Int J Adv Manuf Technol (2004) 23: 896–902 DOI 10.1007/s00170-003-1733-8 O R I GI N A L A R T IC L E C.-M. Hsu Æ C.-T. Su Æ D. Liao Simultaneous optimisation of the broadband tap coupler optical performance based on neural networks and exponential desirability functions Received: 14 October 2002 / Accepted: 16 January 2003 / Published online: 18 February 2004
Springer-Verlag London Limited 2004 Abstract This study presents an integrated procedure using neural networks and exponential desirability functions to resolve multi-response parameter design problems. The proposed procedure is illustrated through optimising the parameter settings in the fused bi-conic taper process to improve the performance and reliability of the 1% (1/99) single-window broadband tap coupler. The proposed solution procedure was implemented on a Taiwanese manufacturer of fibre optic passive components and the implementation results demonstrated its practicability and effectiveness. A pilot run of the fused process revealed that the average defect rate was reduced to just 2.5%, from a previous level of more than 35%. Annual savings from implementing the proposed procedure are expected to exceed 0.5–1.0 million US dollars. This investigation has been extensively and successfully applied to develop optimal fuse parameters for other coupling ratio tap couplers. Keywords Parameter design Æ Multi-response problem Æ Neural network Æ Exponential desirability function Æ Single-window broadband tap coupler 1 Introduction Optical performance in a coupler manufacturing process is usually influenced by more than one variable. These variables include machine parameters, raw materials, the C.-M. Hsu (&) Department of Business Administration, Minghsin University of Science and Technology, Hsinchu, Taiwan R.O.C. E-mail: cmhsu@must.edu.tw C.-T. Su Æ D. Liao Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu, Taiwan R.O.C. process followed, environmental conditions and so on. From the perspective of cost or feasibility, some variables cannot be precisely controlled. Furthermore, even when these variables are controllable, the optimal combination of parameter levels that maximises product quality may be unknown. The Taguchi method is a conventional approach to resolving this problem. This method allows engineers to determine a feasible combination of design parameter levels such that the variability of a product’s response is reduced and the mean is close to the target. However, optimising a multi-response problem using the standard Taguchi method is difficult. The usual recommendation for the optimisation of a process/product with multiple responses is left to engineering judgment and is verified by experiments [1]. However, the introduction of human judgment increases uncertainty in the decision-making process. Logothetis and Haigh [2] applied the multiple regression technique and linear programming approach to optimise a fiveresponse process by the Taguchi method. Their method was limited when the t-values of the regression coefficients were insignificant or when the coefficient of determination was low. Pignatiello [3] presented a quadratic loss function for multi-response problems and established a predictive regression model using controllable variables. Following the descent direction and repeatedly establishing a new local experimentation region, this method minimised the expected loss. However, it was difficult to determine the cost matrix and additional experimental observations were required. Tong et al. [4] proposed a procedure to determine the multiresponse signal-to-noise (MRSN) ratio through integrating the quality loss of each response. However, determining the weight ratios for responses was difficult, and the optimal combination of factor levels was likely to be dominated by the ‘‘maximum quality loss’’ in the total of the trials. Antony [5] proposed an approach using the Taguchi loss function and principal component analysis to optimise a submerged arc-welding process. In this study, it was difficult to determine the optimal parameter settings if two or more eigenvalues 897 greater than one were obtained according to Kaiser’s criterion [6]. Superimposing the response contour plots and finding an optimal solution by visual inspection is a simple and intuitive approach