Optimization of the Sizing Process with Grey Relational Analysis

Çiğdem Sarpkaya, *Emel Ceyhun Sabir Optimization of the Sizing Process with Grey Relational Analysis DOI: 10.5604/12303666.1172087 Department of Handicrafts, Gaziantep University, Turkey *Department of Textile Engineering, Cukurova University, Turkey E-Mail: emelc@cu.edu.tr Abstract The sizing process is an important one for textile mills and affects the eficiency of the loom machine. In this study, the optimisation of multiple performance characteristics based on the grey relations analysis method, which is a new approach for optimisation of the sizing process was researched using the Taguchi L18 (mixed 3 - 6 level) experimental plan. The process parameters selected: warp yarn count, the viscosity of the sizing solution and the dispatch speed of the warp yarn passing from the sizing machine, were optimised. In the experimental design of Taguchi L18 (mixed 3 - 6 level), the warp yarn count factor was chosen as 3 levels (12, 10 and 8 tex), the viscosity of the sizing solution factor as 3 levels (14, 20, & 24 Ns/m2), and the dispatch speed of the warp yarn passing from the sizing machine factor was selected as 6 levels (40, 50, 60, 70, 80, & 90 m/min). Quality characteristics were determined as the warp yarn strength, and the eficiency of the loom machine. A grey relational grade obtained from the grey relational analysis is used to solve the sizing process with multiple performance characteristics. Optimum levels for the sizing process parameters were determined using the grey relation grade. Key words: sizing, orthogonal array, grey relational analysis, optimization. n Introduction Sizing is a process before weaving which directly affects the performance of the weaving process. The process’ physical length is approximately 60 m. The most important output parameters of the process that will optimise the determination of the levels of the input parameters are an optimisation problem. The Taguchi optimization method reduces the number of experiments, and thus recently using the method has increased for the solution of engineering optimisation problems. In the classical Taguchi applications, quality characteristics are examined one by one; for each characteristic, the optimum level of inputs is determined, but the Taguchi Method based on grey relational analysis, which is a new approach, at least two and more quality characteristics can be considered collectively . Accordingly the optimum quality level desired according to the characteristics of the input parameters can be determined. The Taguchi method’s steps for one output:1. Experiment Design and Execution 2. SignaltoNoise Ratio (S/N) Calculation & 3. Optimal Factor Levels Determination. The steps of the Taguchi method based on grey relation analysis for multiple outputs: 1. Experiment Design and Execution, 2. SignaltoNoise Ratio (S/N) Calculation 3. Establishment of Decision Matrix, 4. Normalisation of Data, 5.Weighting of Normalised Data, 6. Ranking Points’ Calculation of the Alternatives, and 7. Optimal Factor Level Determination [1]. The Taguchi Method based on Grey relational analysis is applied in various engineering sciences. for example, Lin and Lin (2002) in the electrical discharge machining (EDM) process, Tosun (2006) - optimising the drilling process parameters for work piece surface roughness and burr height, Kopac and Krajnik (2007) - optimising the robust design of lank milling parameters, Kuo, Yang and Huang (2008) - to solve multi-response simulation problems, Kuo and Tu (2009) to improve the quality control strategy for calendering, Eşme, Bayramoğlu and Aydın (2009) - to optimize galetaj process parameters affecting the surface roughness and microhardness of the ?????? (forward speed, number of passes, galetaj speed and compression force), Su, Chen, Ma and Lu (2011) optimising of yarn