APPLYING DMAIC PROCEDURE TO IMPROVE PERFORMANCE OF LGP PRINTING PROCESS COMPANIES

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Advaces i Productio Egieerig & Maagemet 6 (2011) 1, 45-56 ISSN 1854-6250 Scietific paper APPLYING DMAIC PROCEDURE TO IMPROVE PERFORMANCE OF LGP PRINTING PROCESS COMPANIES Al-Refaie Abbas*; Li Mig-Hsie**; Al-Tahat M. D.*** & Fouad R. H.**** *Correspodig author, Departmet of Idustrial Egieerig, Uiversity of Jorda, 11942 Amma **Departmet of Idustrial Egieerig ad Systems Maagemet, Feg Chia Uiversity, Taichig, Taiwa ***Departmet of Idustrial Egieerig, Uiversity of Jorda, 11942 Amma ****Departmet of Idustrial Egieerig, Hashimite Uiversity, 13133 Zarqa E-mail: abbas.alrefai@ju.edu.jo, mhli@fcu.edu.tw Abstract: The light-guide-plate (LGP) lumiace plays a importat role i producig liquid crystal displays (LCD) paels of quality images. Poor lumiace usually results i producig LCD paels with color defects. This research aims at improvig the performace of LGP pritig process by followig the defie-measure-aalye-improve-cotrol (DMAIC) procedure. To improve the performace of LGP process, the DMAIC procedure will be implemeted as follows. Process mappig ad cotrol charts will be established i the defie-phase. The process capability aalysis is coducted i the measure-phase. The Taguchi s experimetal desig ad aalysis will be performed i the aalye- ad improve-phases. Fially, the grey model GM (1,1) will be employed i the cotrol-phase. Utiliig the Taguchi s L 27 (3 13 ) array, six key process factors were ivestigated cocurretly; icludig scraper agle, scraper pressure, scraper speed, ik viscosity, ik paller bearig, ad gap betwee board ad LGP. It is foud that the scraper's agle, pressure ad speed, ad ik viscosity sigificatly cotributed to the lumiace variability. The aticipated improvemet i lumiace is foud 512 cd/m 2. The estimated process capability, C pl, is greatly ehaced from 0.69 to 2.44. Statistical quality cotrol tools, the Taguchi method, ad GM (1,1) grey model are employed i the DMAIC procedure to improve the performace of LGP process. Product/process egieers ca adopt this procedure i a similar maer to ehace the performace of ay maufacturig process i a wide rage of busiess applicatios. Key Words: Taguchi Method, DMAIC, Statistical Quality Cotrol, GM (1,1) Grey Model 1. INTRODUCTION Because of its smaller space requiremet, high-quality display ad acceptable cost, the thi film trasistor liquid crystal display (TFT-LCD) has become the most importat visual display termial scree today [1 4]. TFT-LCD is used widely i the idustry of electroic iformatio displays, icludig televisio, mobile phoes, digital cameras ad other cosumer related commuicatios hardware. I such products, image colour-quality has bee recogied as oe of the top cosideratios i the display maufacturig idustry ad has become a bechmark that iflueces cosumers purchasig decisio. The light-guide-plate (LGP) lumiace plays a importat role i producig LCD paels of quality images ad it is used i assessig frot-of-scree quality. Poor lumiace results i producig LCD pael with colour defects, which icrease quality costs. Hece, improvig the performace of LPG process is the mai focus of this research. 45

