nd stndrd devton of th ndex resectvely. Ste 3: The dstnce of every two DMUs for ech ndex s comuted. Ths s done to homogenze the DMUs. For exmle for DMUs nd b, d b = ( xˆ xˆ b = Therefore, the dstnce mtrx D = [d] kx nd vector d = [d] Kxwhere d s the mnmum of th row of mtrx D re dentfed. To dentfy homogenous DMUs, the uer (L nd lower (L lmts of vector d s comuted s L = d + sd nd L = d s d where d nd s d re the men nd stndrd devton of vector d resectvely. If ll ds re wthn L nd L, homogenety s cheved nd we go to next ste. Otherwse, cluster nlyss s erformed untl ll DMUs re homogenous. k d d = = nd s d = k k ( d d k = (7 Ste 4: The dstnce of ech DMU from the del DMU for ech ndex s comuted s: c = ( xˆ xˆ mx (8 = Where x s the mxmum of the th ndex. The growth level for ech DMU s: ˆ mx c * f = where c = c + sc ( * c And c nd s c re men nd stndrd devton of c ' s resectvely. f ' s re between 0 nd wth s the worst nd 0 s the best scores. TOTAL PRODUCTIVITY MODEL To cheve the obectves of ths study, comrehensve study ws conducted to locte ll economc nd techncl ndctors (ndexes whch nfluence mchne erformnce. These ndctors re relted to mchne roductvty, effcency, effectveness nd roftblty. 7 ndctors were dentfed s mor ndexes mctng mchne condtons n mnufcturng systems. Due to dt collecton lmttons, only 0 ndctors were selected for the urose of ths study. The uthorzed body hd no knowledge of our study nd the 7 ndctors. The dt s collected from the nnul 5
reorts of Irn Sttstc Center, whch s the uthorzed body to collect the mnufcturng dt ccordng to ISIC formts. The sectors re selected ccordng to the formt of Interntonl Stndrd for Industrl Clssfcton of ll economc ctvtes (ISIC. Furthermore, Irnn chemcl mnufcturng ndustres re clssfed s 4-dgt ISIC formt. A comrtve study s conducted mong chemcl mnufcturng sectors through PCA by consderng 0 selected ndctors (dscussed n the next secton. The totl roductvty roch s bsed on 0 ndctors dentfed n ths study. The ten ndexes re ctegorzed nto four clsses. The frst clss reflects vlblty of mchne nd s mesured by ndexes number, nd 3. Avlblty s defned s the robblty tht system s oertng stsfctorly t ny ont n tme nd consders only oertng tme nd down tme, thus excludng dle tme. The second clss dels wth mchnery stoge due to lck of good lns, reventve mntennce nd mterl, etc (ndexes number 4 nd5. The thrd clss reresents rndom flures (ndexes number 6, 7 nd 8. The lst clss whch s comosed of ndexes number 9 nd 0 reflects vlblty n relton to vlue dded nd roducton vlue. Currency unt er tme unt mesures ndexes number 9 nd 0. The selected mchnery ndexes (ndctors re lsted s follows: : Avlblty 6 : Oertng tme to mxmum tme : Down tme to vlble tme 7 : Down tme to oertng tme 3 : Avlble tme to mxmum tme 8 : Down tme to neffcent tme 4 : Ineffcent tme to vlble tme 5 : Ineffcent tme to oerton tme 9 : Vlue dded to oertng tme 0 : Producton vlue to oertng tme The vlues of the ten ndexes for the four-dgt ISIC chemcl mnufcturng systems re resented n Tble. Prncl Comonent Anlyss (PCA s used to rnk nd nlyze the dt. Consequently, t dentfes the wek nd strong onts nd ntroduces roductvty mrovng fctors n regrd to mchnery condton n ech sector (DMUs. PCA s cheved through set of well-defned stes s follows: Ste : Normlze the ndex vectors. The ten ndexes must be normlzed nd hve sme order to be used n PCA. Indexes 4 nd 8 hve ooste order thn the rest of the ndexes. To llevte ths roblem, 4 nd 8 re subtrcted from nd ll the ten ndexes from now on re referred to s x for =...0. Ste : Stndrdze the ndexes x to x 0. The ndexes re stndrdzed through redefned men nd stndrd devton for ech ndex. 6