evenness and yarn strength, Yıldırım (2011) - determining of the quality characteristics of washing machine models and the factors affecting the level of the best factor, and the Grey Relational Analysis method was used in [1 - 8]. In optimisation with grey relational analysis, output parameters can be weighted for the degree of importance. Work is usually the output parameters on an equal weighting [2, 3, 9]. However, there are some studies giving different weights to outputs [10 - 13]. be determined. In this study, different weights (0.3 - 0.7; 0.5 - 0.5;0.7 - 0.3) are given the two output parameters to view the results of the method’s weighting steps, and optimisation results were compared. The Taguchi optimisation technique based on grey relation analysis, which is a new multicriteria optimisation method for textile, was applied, and the best input parameters for speciied performance characteristics of the sizing process could The speed input expresses the warp yarn passing on the drying cylinder in the sizing machine. Slow or fast passing on the drying cylinders in the sizing machine affects moisture content on the yarn. When the yarn has too much moisture or is too Sarpkaya Ç, Sabir EC. Optimization of the Sizing Process with Grey Relational Analysis. FIBRES & TEXTILES in Eastern Europe 2016, Vol. 24, 1(115). 49-55. DOI: 10.5604/12303666.1172087 n Material In the study, during the pre-trial process in the weaving, sizing of the ine yarn count was found to be more important than thicker yarns. After this determination, ine yarns produced for shirting and cotton material (because it is especially used for short staple spinning) were decided to be used. Cotton yarns (12, 10 and 8 tex) were selected. n Methods Determiniation of input parameters to be optimized and multiple performance characteristics In this study, the Taguchi method based on Grey Relation Analysis was applied. Therefore the sizing process parameters to be optimised and the best performance characteristics were irstly determined. The input factors affecting the sizing process and the outputs obtained from the process are given in Table 1. 49 Table 1. Factors affecting the sizing process and the sizing process outputs obtained from the process [14]. Test parameters (input variables) Outputs (response variables) Speed, m/min Eficiency, % Viscosity, Ns/m2 Strength, cN/tex Yarn count, tex Table 2. Selected design of experiments L18 (mixed 3 - 6 level) [14, 15]. Factor No. (Code) Factors Level number Levels 1(A) Speed m/min 6 40, 50, 60, 70, 80, 90 2(B) Viscosity, Ns/m2 3 14, 20, 24 3(C) Yarn count, tex 3 12, 10, 8 dry, it may lead to eficiency losses in the weaving machine. The viscosity input determines the luidity of the sizing solution. Low or high sizing solution viscosity causes some problems for the further process. The yarn count input, yarn type and yarn ineness in the appropriate machine setting are determined by selecting a suitable sizing agent for the sizing yarns. The output process parameters se- lected, shown in Table 1, are expressed below. a) Warp yarn strength: In this study, the warp yarn strength is selected as the irst output parameter. The weaving process is the next step after sizing. The sized yarns will be exposed in order to be resistant to the weaving process, as having the highest possible strength is desired. In this paper, for the measurement of yarn strength, TITAN strength test apparatus (origin from England) was used and tests performed according to the EN ISO 2062 standard. b) The eficiency of the weaving machine is selected as the second output parameter. Behaviour against forces of sized yarns in the weaving machine (i.e. warp yarn breakage, hence the number of stoppages of the weaving machine) can be expressed as weaving machine eficiency. In the study, weaving machine eficiency was determined by measuring warp yarn