Al-Refaie Abbas, Li Mig-Hsie, Al-Tahat & Fouad: Applyig DMAIC Procedure to Improve Six sigma [5] is a project-drive maagemet approach to improve products ad processes by cotiually reducig defects. A widely-accepted six sigma approach is the DMAIC procedure, which was adopted to improve the performace for umerous maufacturig processes [6, 7]. Further, the itroductio of robust desig proposed by Taguchi [8] i quality egieerig resulted i sigificat quality ad productivity improvemets i product ad maufacturig process desig. Taguchi method [9] combies egieerig ideas with statistical techiques i ovel ways ad offers tremedous potetial for quality improvemet with miimal cost i a wide rage of idustrial applicatios [7, 10]. This research, therefore, aims at improvig lumiace of LCD for LGP pritig process usig DMAIC procedure icludig the Taguchi method. The remaiig of this paper is outlied i the followig sequece. Sectio two performs the defie-phase. Sectio three carries out the measure-phase. Sectio four performs the aalye- ad improve-phases. Sectio five establishes the cotrol-phase. Sectio six summaries coclusios. 2. DEFINE-PHASE 2.1 Mappig Backlight Module Processes A covetioal LCD backlight module is composed of light sources, LGP, ad optical sheets; such as, reflectio, diffusio, ad prism sheets. I this module, the light rays from the source are icidet o oe of the LGP sides ad are guided iside it based o the priciple of total iteral reflectio. At least oe of LGP surfaces is coated with a ik layer. The ik layer cotais a plurality of diffusig graules for diffusig lights to produce uiform lumiace. The flow chart of backlight module is routed i Figure 1. Iitially, the LGP cuttig ad cleaig take place. Dot patters are the prited o its surface. The LGP is fitted with lamp set the assembled with module frame ad optical film. Scree ispectio, testig, ad film protectio activities follow. Packig of the back-light module is fially performed. Amog the back-light module processes, the LGP pritig process is a critical process i producig quality modules, which is performed o LGP pritig machie show i Figure 2. 2.2 Assessig the process performace The x ad R cotrol charts are widely applied for o-lie moitorig of the mea ad variability of the maufacturig processes [11]. They are a prove techique for improvig productivity, defect prevetio, prevetig uecessary process adjustmet, ad providig iformatio about process capability. Let UCL, CL, ad LCL deote the upper cotrol limit, the cetral lie, ad lower cotrol limit, respectively. The x ad R cotrol charts are cocluded i cotrol if all poits fall withi cotrol limits ad o idicatio of sigificat patters or rus betwee the cotrol limits. 46

Al-Refaie Abbas, Li Mig-Hsie, Al-Tahat & Fouad: Applyig DMAIC Procedure to Improve Figure 1: Flow chart for back-light module. Figure 2: LGP pritig machie. Five LGP plates are radomly chose the ispected every two hours for 15 workig hours. O each plate, the lumiace is measured with BM7 at five poits (L 1, L 2, L 4, L 7, L 9 ) as depicted i Figure 3. The lumiace average ad rage are calculated for each LGP. The correspodig x ad R cotrol charts are fially costructed the show i Figure 4. The LCL, CL, ad UCL for the x chart are calculated ad foud equal to 4480.3, 4625.2, ad 4770.2 cd/m 2, respectively. For the R chart, the LCL, CL, ad UCL are estimated 0.0, 251.3, ad 531.4, respectively. I Figure 4, o poit is detected outside the cotrol limits or are ay sigificat patters or rus observed withi the limits of both cotrol charts. Cosequetly, the x ad R cotrol charts are cocluded i cotrol. 47