to resolving multi-response problems [7]. However, such a method is severely limited by the number of input variables and/or responses [8]. The use of a dimensionality reduction strategy has thus become a popular means of simultaneously optimising (compromising) multiple responses. This method converts a multi-response problem into a single-response problem with an aggregated measure, which has often been defined as a desirability function [9, 10] or as an estimated distance from the ideal design point [11]. Kim and Lin [8] developed a modelling approach based on maximising exponential desirability functions for optimising a multi-response system. Their approach aimed to identify the settings of the input variables to maximise the degree of overall minimal level of satisfaction with respect to all the responses. Furthermore, the method required no assumptions regarding the form or degree of the estimated response models and was sufficiently robust to handle the potential dependences between response variables. In this study, an integrated procedure based on neural networks and exponential desirability functions was proposed to optimise the parameter settings in the fused bi-conic taper (FBT) process that fabricates 1% (1/99) single-window broadband tap couplers. The proposed optimisation procedure can help manufacturers of fibre-optic passive components by greatly improving the performance and reliability of 1% (1/99) single-window broadband tap couplers at minimum cost. are being used in numerous commercial applications, such as optical fibre communications, optical fibre amplifiers and lasers and so on. The FBT technology is used to produce both WDMs and couplers. This technology relies on bringing bare fibre into contact, then melting and drawing the cross-section to produce a tapered region, as illustrated in Fig. 1a [12]. This procedure produces a very thin tapered region, which must be processed extremely carefully, and must be packaged to protect the components during shipping, handling and installation. In a typical package, as illustrated in Fig. 1b [13], the fused section of the fibres is suspended above the quartz substrate, and positioned between two epoxy supports for mechanical stability. This assembly is then enclosed in a metal tube and sealed. The FBT process has been used for over a decade to fabricate most of the coupler components used in various fibre optic telecommunication, instrumentation, and sensor systems. The FBT process is used extensively not only because of its ready availability and relatively low cost, but also because of its inherent environmental stability and versatility. 3 Optimisation methodologies The optimisation methodologies, neural networks and desirability functions needed for developing the proposed solution procedure are briefly introduced in this section. 3.1 Back-propagation neural networks 2 Characteristics and construction of couplers Branching components (sometimes given the synonyms couplers and splitters) are passive components with more than two ports that distribute optical power among fibres in a predetermined fashion. Wavelength insensitive couplers are branching components in which power is routed independently of the wavelength composition of the optical signal. Each component may combine and divide optical signals simultaneously, as in bi-directional (duplex) transmission over a single fibre. However, the wavelength-division multiplexers/de-multiplexers (WDMs) are branching components in which power is routed based on the wavelength composition of the optical signal. Passive optical branching components Fig. 1 a Fabrication of a FBT device. b Metal tube package for a FBT device Neural networks mimic the way by which biological brain neurons generate intelligent decisions. Numerous neural network models exist that simulate various aspects of intelligence. To resolve parameter design problems with multiple responses, the back-propagation (BP) neural networks are applied to construct the functional relationship between control factors and output responses in an experiment. A standard BP neural model consists of three or more layers, including an input layer, one or more hidden layers and an output layer. The theoretical results revealed that a single hidden layer is sufficient to allow