breakage over 1000 m. A Vamatex weaving machine (2002 brand, origin from Italy) was used in the study. Preparation of the test plan In this study, the input parameters and levels selected are shown in Table 2. Ac- cording to the schedule in the full factorial design of experiments, the necessary number of experiments will be 54. However, the number of experiments can be reduced to 18 by the Taguchi Method. This method, supported by the literature, can obtain overall results by a lesser test. According to the factors and levels in the Taguchi experimental design selected, the L18 (mixed 3 - 6 level) orthogonal layout was decided. Table 2 shows the design. In this study, a total of 18 experiments were applied. Grey relationship analysis method The multiple performance response is converted to a single one using Multicriteria decision-making methods with the Taguchi method. In this way, the problem would be formed into an optimisation problem with a single response. In Figure 2, the application procedure of the Taguchi method based on grey relational analysis is given. According to this igure, in steps 1, 2 & 7, the general procedure of the Taguchi method is given, and in steps 3 - 6 that of the Multi-criteria decision making method [1, 8]. Grey relational analysis method steps of the calculation are as follows. Step 1. The reference sequence of length n is as follows in Equations 1. 1. Experiment design and execution 4. Normalization of data Step 2. Data to be normalised Normalisation in the theory of grey system projects is called Grey Relational Generating. The normalisation of data in one of the most commonly used methods is preprocessing linear data. Being considered in the normalisation of the factor series is which criteria („The Larger – The Better”, „The Smaller – The Better” and “The Nominal – The Better”) relect the feature of the series. For example, if the smaller values are desired in the series, the linear normalization values should be closer “1”, if the bigger values are desired in the series, the linear normalization values should be closer “0”. 5. Weighting of normalized data In the “The Larger – The Better”, normalization is as follows in Equation 2 2. Signal to noise ratio calculation Single responce Multiresponse Taguchi method Multi-criteria decision-making methods 3. Establishment of decision matrix 7. Optimal factor levels determination 6. Ranking point calculation of the alternatives Figure 1. Application procedure of the Taguchi method based on grey relational analysis [1, 8]. 50 x0 = (x0(1), x0(2), x0(3), ..., x0(n)) (1) xi ( k ) = xio (k ) − min xio (k ) max xio (k ) − min xio (k ) (2) xio (k ) , the i series is the original value of the k. order; xi (k ) the value which is the i series and k order after normalisation, max min xio (k ) the minimum value in FIBRES & TEXTILES in Eastern Europe 2016, Vol. 24, 1(115) the i series, and max max xio (k ) the maximum value in the i series. In the “The Smaller – The Better”, normalisation is as follows in Equation 3. xi ( k ) = max x (k ) − x (k ) (3) max xio (k ) − min xio (k ) o i o i In the “The Nominal – The Better”, Normalization is as follows in Equations 4. xi ( k ) = 1 − Here, cates. xo x (k ) − x o i o max xio (k ) − x o (4) the ideal desired value indi- Step 3. The m number series is compared with the x o series, deined in Equation 5. xi = (xi(1), xi(2), xi(3), ..., xi(n)) (5) i = 1, 2, 3, ..., m Step 4. k shows the k order over the length of the n series. e(x0(k), xi(k)) is the grey relational coeficient in the k order, and can be calculated in Equations 6, 7, 8 & 0i 9. ), xi(k)) (k ) ) = ee((x0((k), D min + ξD max D oi (k ) + ξD max D0i = |x0(k) - xi(k)| Dmin = minj mink |x0(k) - xi(k)| Dmax = maxj maxk |x0(k) - xi(k)| (6) (7) (8) (9) ξ∈(0,1) is the distinguishing coeficient in 0 - 1, j = 1, 2, …, m; k = 1, 2, ..., n. The purpose of ξ is