Al-Refaie Abbas, Li Mig-Hsie, Al-Tahat & Fouad: Applyig DMAIC Procedure to Improve 3. MEASURE PHASE Figure 3: Lumiace measuremet (red circles) usig BM7. Process capability aalysis [12] is a vital part of a overall quality-improvemet program by which the capability of a maufacturig process ca be measured ad assessed. I practice, the process stadard deviatio,, is ukow ad frequetly estimated as: = R / d2 where d 2 is a costat related to sample sie. The oe-sided actual process capability, C, attempts to take the process mea ito accout [13]. The estimator of C pk, as: C pk pk, is calculated ˆ USL ˆ ˆ LSL Cpk mi( Cpu, Cpl ) (2) ˆ ˆ where USL ad LSL are the upper ad lower specificatio limits, respectively. The ˆ is the estimate of ad is equal to the CL, x, of the x chart. A value of 1.67 is cosidered the stadard miimum boudary for C pk. I this research, the LSL of lumiace is 4450 cd/m 2 (cadelas per square meter). Usig the x (= 4625.2 cd/m 2 ) ad R (= 251.3 cd/m 2 ), ad the d 2 for a sample sie of five is equal to 2.326, the ad Ĉ pk values are calculated by Equatios ad (2) ad foud equal to 108.04 cd/m 2 (=251.3/2.326) ad 0.695 (= (4625.2-4450)/(3108.04)), respectively. Evidetly, the LGP pritig process is cocluded icapable for providig acceptable lumiace. 48

(a) The cotrol chart. (b) The R cotrol chart. Al-Refaie Abbas, Li Mig-Hsie, Al-Tahat & Fouad: Applyig DMAIC Procedure to Improve Figure 4: The x ad R charts at iitial ad optimal factor settigs. 49

Al-Refaie Abbas, Li Mig-Hsie, Al-Tahat & Fouad: Applyig DMAIC Procedure to Improve 4. ANALYZE- AND IMPROVE- PHASES 4.1 Ivestigatig critical QCH ad process factors The LGP lumiace is cosidered the key measurable ad cotiuous QCH of mai iterest. The cause-ad-effect diagram for o-uiformity of LGP lumiace is show i Figure 5. Figure 5: The cause-ad-effect diagram for lumiace o-uiformity. Six cotrol factors may affect the capability of the LGP pritig process icludig: (A) scraper agle, (B) scraper pressure, (C) scraper speed, (D) ik viscosity, (E) ik paller bearig, ad (F) gap betwee board ad LGP. Based o process kowledge, all factors A to F are assiged at three levels. The correspodig level values are displayed i Table I. The combiatio of factor settigs of the LGP pritig process at iitial stage is A 1 B 2 C 2 D 2 E 1 F 2. Table I: The physical values of factor levels. Cotrol factor Level 1 Level 2 Level 3 A. Scraper agle (degree) 65 75 85 B. Scraper pressure (bar) P 0-1 P 0 P 0 +1 C. Scraper speed (mm/sec) S 0-20 S 0 S 0 +20 D. Ik viscosity (cp) * C 0-5 C 0 C 0 +5 E. Ik paller bearig (bar) T 0 T 0 +5 T 0 +10 F. Gap (mm) 3 5 7 * The poise is the most commoly ecoutered uit of viscosity, ofte as the cetipoise (cp). 4.2 Improvig performace usig Taguchi method Taguchi method maily focuses o fidig the optimal settig of cotrol factors ivolved i a system to make its performace isesitive to oise. A orthogoal array (OA) is used to provide a experimetal desig. Sigal-to-oise (S/N) ratio is the employed to measure performace ad decide optimal factor levels. I this research, the L 27 (3 13 ) array show i Table II is selected to ivestigate the six process factors cocurretly. 50