a BP neural model to approximate any continuous mapping from the input patterns to the output patterns to an arbitrary degree of freedom [14]. The training of a BP neural network involves three 898 stages: (1) feed-forward the input training pattern, (2) associated error calculation and back-propagation, and (3) weight and bias adjustments. Once network performance is satisfactory, the relationships between input and output patterns are determined and then the weights are used to recognise new input patterns. The two parameters with the greatest effect on the training performance of a BP neural network are the learning rate and momentum. The learning rate controls the degree of weight change during training. The momentum avoids significantly disrupting learning direction when some training data differ markedly from the majority from most of the data (and may even be incorrect). A smaller learning rate and larger momentum reduce the likelihood of the network finding weights that are only a local minimum, but not a global one [14]. The detailed algorithm of the BP neural network and the guidelines for selecting appropriate training parameters can be found in Fausett [14] and Hagan et al. [15]. 3.2 Desirability functions Suppose that there are r output responses y=(y1, y2, ..., yr), determined by a set of input variables x=(x1, x2, ..., xp). The general multi-response problem can be defined as
yj ¼ fj x1 ; x2 ; :::; xp þ ej for j ¼ 1; 2; :::; r ð1Þ where fj denotes the response function between the jth response and the input variables; and j represents the error term. Usually, the exact form of fj cannot be known, but can be estimated over a limited experimental region by using model-building techniques, such as regression and neural networks. Integrating all the different responses simplifies such a complicated multiresponse problem as a single objective optimisation problem. The desirability function approach transforms an estimated response (e.g. the jth estimated response ^yj ) to a scale-free value dj (0 £ dj £ 1), called desirability. The larger value of dj increases as the desirability of the corresponding response increases. Hence, the multi-response problem can be stated as [8]: maximize k x subject to  dj ^yj ðxÞ >k for j ¼ 1; 2; :::; r x2X ð2Þ where t is a constant ()¥<t<¥), called exponential constant, and z denotes a standardised parameter representing the distance between the estimated response and its target in units of the maximum allowable deviation. For example, for the nominal-the-best (NTB), smaller-the-better (STB), and larger-the-better (LTB) type responses [16], the parameter z can be defined, respectively, as [8]: ^yj ðxÞ
Tj ^yj ðxÞ
Tj z ¼ max ; for yjmin 6^yj ðxÞ6yjmax ð6Þ ¼ yj
Tj Tj
yjmin z¼ z¼ ^yj ðxÞ
yjmin yjmax
yjmin yjmax
^yj ðxÞ yjmax
yjmin ; for yjmin 6^yj ðxÞ6yjmax ð8Þ 3.3 Proposed optimisation procedure The proposed procedure for resolving a multi-response parameter design problem comprises seven steps and is summarised as below: Step 1 Step 2 Step 3 ð3Þ where W denotes the experimental region. The exponential desirability function is suggested as follows [8]: ( exp ðtÞ
exp ðtj zjÞ ; if t 6¼ 0 exp ðtÞ
1 d ð zÞ ¼ ð5Þ 1
j zj; if t ¼ 0 ð7Þ where the bounds on a response (yminj and ymaxj) should be specified in advance. The bounds may be determined according to the specification limits of the product or process, the regulations or standards of the organisation, the physical range of the response or the subjective judgments of the decision makers. z ranges between -1 and 1 for an NTB type response, and otherwise ranges between 0 and 1. In either case, the desirability function value d(z) achieves its maximum value of 1 when z=0. The function d(z) given in Eq. 5 has been proven to provide a reasonable and flexible representation of human perception [17, 18] and is convenient to handle analytically [8]. Step 4 ð4Þ ; for yjmin 6^yj ðxÞ6yjmax Step 5 Step 6 Step 7 Identify the quality characteristics (responses), major control factors, noise factors and exponential constant for each response. Assign control and noise factors to the orthogonal arrays; conduct the experiment and collect the experimental data. Design a BP neural network to represent the relationship between input control factors and output responses. Present all possible factor level combinations to the developed network (in step 3) and compute the estimated responses. Apply the exponential desirability functions to transform the multiple responses into an aggregated performance measure. Optimise the parameter settings by selecting the combination that maximizes the overall satisfaction (k). Conduct the confirmation experiment, and if the result is unsatisfactory, return to step 1 and repeat the proposed procedure. 