to adjust the difference between D0i and Dmax. Studies indicated that when different distinguishing coeficients are adopted, the grey relational coeficient results are always the same [1, 16, 17]. lation of the weighted grey relationship degree. γ ( x 0 , xi ) = ∑W n k =1 1 n ∑Wk ee((xx0(k), xi(k)) n k =1 rameters that signiicantly affect the multiple performance characteristics. h = h m + ∑ (h i − h m ) j γ ( x0 , xi ) is a measure of the geometric similarity between xi in a grey system and x0 reference sequences. The size of the grey relational degree is an indication that there is a strong relationship between xi and x0. If two the series compared are the same, the grey relational grade is found as 1. The grey relational grade shows that the reference series are somewhat similar with the series compared [3, 9, 18 - 22]. 1 In this study, 3 different weights were chosen: the weaving eficiency (0.5) – yarn strength (0.5), eficiency (0.7) – strength (0.3) and eficiency (0.3) – strength (0.7). Step 6. Determination of the new levels of the test factors. Step 7. Performing an ANOVA test. Step 8. Performing a conirmation test. The grey relational grade h estimated using the optimal level of the parameters is calculated as Equation 12. Where hm is the total mean of the grey relational grade, hi the grey relational grade at the optimal level, and j is the number of pa- (12) i =1 (11) Application of the grey relational analysis method to the sizing process The Taguchi L18 (mixed 3 - 6 level) experimental plan and results of the experiments are shown in Table 3. In the irst row, factors affecting the process (A - C) and response variables are given. The irst column in the table refers to the experiment’s number. In the last two columns, the results of experiments carried out by the experimental study are given. Minitab 15® software program was used for application of the Taguchi Method. The grey relational grade, which is calculated by Equation 10, is placed from the largest to the smallest in the irst column. The grey relational grade in the second and third columns is calculated by Equation 11. As a result of this sorting, experiments with a combination of the largest grey relational grade has the best multi-performance characteristics. In Table 4 (seee page 52), the grey relational grade is given for the weighted eficiency (0.5) – strength (0.5), weighted eficiency (0.7) – strength (0.3), weighted eficiency (0.3) – strength (0.7). Ordering from the largest to the smallest is also seen in Table 4. Table 3. Results of the experiments for the sizing process [14]. Experiment number Experiment parameters (Input variables) Outputs (Response variables) A (Speed, m/min) B (Viskostiy, Ns/m2) C (Yarn count, tex) Eficiency, % Strength, cN/tex 1 40 (1) 14 (1) 12 (1) 61.3 33.59 2 40 (1) 20 (2) 10 (2) 84.8 37.78 3 40 (1) 24 (3) 8 (3) 52.9 53.34 4 50 (2) 14 (1) 12 (1) 72.6 32.46 5 50 (2) 20 (2) 10 (2) 86.3 35.22 1 n ∑ e(x( x0(k), xi(k)) (10) n k =1 6 50 (2) 24 (3) 8 (3) 78.9 34.49 7 60 (3) 14 (1) 10 (2) 71.2 30.32 8 60 (3) 20 (2) 8 (3) 83.3 34.50 9 60 (3) 24 (3) 12 (1) 69.5 33.81 Different levels of performance effects (in weight) should be taken into account in the calculation of this weight. If the outputs have equal weight for quality, the total weight must be equal to “1”. Thus two outputs share the total weight as equal (0.5 - 0.5). If one of the outputs has more inluence than the other, its weight is larger. Equation 11 is used for calcu- 10 70 (4) 14 (1) 8 (3) 81.9 32.39 Step 5. If impact on the performance of the output is equal, Grey Relational Degree is calculated by Equation 10. γ ( x 0 , xi ) = FIBRES & TEXTILES in Eastern Europe 2016, Vol. 24, 1(115) 11 70 (4) 20 (2) 12 (1) 87.3 35.26 12 70 (4) 24 (3) 10 (2) 80.9 29.55 13 80 (5) 14 (1) 10 (2) 79.8 33.52 14 80 (5) 20 (2) 8 (3) 63.1 34.61 15 80 (5) 24 (3) 12 (1) 86.8 34.37 16 