Al-Refaie Abbas, Li Mig-Hsie, Al-Tahat & Fouad: Applyig DMAIC Procedure to Improve Exp. (j) Table II: Experimetal results for L 27 (3 13 ) array. Factor-colums assigmet Test QCH value (y i) Average lumiac A B C D E F e e e e e e e Test Test e 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4498 4536 4536 4523.33 73.11 2 1 1 1 1 2 2 2 2 2 2 2 2 2 4526 4550 4522 4532.67 73.13 3 1 1 1 1 3 3 3 3 3 3 3 3 3 4584 4692 4552 4609.33 73.27 4 1 2 2 2 1 1 1 2 2 2 3 3 3 4850 4740 4740 4776.67 73.58 5 1 2 2 2 2 2 2 3 3 3 1 1 1 4868 4858 4824 4850.00 73.71 6 1 2 2 2 3 3 3 1 1 1 2 2 2 4920 4908 4894 4907.33 73.82 7 1 3 3 3 1 1 1 3 3 3 2 2 2 5044 5080 5156 5093.33 74.14 8 1 3 3 3 2 2 2 1 1 1 3 3 3 5160 5084 5176 5140.00 74.22 9 1 3 3 3 3 3 3 2 2 2 1 1 1 5216 5096 5048 5120.00 74.18 10 2 1 2 3 1 2 3 1 2 3 1 2 3 4732 4838 4912 4827.33 73.67 11 2 1 2 3 2 3 1 2 3 1 2 3 1 4850 4752 4698 4766.67 73.56 12 2 1 2 3 3 1 2 3 1 2 3 1 2 4904 4794 4784 4827.33 73.67 13 2 2 3 1 1 2 3 2 3 1 3 1 2 4882 4954 4964 4933.33 73.86 14 2 2 3 1 2 3 1 3 1 2 1 2 3 4878 4796 4942 4872.00 73.75 15 2 2 3 1 3 1 2 1 2 3 2 3 1 4838 4944 4940 4907.33 73.82 16 2 3 1 2 1 2 3 3 1 2 2 3 1 5058 4940 4924 4974.00 73.93 17 2 3 1 2 2 3 1 1 2 3 3 1 2 5072 5112 5222 5135.33 74.21 18 2 3 1 2 3 1 2 2 3 1 1 2 3 5238 5160 5180 5192.67 74.31 19 3 1 3 2 1 3 2 1 3 2 1 3 2 4904 4994 4912 4936.67 73.87 20 3 1 3 2 2 1 3 2 1 3 2 1 3 4850 4930 4922 4900.67 73.80 21 3 1 3 2 3 2 1 3 2 1 3 2 1 5064 4954 4944 4987.33 73.96 22 3 2 1 3 1 3 2 2 1 3 3 2 1 4882 4954 4804 4880.00 73.77 23 3 2 1 3 2 1 3 3 2 1 1 3 2 4878 4796 4942 4872.00 73.75 24 3 2 1 3 3 2 1 1 3 2 2 1 3 4838 4944 4812 4864.67 73.74 25 3 3 2 1 1 3 2 3 2 1 2 1 3 5058 4940 4924 4974.00 73.93 26 3 3 2 1 2 1 3 1 3 2 3 2 1 5072 5112 5222 5135.33 74.21 27 3 3 2 1 3 2 1 2 1 3 1 3 2 5238 5160 5180 5192.67 74.31 Test 3 S/N ratio ( i) I practice, larger lumiace provides better performace. The correspodig S/N ratio, j, is expressed as: 1 log y i I j J (3) j 2 10 10( 1/ ij ), =1,..., ; =1,..., i1 where y ij is the lumiace average of each test i for experimet j. Three repetitios ( = 3) are coducted at the same factor levels of each experimet. The last colum of Table 2 summaries the estimated S/N ratios values for all experimets. For illustratio, the S/N ratio, 1, of 73.11 db for the first experimet is calculated as usig Eq. (3) as follows = 73.11 db 2 2 2 1 10log 10(1/ 4498 1/ 4536 1/ 4536 ) /3 The j values for the other 26 experimets are estimated similarly. Typically, a larger S/N ratio idicates better performace. The S/N ratios averages are calculated at each factor level the depicted i Figure 6. Cosequetly, the combiatio of optimal factor levels is A 3 B 3 C 3 D 2 E 3 F 2. Table 3 tabulates the lumiace averages for all factor levels. The aticipated improvemet i lumiace, due to settig process factors at A 3 B 3 C 3 D 2 E 3 F 2, is calculated for each factor as the lumiace at optimal factor level mius that at iitial factor level. The last colum of Table 3 lists the obtaied results. The total 51

