Showing papers on "Taguchi methods published in 2006"
TL;DR: In this paper, the authors classified robust design into three methods: the Taguchi method, robust optimization, and robust design with the axiomatic approach, and examined them from a theoretical viewpoint and discussed from an application viewpoint.
Abstract: Robust design has been developed with the expectation that an insensitive design can be obtained. That is, a product designed by robust design should be insensitive to external noises or tolerances. An insensitive design has more probability to obtain a target value, although there are uncertain noises. Theories of robust design have been developed by adopting the theories of other fields. Based on the theories, robust design can be classified into three methods: 1) the Taguchi method, 2) robust optimization, and 3) robust design with the axiomatic approach. Each method is reviewed and investigated. The methods are examined from a theoretical viewpoint and are discussed from an application viewpoint. The advantages and drawbacks of each method are discussed, and future directions for development are proposed.
489 citations
TL;DR: A hybrid Taguchi-genetic algorithm (HTGA) is applied to solve the problem of tuning both network structure and parameters of a feedforward neural network and can obtain better results than the existing method reported recently in the literature.
Abstract: In this paper, a hybrid Taguchi-genetic algorithm (HTGA) is applied to solve the problem of tuning both network structure and parameters of a feedforward neural network. The HTGA approach is a method of combining the traditional genetic algorithm (TGA), which has a powerful global exploration capability, with the Taguchi method, which can exploit the optimum offspring. The Taguchi method is inserted between crossover and mutation operations of a TGA. Then, the systematic reasoning ability of the Taguchi method is incorporated in the crossover operations to select the better genes to achieve crossover, and consequently enhance the genetic algorithms. Therefore, the HTGA approach can be more robust, statistically sound, and quickly convergent. First, the authors evaluate the performance of the presented HTGA approach by studying some global numerical optimization problems. Then, the presented HTGA approach is effectively applied to solve three examples on forecasting the sunspot numbers, tuning the associative memory, and solving the XOR problem. The numbers of hidden nodes and the links of the feedforward neural network are chosen by increasing them from small numbers until the learning performance is good enough. As a result, a partially connected feedforward neural network can be obtained after tuning. This implies that the cost of implementation of the neural network can be reduced. In these studied problems of tuning both network structure and parameters of a feedforward neural network, there are many parameters and numerous local optima so that these studied problems are challenging enough for evaluating the performances of any proposed GA-based approaches. The computational experiments show that the presented HTGA approach can obtain better results than the existing method reported recently in the literature.
288 citations
TL;DR: In this paper, a multi response optimization method using Taguchi's robust design approach is proposed for wire electrical discharge machining (WEDM) operations, where the machining parameters are optimized with the multi response characteristics of the material removal rate, surface roughness, and wire wear ratio.
Abstract: In this present study a multi response optimization method using Taguchi’s robust design approach is proposed for wire electrical discharge machining (WEDM) operations. Experimentation was planned as per Taguchi’s L16 orthogonal array. Each experiment has been performed under different cutting conditions of pulse on time, wire tension, delay time, wire feed speed, and ignition current intensity. Three responses namely material removal rate, surface roughness, and wire wear ratio have been considered for each experiment. The machining parameters are optimized with the multi response characteristics of the material removal rate, surface roughness, and wire wear ratio. Multi response S/N (MRSN) ratio was applied to measure the performance characteristics deviating from the actual value. Analysis of variance (ANOVA) is employed to identify the level of importance of the machining parameters on the multiple performance characteristics considered. Finally experimental confirmation was carried out to identify the effectiveness of this proposed method. A good improvement was obtained.
246 citations
TL;DR: In this article, a series of mold analyses were performed to exploit the warpage and sink index data to solve the quality problem occurring the injection-molded thermoplastic parts.
201 citations
TL;DR: Wang et al. as mentioned in this paper proposed a weighted principal components (WPC) method to solve the multi-response problem in the Taguchi method, and three cases in their papers were illustrated and compared in the application of WPC method.