Tble : The nut dt for the ten ndexes of four-dgt ISICs ISIC x code x x 3 x4 x5 x6 x7 x8 x9 x0 4 0.84 0.6 0.7 0.46 0.36 0.8 0.84 0.7 56774 5497 4 0.94 0.65 0.69 0.50 0.46 0.94 0.94 0.88 63440 844778 43 0.88 0.64 0.73 0.5 0.44 0.86 0.88 0.75 0309 377009 4.00 0.67 0.67 0.5 0.5.00.00.00 04 75380 4 0.87 0.6 0.7 0.48 0.40 0.85 0.87 0.75 07499 7308 43 0.88 0.63 0.7 0.48 0.4 0.87 0.88 0.78 45574 6757 44 0.87 0.6 0.70 0.45 0.36 0.85 0.87 0.76 47590 56 49 0.90 0.65 0.7 0.5 0.45 0.89 0.90 0.79 9556 566846 430 0.88 0.66 0.75 0.55 0.48 0.86 0.88 0.73 35 56689 Ste 3: Evlute the correlton mtrx. Ths mtrx shows the vlues of lner correlton between ndexes x to x 0. Ste 4: Clculte egenvlues, egenvectors nd roorton of the smle vrnce for ll the ten rncl comonents (new vrbles. The egenvlues nd roorton of the smle vrnce for ll the 0 ndexes (rncl comonents re resented n Tble. It s noted tht frst three rncl comonents y3 ccount for 99.5 ercent of the smle vrnce. Therefore, the coeffcents of the frst three rncl comonents re resented n the lst three column of Tble 4. Ste 5: Evlute the rncl comonents nd ggregted weghts. The vlues of rncl comonents nd consequently ther ggregted weghts re resented n Tble 3. Tble : Egennlyss for the four-dgt chemcl mnufcturng systems Vrble Egenvlue Weght Egenvectors ( λ ( w 6.8 0.6 0.395 0.044-0.3.8 0.3 0.346-0.308 0.65 3.537 0.54-0.64-0.389 0.386 4 0.05 0.00 0.03-0.498 0.353 5 0.003 0.000 0.343-0.38 0.63 6-0.00 0.000 0.395 0.09-0.3 7 0.00 0.000 0.395 0.044-0.3 8 0.000 0.000 0.380 0.35-0.97 9 0.000 0.000-0.09-0.466-0.53 0 0.000 0.000-0.63-0.406-0.548 l l l 3 7
Tble 3: The vlues nd scores of Prncl comonents for chemcl mnufcturng Four-dgt z ISIC (DMU y y y3 (PCA scores Rnk 4 -.88.475 0.404 -.44 9 4.05 0.63-0.690.44 43 -.305 -.84 -.00 0.3 4 4 5.384 0.794-0.89 3.6 4 -.334 0.79 0.493 -.068 7 43-0.7 0.446-0.54-0.503 6 44 -.897.498-0.90 -.375 8 49 0.544-0.304 0.898 0.68 3 430-0.065 -.959.36 0.033 5 MODEL VALIDATION To verfy the results of PCA, numercl txonomy roch s emloyed nd descrbed next. Frst, the summry of numercl txonomy nlyss s descrbed. Second, the rnkng of the two roches re nlyzed by Sermn correlton technque. The dstnce mtrx s comuted nd the vlues of vector d re shown n Tble 4. As noted, d s reresent the smllest vlue n ech row of the dstnce mtrx for ech DMU. By comutng the lower nd uer lmts of d [.07, 3.786], t s observed tht ll DMUs re wthn the rnge of ds. Therefore cluster nlyss s not requred to dentfy homogenous DMUs. The vlues of f s for homogenous DMUs nd ther rnks re resented n Tble 5. Tble 4: The results of dstnce mtrx for numercl txonomy roch Two-dgt ISIC Selected ISIC d (DMU (DMU 4.696 4 4.348 49 43 3.786 43 4 3.75 4 4.07 43 43.07 4 44.634 4 49.9 4 430.9 49 d : mnmum of th row of the dstnce mtrx (D 8