Al-Refaie Abbas, Li Mig-Hsie, Al-Tahat & Fouad: Applyig DMAIC Procedure to Improve aticipated improvemet is calculated ad foud equal to 512 cd/m 2, where factors A, B, ad C cotributed the largest effect o the aticipated improvemet of lumiace. Figure 6: Plot of S/N ratios averages (optimal level is idetified by circle). Table III: Lumiace averages for all factor levels. Factor Lumiace (cd/m 2 ) Aticipated Level 1 Level 2 Level 3 Improvemet A. Scraper agle (degree) 4839 4937 4971 132 B. Scraper pressure (bar) 4768 4874 5106 232 C. Scraper speed (mm/sec) 4843 4917 4988 71 D. Ik viscosity (cp) 4853 4962 4932 0 E. Ik paller bearig (bar) 4880 4912 4957 77 F. Gap (mm) 4914 4922 4911 0 Total Improvemet (cd/m 2 ) 512 4.3 Determiig sigificat factor effects To determie the process factor with sigificat effects o LGP lumiace, aalysis of variace (ANOVA) is coducted. The results are displayed i Table IV. 52

Al-Refaie Abbas, Li Mig-Hsie, Al-Tahat & Fouad: Applyig DMAIC Procedure to Improve Table IV: ANOVA for lumiace. Factor SS f * df f f (%) MS f F ratio SS' f ' f (%) A 84905.73 2 9.99 % 10.35 76705.03 9.02% 42452.87 B 539602.07 2 63.5 % 269801 65.80 531401.4 62.50 % C 94882.98 2 11.16 % 47441.49 11.57 86682.28 10.19 % D 57047.48 2 6.71 % 6.96 48846.78 5.75% 28523.74 E 26707.76 2 3.14 % F 602.23 2 0.07 % Error 46496.35 14 Pooled error (73806.34) 18 (4100.35 ) 12.54 % Total 850244.61 26 100 % * Pooled sum of squares (SSs) are idetified by a uderscore. I ANOVA, the sum of squares (SS f ) cotributed by each of the cotrol factors A to F. The percetage cotributio ( f ) by factor f i total sum of squares (SS T ) is the adopted to evaluate its importace o the quality characteristic of iterest, which ca be expressed as [14]: f =SS f / SS T 100 % (4) The pure percetage cotributio by factor f, ' f, is calculated as: ' f =SS' f / SS T 100 % (5) where SS' f is the pure sum of squares cotributed by factor f. Give the degrees of freedom, df f, associated with factor f, the SS' f is calculated as: (6) SS SS df Ve f f f where V e is the pooled error mea square obtaied as pooled error variace divided by degree of freedom associated with pooled error. I this research, a factor effect is cosidered egligible if it is associated with a percetage cotributio (f) less tha 5 %. Cosequetly, the effects of factors E (E = 3.14%) ad F (F = 0.07%) are cosidered egligible ad hece their sum of squares values are pooled ito error. Moreover, the effects of factor A to D are sigificat as their correspodig F ratios of 10.35, 65.80, 11.57, ad 6.96, respectively, are greater tha 4. The values of ' A, ' B, ' C ad ' D for factors A to D are foud 9.02 %, 62.50%, 10.19 %, ad 5.75, respectively. Obviously, the scraper pressure (factor B) cotributes the largest pure sum of squares ad hece is cosidered the most ifluetial factor o lumiace. Moreover, factors A, B, C, ad D cotribute about 87 % of the total variability i LGP lumiace. 4.4 Cofirmatio experimets Coductig cofirmatio experimets is a crucial fial step of a robust desig which verifies that the optimal factor levels do ideed the projected improvemet. Settigs process factors at the combiatio of optimal levels A 3 B 3 C 3 D 2 E 3 F 2, five samples are radomly selected every half hour for 15 workig hours. Their correspodig x ad R cotrol charts are costructed the also show i Figure 4. At improvemet stage, the LCL, CL, ad UCL values for the x 53