Abstract: Taguchi method is a very popular offline quality design However, it cannot solve the multi-response problem which occurs often in today’s society Research shows that the multi-response problem is still an issue with the Taguchi method Researchers have tried to find a series of theories and methods in seeking a combination of factors/levels to achieve the situation of optimal multi-response instead of using engineers’ judgement to make a decision in the Taguchi method In 1997, Su et al submitted the multivariate method, and in 2000 Antony proposed principal component analysis (PCA), to solve this problem But with the PCA method, there are still two main shortcomings In this study, the weighted principal components (WPC) method is proposed to overcome these two shortcomings, and three cases in their papers will be illustrated and compared in the application of WPC method The result shows that the WPC method offers significant improvements in quality
177 citations
TL;DR: In this article, a reliable set of parameters that demonstrate versatility, and numerous and diverse range based on experience and technology is presented for the machining of aluminium-reinforced silicon carbide metal matrix composite (Al/SiC-MMC).
Abstract: Machining parameters tables provided by the machine tool manufacturers often do not meet the operator requirements and sometimes even do not provide efficient guidelines to manufacturing engineers. Hence, a suitable selection of machining parameters of CNC wire cut electrical discharge machining (EDM) process is necessary. This paper present a reliable set of parameters that demonstrate versatility, and numerous and diverse range based on experience and technology. We offer an experimental investigation to determine the parameters setting during the machining of aluminium-reinforced silicon carbide metal matrix composite (Al/SiC-MMC). The Taguchi method, a powerful tool for experimental design, is used to optimize the CNC-wire cut-EDM parameters. According to the Taguchi quality design Concept, a L18 (21×37) mixed orthogonal array was used to determine the S/N ratio, and an analysis of variance (ANOVA) and the F-test values were used to indicate the significant machining parameters affecting the machining performance. From experimental results and through ANOVA and F-test values, the significant factors are determined for each machining performance criteria, such as the metal removal rate, surface roughness, gap current and spark gap (gap width). Considering these significant CNC wire cut-EDM parameters, verification of the improvement in the quality characteristics for machining Al/SiC-MMC was made with a confirmation test with respect to the chosen initial or reference parameter setting. Mathematical models relating to the machining performance are established using the Gauss elimination method for the effective machining of Al/SiC-MMC. Yet again, confirmation test results also show that the developed mathematical models are appropriate for the effective machining of Al/SiC-MMC. The determined optimal combination of CNC-wire cut-EDM parameters obtained from the study satisfy the real requirement of quality machining of Al/SiC MMC in practice.
162 citations
TL;DR: The computational experiments show that the proposed HTGA approach can obtain better digital IIR filters than the existing GA-based method reported recently in the literature.
Abstract: A hybrid Taguchi genetic algorithm (HTGA) is applied in this paper to solve the problem of designing optimal digital infinite-impulse response (IIR) filters. The HTGA approach is a method of combining the traditional GA (TGA), which has a powerful global exploration capability, with the Taguchi method, which can exploit the optimum offspring. The Taguchi method is inserted between crossover and mutation operations of a TGA. Based on minimizing the L/sub p/-norm approximation error and minimizing the ripple magnitudes of both passband and stopband, a multicriterion combination is employed as the design criterion to obtain the optimal IIR filter that can fit different performance requirements. The proposed HTGA approach is effectively applied to solve the multiparameter and multicriterion optimization problems of designing the digital low-pass (LP), high-pass (HP), bandpass (BP), and bandstop (BS) filters. In these studied problems, there are many parameters and numerous local optima so that these studied problems are challenging enough for evaluating the performances of any proposed GA-based approaches. The computational experiments show that the proposed HTGA approach can obtain better digital IIR filters than the existing GA-based method reported recently in the literature.
135 citations
TL;DR: In this article, a study of Taguchi optimization method for low surface roughness value in terms of cutting parameters when face milling of the cobalt-based alloy (stellite 6) material.