899 Table 1 The specifications of 1% (1/99) single-window broadband tap couplers, the exponential constants and values of yminj and ymaxj Grade Premium A B Exponential constant yminj ymaxj CR (%) EL (dB) IL-A (dB) IL-B (dB) PDL-A (dB) PDL-B (dB) 99±0.2 99±0.2 99±0.2 2.5 £ 0.20 £ 0.40 £ 0.60 2 £ 21.50 £ 22.00 £ 23.00 )1 £ 0.20 £ 0.30 £ 0.60 1.5 £ 0.30 £ 0.35 £ 0.40 1 £ 0.30 £ 0.35 £ 0.40 3 98.8 99.2 0.00 0.60 18.00 23.00 0.00 0.60 0.00 0.40 0.00 0.40 4 Case study may depend on the following process-related control factors: This section demonstrates the effectiveness of the proposed procedure using a case study, which was undertaken to optimise the fused process parameters and hence improve the performance and reliability of the 1% (1/99) single-window broadband tap coupler. 1. 2. 3. 4. 5. 6. 4.1 Problem encountered Table 2 lists the experimental levels of the critical process control factors mentioned above. The problems encountered in a factory’s mass-production of versatile couplers are machine instability, environmental influences (such as temperature, humidity, and airflow) and product diversity. In addition, each machine must be sufficiently stable to copy the optimal parameter and mass production is ineffective without the optimal parameter. To apply the proposed procedure to optimise the parameter settings in the FBT process, the quality characteristics of interest must be identified first. Discussion with the personnel managing quality and reliability engineering identified six crucial quality characteristics (responses), and these characteristics were selected herein to enhance quality performance, as follows: 1. 2. 3. 4. CR (%) EL (dB) IL-A (dB) IL-B (dB) 5. PDL-A (dB) 6. PDL-B (dB) Coupling ratio (NTB) Excess loss (STB) Insertion loss at 1% tap port (STB) Insertion loss at 99% through port (STB) Polarization dependent loss (at 1% tap port) (STB) Polarization dependent loss (at 99% through port) (STB) The engineering management agreed that convex exponential desirability functions should be employed for the responses IL-A, while concave exponential desirability functions should be employed for the responses, CR, EL, IL-B, PDL-A and PDL-B. Table 1 lists the specifications of different grades of 1% (1/99) single-window broadband tap couplers. The table also lists the exponential constants, and values of yminj and ymaxj in Eqs. 6, 7, and 8. Several variables influence the performance of the tap coupler. Discussion with the product engineer revealed that tap coupler optical performance in the fused process DS PRL HMF TH PHT HP Drawing speed Pre-drawing length Hydrogen (H2) mass flow Torch height Pre-heating time Hydrogen (H2) pressure 4.2 Experiments and data collection Six control factors at three levels require 36=729 trials for a full factorial experiment, a lengthy process. The main effects of control factors could be accurately estimated by conducting 18 experimental trials arranged according to a Taguchi L18(21·37) orthogonal array [19]. Hence, the six control factors were assigned to columns 3 to 8 in the Taguchi L18 orthogonal array and Table 3 lists the collected experimental data. Notably, the four responses, CR, EL, IL-A and IL-B, were collected at three wavelength levels, namely 1510 nm, 1550 nm, and 1590 nm. Table 3 lists the data for the worst case in the three wavelength conditions for further analysis. 4.3 Data analysis The experimental results presented in Table 3 were analysed using the proposed procedure. Randomly Table 2 Critical process control factors and their experimental levels Control factor Drawing speed Pre-drawing length Hydrogen (H2) mass flow Torch height Pre-heating time Hydrogen (H2) pressure Level 2 is the existing level Code A B C D E F Level 1 2 3 DS1 PRL1 HMF1 TH1 PHT1 HP1 DS2 PRL2 HMF2 TH2 PHT2 HP2 DS3 PRL3 HMF3 TH3 PHT3 HP3 900 Table 3 Collected experimental data Trial Factor Response A B C D E F CR EL IL-A IL-B PDL-A PDL-B Rep. 1 Rep. 2 Rep. 1 Rep. 2 Rep. 1 Rep. 2 Rep. 1 Rep. 2 Rep. 1 Rep. 2 Rep. 1 Rep. 