Al-Refaie Abbas, Li Mig-Hsie, Al-Tahat & Fouad: Applyig DMAIC Procedure to Improve chart are estimated 4857.60, 4949, ad 5040.40 cd/m 2, respectively. Whereas, for the R chart the LCL, CL, ad UCL values are calculated 0, 158.4, ad 334.86 cd/m 2, respectively. Obviously, the x ad R cotrol limits at improvemet stage are tighter tha those at iitial stage. Moreover, the value at improvemet stage is 68.10 cd/m 2. The C pk value at improvemet stage is ehaced to 2.44, which idicates that the LGP pritig process become highly capable. 5. CONTROL PHASE The grey system theory, origially preseted by Deg [15], focuses o model ucertaity ad iformatio isufficiecy i aalyig ad uderstadig systems via research o coditioal aalysis, forecastig ad decisio makig. The grey model GM(1,1) has bee successfully applied to various applicatios [16]. The beefits from the use of grey forecastig models are that: (i) it ca be used to situatios with the miimum data dow to four observatios; (ii) it utilies a first-order differetial equatio to characterie a system; ad (iii) the computatio is very simple usig computer software. The GM(1,1) grey model is summaried as follows [17]: Step 1. For a iitial time sequece where X x x x i x, (2),..., ( ),..., ( ) (7) x () i the time series data at time i, must be equal to or larger tha four. Step 2. Establish a ew sequece X through the accumulated geeratig operatio i order to provide the middle message of buildig a model ad to weake the variatio, that is where X x x x i x, (2),..., ( ),..., ( ) (8) k x ( k ) x ( i ) k =1, 2,..., (9) i1 Step 3. Costruct a first-order differetial equatio of grey model GM(1,1) as follows dx dt ax b (10) ad its differece equatio is X az b k=2,3,..., (11) where a ad b are the coefficiets to be estimated usig a, b 1 T T Z (2) 1 Z (2) 1 Z (2) 1 Z (3) 1 Z (3) 1 Z (3) 1 x (2), x (3),..., x ( ) Z ( ) 1 Z ( ) 1 Z ( ) 1 T (12) 54

Al-Refaie Abbas, Li Mig-Hsie, Al-Tahat & Fouad: Applyig DMAIC Procedure to Improve ad Z ( k1) is the (k+1) th backgroud value calculated as Z k x k x k k ( 1) ( ( ) ( 1))/ 2 =1,2,...,( -1) (13) Solvig Equatio (12) gives a k2 k 2 ( 1) x k 2 ( 1) 2 k 2 k 2 x 2 (14) ad b k2 2 k 2 ( 1) x k 2 k 2 2 k2 k 2 x 2 (15) Step 4. Obtai the predicted x ( 0 ( p ) at time (+p) usig ˆ ) ˆ b a a a( p1) x ( p) x.(1 e ). e (16) Utiliig the 10 cofirmatio experimets i Figure (4) as a iitial sequece, the steps of GM (1,1) grey model were performed. The a ad b values are calculated usig Equatio (14) ad (15) ad foud equal to 0.00153233 ad 4993.25839, respectively. The predicted lumiace is calculated usig Equatio (16) ad foud as: ˆ 0.00153233 (10 p1) x ( p) 4989.53104. e (17) where p is the umber of periods to be predicted ahead from the 10th period. Figure 4 also displays the predicted lumiace for samples 11 20. The above model was verified by predictig the cofirmatio values, where the square root of mea square error is foud equals 47.69 cd/m 2, which is cosidered egligible. For a three sigma quality-level, the rage for predicted lumiace is about 150 cd/m 2. which is very small. Cosequetly, the predictio model may provide good estimate of lumiace for future productio. 6. CONCLUSIONS This research aims at improvig LGP pritig process by adoptig DMAIC methodology. The process mappig, x ad R cotrol charts, process capability, Taguchi method, ad GM(1,1) model are the mai tools used i this methodology. Six process factors were ivestigated cocurretly, icludig: scraper agle, scraper pressure, scraper speed, ik viscosity, ik paller bearig, ad gap betwee board ad LGP utiliig the L 27 (3 13 ) array. The S/N ratio was the employed to decide optimal factor levels. By implemetig DMAIC, the aticipated improvemet i lumiace is 411.13 cd/m 2. The C pk was greatly ehaced from 0.69 to 2.44. Moreover, the scraper's agle, pressure ad speed, ad ik viscosity were foud sigificatly cotributig to the total variatios of LGP pritig process. 55