90 (6) 14 (1) 8 (3) 78.5 35.00 17 90 (6) 20 (2) 12 (1) 77.9 32.10 18 90 (6) 24 (3) 10 (2) 76.9 31.88 51 Table 4. Grey relational grade for the outputs of eficiency and strength and sorting from largest to smallest with weighting [14]. Grey relational grade Experiment number Weighted eficiency 0.5 – strength 0.5 Weighted eficiency 0.7 – strength 0.3 Weighted eficiency 0.3 – strength 0.7 result order result order result order 1 0.56 18 0.28 18 0.28 18 2 0.77 4 0.42 4 0.35 2 3 0.75 5 0.33 14 0.43 1 4 0.62 14 0.33 13 0.29 14 5 0.77 3 0.43 3 0.34 4 6 0.68 9 0.36 9 0.32 8 7 0.59 16 0.31 15 0.28 17 8 0.73 6 0.40 5 0.33 6 9 0.60 15 0.31 16 0.29 15 10 0.70 7 0.38 6 0.32 9 11 0.78 1 0.44 1 0.35 3 12 0.67 11 0.37 7 0.30 12 13 0.68 8 0.37 8 0.31 10 14 0.57 17 0.29 17 0.28 16 15 0.77 2 0.43 2 0.34 5 16 0.68 10 0.36 10 0.32 7 17 0.66 12 0.35 11 0.30 11 18 0.65 13 0.35 12 0.30 13 Table 5. Calculation of new levels for factors of speed, viscosity and yarn count. Factor and its level New level Weighted eficiency 0.5 – strength 0.5 Weighted eficiency 0.7 – strength 0.3 Weighted eficiency 0.3 – strength 0.7 A1 0.6921 0.3411 0.3510 A2 0.6890 0.3718 0.3173 A3 0.6419 0.3416 0.3003 A4 0.7179 0.3959 0.3220 A5 0.6758 0.3623 0.3135 A6 0.6614 0.3551 0.3063 B1 0.6385 0.3393 0.2992 B2 0.7132 0.3864 0.3268 B3 0.6874 0.3582 0.3292 C1 0.6651 0.3562 0.3089 C2 0.6891 0.3740 0.3151 C3 0.6849 0.3537 0.3312 Table 6. New levels calculated for the factors of speed, viscosity and yarn count. Weights Weighted eficiency 0.5 – strength 0.5 Weighted eficiency 0.7 – strength 0.3 Weighted eficiency 0.3 – strength 0.7 Factors Levels 1 3 4 5 6 Maxmin A 0.6921 0.6890 0.6419 0.7179 0.6758 0.6614 0.0760 B 0.6385 0.7132 0.6874 - - - 0.0747 C 0.6651 0.6891 0.6849 - - - A 0.3411 B 0.3393 0.3864 0.3582 - - - C 0.3562 0.3740 0.3537 - - - A 0.3510 0.3173 0.3003 0.3220 0.3135 0.3063 0.0508 B 0.2992 0.3268 0.3292 - - - 0.0300 C 0.3089 0.3151 0.3312 - - - 0.0223 A grey relational grade graph is shown in Figure 2. As is seen in Figure 3.a, in experiment No. 11, the grey relational grade is the highest for the weighted eficiency (0.5) – strength (0.5). As is seen 52 2 0.3718 0.3416 0.3959 0.3623 0.3551 0.0240 0.0548 0.0471 0.0202 in Figure 2.b, in experiment No. 11, the grey relational grade is the highest for weighted eficiency (0.7) – strength (0.3). As is seen in Figure 2.c, in experiment No. 3, the grey relational grade is the highest for weighted eficiency (0.3) – strength (0.7). After calculating the grey relational grade, new levels of experiment factors are determined. Calculation of the new level of the factors is provided in Table 5 collectively. In Table 6 new calculated levels of the factors are given. The irst column of the Table represents factors and the irst line represents the levels. In the last column the difference between maximum and minimum levels are given. Looking at the charts, the highest level of factors gives the optimum process level. As understood from the table, the forth level of (Speed) factor A, the second level of factor B (viscosity), and the second level of factor C (Yarn count) are the highest grey relational grades for weighted eficiency (0.5) – strength (0.5) . Accordingly the optimal process parameters are determined as A4B2C2. A4B2C2 is not included in the study’s design experiment (Table 3). Hence the optimum process conditions are 70 m/min of the warp yarn, 20 Ns/m2 viscosity and 10 tex yarn count. In the last column of the chart, the biggest difference between the levels of the factors is in A (Speed), which means the most effective is factor A (Speed), inluencing the quality parameter in the sizing process parameters for these three factors. For weighted eficiency (0.7) – strength (0.3), the optimal process parameters are determined as A4B2C2 (Table 4 is not included in this experiment). Thus the optimum process conditions are 70 m/min, 