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2 1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1 1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1 2 1 2 3 3 1 2 2 3 1 2 3 1 3 1 2 1 2 3 1 2 3 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1 98.644 98.733 98.798 98.689 98.748 98.747 98.797 98.617 98.738 98.612 98.954 98.779 98.720 98.791 98.662 99.105 98.682 98.775 98.775 98.791 98.728 98.830 98.783 98.817 98.831 98.709 98.783 98.720 98.768 98.759 98.632 98.811 98.793 98.731 98.758 98.613 0.053 0.011 0.060 0.049 0.025 0.059 0.025 0.134 0.045 0.039 0.075 0.038 0.068 0.070 0.190 0.051 0.060 0.061 0.047 0.021 0.084 0.034 0.097 0.017 0.160 0.024 0.056 0.109 0.100 0.022 0.075 0.086 0.083 0.058 0.059 0.390 19.715 20.464 20.287 20.005 20.367 20.211 20.326 19.960 20.135 19.951 20.302 20.227 20.350 20.048 19.772 20.410 19.687 20.314 selecting the training and testing data sets from the experimental results, a BP neural network model was constructed to model the functional relationship between input control factors and output responses. A smaller learning rate and larger momentum are recommended for finding global minimum weights [14], and thus the learning rate and momentum were set at 0.25 and 0.8, respectively. The candidate neural models were obtained using the NeuralWorks Professional II/Plus [20] software, as shown in Table 4. The 6-7-6 neural Table 4 The candidate BP neural models Structure Training RMSEa Testing RMSEa 6-4-6 6-5-6 6-6-6 6-7-6 6-8-6 6-9-6 6-10-6 6-11-6 6-12-6 0.0732 0.0732 0.0687 0.0642 0.0706 0.0565 0.0621 0.0652 0.0660 0.1208 0.0647 0.0573 0.0494 0.0795 0.0625 0.0828 0.0832 0.0687 a 20.239 20.271 20.201 20.379 20.458 20.584 20.440 20.208 19.964 20.515 20.205 20.173 19.735 20.389 20.094 20.060 20.245 20.128 0.104 0.050 0.103 0.097 0.079 0.101 0.066 0.194 0.100 0.100 0.145 0.091 0.117 0.130 0.248 0.095 0.114 0.106 0.090 0.061 0.139 0.085 0.151 0.054 0.211 0.067 0.109 0.158 0.146 0.071 0.056 0.138 0.136 0.113 0.101 0.443 0.180 0.240 0.310 0.180 0.200 0.490 0.200 0.340 0.270 0.170 0.210 0.360 0.210 0.320 0.290 0.170 0.210 0.300 0.170 0.230 0.280 0.190 0.270 0.410 0.220 0.280 0.250 0.170 0.240 0.390 0.220 0.290 0.280 0.180 0.240 0.280 0.010 0.030 0.020 0.020 0.020 0.030 0.030 0.020 0.020 0.100 0.010 0.030 0.020 0.020 0.030 0.020 0.010 0.030 0.010 0.020 0.020 0.010 0.010 0.020 0.020 0.010 0.010 0.020 0.010 0.020 0.010 0.030 0.030 0.030 0.020 0.020 network model with minimal training and testing RMSEs was selected based on the table. Through the well-trained BP neural model, the output responses under all possible control factor parameter combinations can be accurately predicted. Meanwhile, by applying the exponential desirability functions with pre-specified exponential constants in Table 1, multiple responses are transformed into a single response. Table 5 summarises five combinations of control factor parameter settings that produce larger values for the objective function (k) and the corresponding desirability function (d(z)). Following consultations with engineers, the optimal levels of control factors were set as A=DS2, B=PRL3, C=HMF2, D=TH2, E=PHT1 and F=HP3. 4.4 Confirmation experiment A confirmation was carried out by processing thirty (30) pieces of 1% (1/99) single-window broadband tap couplers at the optimal parameter levels of control factors. Table 6 lists the confirmatory results, and indicates that all of the thirty trials conform to the specification of 1% (1/99) single-window broadband tap couplers. RMSE: root mean squared error [20] Table 5 Five combinations of control factor parameter settings that produce larger values for the objective function (k) No. 1 2 3 4 5 Control factor k d(z) A B C D E F CR EL IL-A IL-B PDL-A PDL-B DS2 DS2 DS3 DS2 DS2 PRL3 PRL3 PRL3 PRL3 PRL3 HMF2 HMF3 HMF3 HMF2 HMF1 TH2 TH3 TH3 TH3 TH2 PHT1 PHT1 PHT1 PHT1 PHT1 HP3 HP3 HP3 HP3 HP2 0.5636 0.4596 0.4972 0.6118 0.5027 0.9860 0.9965 0.9961 0.9787 0.9754 0.4535 0.4440 0.4407 0.4396 0.4392 0.9411 0.9571 0.9555 0.9294 0.9238 0.4658 0.5361 0.6191 0.5741 0.4731 0.9951 0.9951 0.9947 0.9940 0.9945 0.4535 0.4440 0.4407 0.4396 0.4392 901 Table 6 Confirmatory