Al-Refaie Abbas, Li Mig-Hsie, Al-Tahat & Fouad: Applyig DMAIC Procedure to Improve REFERENCES [1] Yamaaki, T.; Kawakami, H.; Hori H. (1995). Color TFT Liquid Crystal Displays. (SEMI Stadard FPD Techology Group: Tokyo) [2] Ide, T.; Miuta, H.; Numata, H.; Taira, Y.; Suuki, M.; Noguchi, M; Katsu, Y. (2003). Dot patter geeratio techique usig molecular dyamics. Joural of the Optical Society of America A 20, 248 55 [3] Feg D., Ya Y., Yag X., Ji G.; Fa S. (2005). Novel itegrated light-guide plates for liquid crystal display backlight. Joural of Optics A: Pure ad Applied Optics, 7, 111-117. [4] Tamura, T.; Satoh, T.; Uchida, T.; Furuhata, T. (2006). Quatitative Evaluatio of Lumiace Nouiformity Mura i LCDs Based o Just Noticeable Differece (JND) Cotrast at Various Backgroud Lumiaces. IEICE TRANSACTIONS o Electroics, E89 C (10), 1435-1440 [5] Kwak, Y.K.; Abari, F.T. (2006). Beefits, obstacles, ad future of six sigma approach. Techovatio, 26, 708 715 [6] Li, M.H.; Al-Refaie A. (2008). Improvig woode parts quality by adoptig DMAIC procedure. Quality ad Reliability Egieerig Iteratioal, 24, 351 360 [7] Li, M.H.; Al-Refaie, A.; Yag C.Y. (2008). DMAIC approach to improve the capability of SMT solder pritig process. IEEE Trasactios o Electroics Packagig Maufacturig, 24, 351-360 [8] Taguchi, G. (1991). Taguchi Methods, Research ad Developmet, Vol. 1, Dearbor, MI: America Suppliers Istitute Press [9] Phadke, M.S. (1989). Quality Egieerig Usig Robust Desig. NJ: Pretice-Hall, Eglewood Cliffs [10] Khoei, A.R.; Masters, I.; Gethi D.T. (2002). Desig optimiatio of Alumiium recyclig processes usig Taguchi techique. Joural of Materials Processig Techology, 127: 96-106 [11] Motgomery, D.C. (2009). Itroductio to Statistical Quality Cotrol. New York: Joh Wiley & Sos Ic. [12] Kot, S.; Lovelace, C.R. (1998). Process capability idices i theory ad practice. Arold, Lodo [13] Kae, V.E. (1986). Process capability idices, Joural of Quality Techology, 18, 41-52, 1986 [14] Belavedram N. (1995). Quality by Desig-Taguchi techiques for idustrial experimetatio. Pretice Hall Iteratioal. [15] Deg, J.L. (1989). Itroductio to grey system theory, Joural of Grey System, 1, 1 24 [16] Mao, M.; Chirwa, E.C. (2006). Applicatio of grey model GM (1,1) to vehicle fatality risk estimatio, Techological Forecastig & Social Chage, Vo.l. 73, 588 605 [17] Ta, G. J. (2000). The structure method ad applicatio of backgroud value i grey system GM(1,1) Model (I), Systems Egieerig - Theory & Practice, 20 (4), 98 103 56

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