Tble 5: Txonomy vlues of the homogenous rocess for the four-dgt ISICs DMUs f Rnk 4 0.984 9 4 0.576 43 0.60 4 0.639 3 4 0.835 7 43 0.75 6 44 0.889 8 49 0.675 4 430 0.77 5 The f s show the vlues of txonomy for ech DMU (four-dgt ISIC. As mentoned, vlues of f s rnge between 0 nd wth the worst nd 0 best scores. Consderng the scores of PCA nd Txonomy n Tble 6 rnks the DMUs. Ths tble lso reorts the non-rmetrc test of reltonsh (Sermn between PCA rnkngs nd Txonomy rnkngs, whch result n the reecton of H o t 0.0 level. Also, the Kendll s Tu test of correlton verfes ths fndng t the sme level of sgnfcnce. There s drect reltonsh between PCA nd Txonomy n terms of dt set resented for the four-dgt ISIC code. Hence, the results of PCA re verfed by Numercl Txonomy. Tble 6: Test of correlton between PCA nd Txonomy rnkngs of four-dgt ISIC Two-dgt ISIC Txonomy Sermn PCA rnk (U (DMU rnk (V (U V 4 9 9 0 4 43 4 4 4 3 4 4 7 7 0 43 6 6 0 44 8 8 0 49 3 4 430 5 5 0 Result of tests of correlton between Totl 0 PCA nd Txonomy rs = 0.9 & τ = 0.83 Reect t 0.0 CONCLUSION Verfyng nd vldtng the PCA rnkngs by Txonomy roch my further nlyze the PCA results. It ws shown tht rncl comonents wth weghts w 9
=6.% nd w =.3% comose bout 84.5% of the smle vrnce. Therefore, by ncresng the frst nd second comonents wth the rnkng my be gretly mroved. Furthermore, ndustres n the bottom of the rnkng my enhnce ther erformnce by mrovng the frst nd second rncl comonents. The frst nd second rncl comonents re further nlyzed by referrng to ther coeffcents (egenvectors. Also, DMUs 4 nd 4 show the worst nd best rnks resectvely, wth resect to the 0 selected mchne ndctors. As seen n Tble 4,the three techncl ndctors x, x 6, x 7 nd the two economcl x 9, x 0 re selected by PCA. Also, the three techncl ndctors re locted s the most sgnfcnt grou n roortonl to economcl grou by whch the mchne erformnce n ndustrl sectors cn mrove. These grous re nfluenced by the two ndeendent chrcterstcs, oertng tme nd down tme. In other words, t cn be exected tht the system erformnce cn be enhnced by mrovng the oertng tme nd down tme. REFERENCES Azdeh, M.A.; Otmzng the exstng mchnery resources, Techncl reort, volume 3, Unversty of Tehrn nd Ntonl reserch Councl of Irn (000 Interntonl Stndrd Industres Clssfcton of All Economc Actvtes, Seres M No.4/Rev.3, 0, U.N (993 Industrl develoment: Globl Reort, UNIDO (997 Interntonl Yer Book of Industrl Sttstcs, UNIDO (999 World Develoment Reort, World Bnk (995 World Develoment Indctors, World Bnk (998 Azdeh, M.A. nd S. Jll; Identfyng the Economc Imortnce of Industrl Sectors by Multvrte Anlyss, Journl of the Fculty of Engneerng, Unversty of Tehrn, Irn (00 Zhu, J.; Dt Enveloment Anlyss vs. Prncl Comonent Anlyss: An Illustrtve Study of Economc Performnce of Chnese ctes, Euroen, Journl of Oerton Reserch,, 50-6 (998 Ng, E.W.T. nd T.C. Cheng; Potentl Brrers to Totl Qulty Mngement Usng Prncl Comonent Anlyss nd Corresondence Anlyss, Interntonl Journl of qulty Relblty Mngement, Vol.4 No.4, 39-408 (997 Agrwl, R.; On the Aroxmblty of Numercl Txonomy (fttng dstnces by tree metrcs, SIAM Journl on Comutng, 8(3,.073-085(999 Cohen, J nd M. Frch; Numercl Txonomy on Dt: Exermentl Results, Dertment of Comuter Scence, Rutgers Unversty (999 0