results Tube no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Response Quality grade CR (%) EL (dB) IL-A (dB) IL-B (dB) PDL-A (dB) PDL-B (dB) 99.1454 99.1467 98.8475 98.8470 99.1564 98.8429 99.1583 99.1608 98.8367 99.1639 99.1640 98.8763 99.1655 98.8343 99.1657 99.1669 99.1681 98.8297 99.1703 99.1731 98.8259 98.8165 98.8144 98.8123 98.8116 98.8089 98.8084 99.1930 98.8059 98.8053 0.0750 0.0693 0.0397 0.0483 0.1351 0.0931 0.0590 0.0338 0.0917 0.0340 0.0500 0.1817 0.1420 0.1174 0.0499 0.0410 0.0872 0.0925 0.0591 0.0421 0.0592 0.0588 0.0941 0.0245 0.0842 0.0468 0.0325 0.1654 0.0859 0.0521 20.7492 20.7476 20.2982 20.3336 20.8581 20.2487 20.8036 20.7816 20.3342 20.8063 20.8259 20.6937 20.9280 20.6461 20.8220 20.8273 20.8694 20.2815 20.8585 20.8661 20.3308 20.2778 20.3265 20.3064 20.4651 20.1464 20.3034 21.0803 20.3388 20.2461 0.1170 0.1189 0.0850 0.0986 0.1779 0.1396 0.0998 0.0800 0.1378 0.0800 0.0899 0.2308 0.1783 0.1561 0.0912 0.0843 0.1339 0.1343 0.1067 0.0855 0.1002 0.1015 0.1407 0.0764 0.1361 0.0988 0.0789 0.2062 0.1335 0.1019 0.1821 0.1389 0.1533 0.1176 0.1809 0.1023 0.0725 0.1762 0.0977 0.1918 0.1060 0.1483 0.1057 0.1513 0.1174 0.1037 0.1275 0.1266 0.1426 0.1929 0.1553 0.1320 0.1142 0.1239 0.1737 0.1211 0.1616 0.0778 0.1348 0.0889 0.1186 0.0070 0.0105 0.0101 0.0075 0.0074 0.0100 0.0110 0.0114 0.0106 0.0110 0.0094 0.0222 0.0147 0.0038 0.0116 0.0211 0.0104 0.0134 0.0146 0.0090 0.0090 0.0062 0.0153 0.0170 0.0055 0.0116 0.0112 0.0189 0.0076 Moreover, 28 of the 30 couplers are graded as ‘‘Premium’’ and the others are graded as ‘‘A’’. The authors are confident that the obtained optimal combination of process control factor parameters can be directly applied to mass producing fused optical couplers. 4.5 Implementation The optimal levels of process control factors were implemented in a pilot run of the fused process in a phase over 20 days. Evaluation of 200 couplers revealed that the average defect rate was reduced to 2.5%, from over 35% previously. Meanwhile, the monthly device output from the factory is approximately 10,000 pieces this year. The demand is expected to grow rapidly in the coming months, with annual growth of over 50% being assumed. Consequently, this valuable investigation to optimise the fused process parameters can not only increase throughput by 30% through increasing the yield ratio, but can also increase the price by 25% through producing more reliable high performance couplers. Given these achievements, annual savings are expected to reach USD 500,000–1,000,000, well above the cost of the experiment, at only around USD 3,000. Premium Premium Premium Premium Premium Premium Premium Premium Premium Premium Premium A Premium Premium Premium Premium Premium Premium Premium Premium Premium Premium Premium Premium Premium Premium Premium A Premium Premium 5 Conclusions This investigation proposed an integrated procedure based on neural networks and exponential desirability functions to resolve the parameter design problem with multiple responses. Effectiveness of the proposed procedure was demonstrated using a case study which was undertaken to optimize the fused process parameters that have been made in the development of FBT couplers to enhance the performance and reliability of the 1% (1/99) single-window broadband tap coupler. A pilot run of the fused process over 20 days was implemented and evaluation of 200 pieces of couplers revealed that the average defect rate reduced to just 2.5%, from over 35% previously. Annual savings from implementing the proposed procedure are expected to exceed 0.5–1.0 million US dollars, whereas the expenditure for the experiment was below USD 3,000. This investigation has been extensively and successfully applied to develop the optimal fuse parameters for other coupling ratio tap couplers, such as 2/98, 3/97, 4/96, ..., 50/50. Acknowledgements The authors would like to thank the National Science Council, Taiwan, R.O.C. for partially supporting this research under Contract No. NSC 91-2213-E-159-013 902 References 1. Phadke MS (1989) Quality engineering using robust design. Prentice-Hall, New Jersey 2. Logothetis N, Haigh A (1988) Characterizing and optimizing multi-response processes by the Taguchi method. Qual Reliab Eng Int 4:159–169 3. 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