20 Ns/m2 viscosity and 10 tex. In the last column of the chart, the biggest difference between the levels of the factors is in A (Speed), which means the most effective is factor A (Speed), inluencing the quality parameter in the sizing process parameters, for these three factors. For weighted eficiency (0.3) – strength (0.7), the optimal process parameters are determined as A1B3C3. Table 3 includes the A1B3C3 combination as experiment number 3. The optimum process conditions are 40 m/min of the warp yarn, 24 Ns/m2 viscosity and 8 tex yarn count for weighted eficiency 0.7 – strength 0.3. In the last column of the chart, the biggest difference between the levels of the factors is in A (Speed), which means the most effective factor is A (Speed), inluencing the quality parameter in the FIBRES & TEXTILES in Eastern Europe 2016, Vol. 24, 1(115) weighted eficiency 0.3 – strength 0.7 in Figure 3.c. In Figure 3 (see page 54), the grey relational grade graphics of the sizing process parameters levels are given. Here the optimum parameter levels are shown for weighted eficiency 0.5 – strength 0.5 in Figure 3.a. In Figure 3.b, the optimum parameter levels are given for weighted eficiency 0.7 – strength 0.3. Optimum parameter levels are shown for After these assessments, an ANOVA test is performed. The factor that has the highest F value is determined as the most effective, inluencing process parameter performance. The ANOVA test of the grey relational grade for weighted eficiency 0.5 – strength 0.5 is given in Table 7.a (see page 54), in which the output parameter with the highest F value is shown as B (Viscosity). The contribution value in % also supports the result. The ANOVA test of the grey relational grade for weighted eficiency 0.7 – strength 0.3 is given in Table 7.b. In the table, the output parameter with the highest F value is shown as B (Viscosity). The contribution value in % also supports the result. The ANOVA test of the grey relational grade for weighted eficiency 0.3 – strength 0.7 is given in Table 7.c, in which the output parameter with the highest F value is shown as B (Viscosity). Grey relation grade sizing process parameters for these three factors. Experiment number Grey relation grade a) Experiment number Grey relation grade b) c) Experiment number Figure 2. Grey relational grade graph for the outputs of eficiency and strength; a) weighted eficiency (0.5) – strength (0.5), b) weighted eficiency (0.7) – strength (0.3), c) weighted eficiency (0.3) – strength (0.7). FIBRES & TEXTILES in Eastern Europe 2016, Vol. 24, 1(115) 53 Grey relational grade In the study, once the optimal level of the parameters is found, the inal step is to predict and verify the improvement of the output parameters using the optimal level of the input parameters. The prediction and experiment grey relational grades with the optimal parameters are calculated using Equation 12. Table 7.a shows the results of the conirmation experiment using the optimal parameters for weighted eficiency 0.5 – strength 0.5. As shown in Table 7.a, yarn strength is improved from 33.59 to 44.79 cN/tex, Weaving eficiency is improved from 61.3 to 71.8%, which clearly shows that the multiple performance characteristics in the sizing process are greatly improved by using of Taguchi based on the grey relational analysis method. a) Grey relational grade Process parameter level Table 8.b shows the results of the conirmation experiment using the optimal parameters for weighted eficiency 0.7 – strength 0.3. As shown in Table 8.b, yarn strength is improved from 33.59 to 44.79 cN/tex and weaving eficiency is improved from 61.3 to 71.8%. b) Grey relational grade Process parameter level c) Process parameter level Figure 3. Graph of sizing process parameters; A) speed, B) viscosity, C) yarn count); a) weighted eficiency 0.5 – strength 0.5, b) weighted eficiency 0.7 – strength 0.3, c) weighted eficiency 0.3 – strength 0.7. Table 7. ANOVA test of the grey relational grade for different weighted eficiency – strength. Weights a) Weighted eficiency 0.5 – strength 0.5 Source Adj SS A 5 0.010628 0.010628 0.002126 0.29 12.06493 B 2 0.017344 0.017344 0.008672 1.19 19.68895 2 0.001911 0.001911 0.000956 0.13 Residual error 8 0.058211 0.058211 0.007276 - 66.08128 17 0.088094 - - - - A 5 0.006419 0.006419 0.001284 0.44 16.89255 B 2 0.006729 0.006729 0.003364 1.15 17.70836 C 2 0.001463 0.001463 0.000731 0.25 Residual error 8 0.023388 0.023388 0.002924 - - - Total 17 0.037999 - 5 0.004733 0.004733 2.16937 3.85010 61.54899 - 0.000947 0.64 21.92930 15.47514 B 2 0.003340 0.003340 0.001670 1.12 C 2 0.001591 0.001591 0.000796 0.53 Residual error 8 0.011919 0.011919 0.001490 - 55.22402 17 0.021584 - - - - Total 54 F C A c) Weighted eficiency 0.3 – strength 0.7 Adj MS Contribution, % Seq SS Total b) Weighted eficiency 0.7 – strength 0.3 Analysis of variance for means DF 7.37154 Table 8.c shows the results of the conirmation experiment using the optimal parameters for weighted eficiency 0.3 – strength 0.7. As shown in Table 8.c, the strength is improved from 33.59 to 53.34 cN/tex and weaving eficiency is down from 61.3 to 52.9%. Decreases in the weaving eficiency cannot be considered as important because the output of yarn strength is more important than weaving eficiency in weighting (weighted eficiency 0.3 – strength 0.7). The results show clearly that the weighted eficiency 0.3 – strength 0.7 and weighted eficiency 0.5 – strength 0.5 show improvement in the grey relational grade, which means that eficiency and strength outputs have same weight for optimisation of the sizing process. n Conclusions In this study, grey relational analysis as a multicriteria optimisation technique is used to optimise the sizing process. It uses Taguchi Design Models. In this study, the Taguchi L18 (mixed 3 - 6 level) experimental design was applied. The effect on the weaving machine eficiency and warp strength of the inputs affecting the sizing process: the speed of warp yarn passing from sizing machine, viscosity and warp yarn count were investigated using the experimental design. In this FIBRES & TEXTILES in Eastern Europe 2016, Vol. 24, 1(115) Table 8. Results of sizing performance using the initial and optimal parameters for different weighted eficiency – strength. Initial process parameters Weights prediction experiment A1B1C1 A4B2C2 A4B2C2 Strength, cN/tex 33.59 - 44.79 Eficiency, % 61.30 - 71.80 0.56 0.76 Level a) Weighted eficiency 0.5 – strength 0.5 Optimum process parameters Grey relational grade Level b) Weighted eficiency 0.7 – strength 0.3 A1B1C1 Strength, cN/tex 33.59 Eficiency, % 61.30 Grey relational grade A4B2C2 Level 71.80 0.28 0.43 A1B1C1 Strength, cN/tex 33.59 Eficiency, % 61.30 Grey relational grade 4. 5. 6. Funding This work was supported by University of Cukurova (Project Number: MMF2009D16). The irst results of the study were presented at AUTEX2014 14th World Textile Conference, (Book of Abstracts) and the conference presentation was inanced by Harran University (Projcet Number: K14020) 7. 8. Acknowledge We would like to thank BOSSA A.Ş. (in Adana/ Turkey) for experimental studies of the project and also the Textile Engineering Department of the University of Cukurova in Adana/Turkey for physical yarn tests. References 1. Kuo Y, Yang T, Huang GW. The use of a grey based taguchi method for optimizing multi response simulation problems. Engineering Optimization 2008; 40: 517-528. 2. Lin JL, Lin CL. The use of the orthogonal array with grey relational analysis to optimize the electrical discharge machining process with multiple performance characteristics. International Journal of FIBRES & TEXTILES in Eastern Europe 2016, Vol. 24, 1(115) 9. 10. 11. 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