Abstract: The aim of this work is to develop a study of Taguchi optimization method for low surface roughness value in terms of cutting parameters when face milling of the cobalt-based alloy (stellite 6) material. The milling parameters evaluated are feed rate, cutting speed and depth of cut, a series of milling experiments are performed to measure the surface roughness data. The settings of face milling parameters were determined by using Taguchi experimental design method. Orthogonal arrays of Taguchi, the signal-to-noise (S/N) ratio, the analysis of variance (ANOVA) are employed to find the optimal levels and to analyze the effect of the milling parameters on surface roughness. Confirmation tests with the optimal levels of cutting parameters are carried out in order to illustrate the effectiveness of Taguchi optimization method. It is thus shown that the Taguchi method is very suitable to solve the surface quality problem occurring the face milling of stellite 6 material.
131 citations
TL;DR: A more accurate and easier method for quantifying the supplier’s attributes to quality-loss using a Taguchi loss function, and these quality losses are also transferred into a variable for decision-making by an analytical hierarchy process (AHP).
Abstract: The purchasing function directly affects the competitive ability of a firm. Purchasing managers need to periodically evaluate supplier performance in order to retain those suppliers who meet their requirements. The importance of incorporating multiple attributes such as quality, on-time delivery, price and service, into vendor evaluation are well established in the literature. This report provides a more accurate and easier method for quantifying the supplier’s attributes to quality-loss using a Taguchi loss function, and these quality losses are also transferred into a variable for decision-making by an analytical hierarchy process (AHP). An example for supplier evaluation and selection is also presented to demonstrate the functional application of the model.
131 citations
TL;DR: In this paper, the effects of the machining parameters in electrical discharge machining (EDM) on machining characteristics of SKH 57 high-speed steel were investigated.
Abstract: The effects of the machining parameters in electrical-discharge machining (EDM) on the machining characteristics of SKH 57 high-speed steel were investigated. A well-designed experimental scheme was used to reduce the total number of experiments. Parts of the experiment were conducted with the L18 orthogonal array based on the Taguchi method. Moreover, the signal-to-noise ratios associated with the observed values in the experiments were determined by ANOVA and F-test. The significant parameters that critically influenced the machining characteristics were examined, and the optimal combination levels of machining parameters for material removal rate, electrode wear rate, and surface roughness were determined.
116 citations
TL;DR: In this article, the use of Taguchi methods in optimizing a switched reluctance motor (SRM) for applications requiring fast actuation is presented. But the performance of the motor designs generated by the Taguchi DOE is not evaluated.
Abstract: This paper presents the use of Taguchi methods in optimizing a switched reluctance motor (SRM) for applications requiring fast actuation. In these applications, the SRM is designed to provide a high electromagnetic torque-to-inertia ratio required for high rates of mechanical acceleration. This is accomplished using two simultaneous robust optimizations of an SRM, namely: 1) an optimization of the motor torque and 2) an optimization of the torque per inertia (mechanical acceleration). The Taguchi two-step optimization method and the zero-point-proportional dynamic response were used successfully in the double optimization. Two orthogonal arrays were used to lead the design of experiments (DOE). Finite-element analysis was used to compute the performance of the motor designs generated by the Taguchi DOE.
TL;DR: In this paper, the effect of machining parameters on the surface roughness is evaluated and optimum machining conditions for maximizing the metal removal rate and minimizing the roughness are determined using response surface methodology.
Abstract: The present investigation focuses on the influence of machining parameters on the surface finish obtained in turning of LM25 Al/SiC particulate composites. The experiments are conducted based on Taguchi's experimental design technique. In this work, the effect of machining parameters on the surface roughness is evaluated and optimum machining conditions for maximizing the metal removal rate and minimizing the surface roughness are determined using response surface methodology. A second-order response surface model for the surface roughness is developed to predict the surface roughness. The predicted values and measured values are fairly close to each other, which indicates that the developed model can be effectively used to predict the surface roughness on the machining of Al/SiC-MMC composites with 95% confidence intervals within the ranges of parameters studied.
TL;DR: The backpropagation artificial neural network and the Taguchi approach to the design of the experiment found the optimum levels of the welding speed, the laser power and the focal position for CO2 keyhole laser welding of medium carbon steel butt weld.
TL;DR: In this paper, the effects of assisted vibration cutting (VC) on the micro-milling quality of aluminum alloy Al 6061-T6 were investigated by examining its geometrical shape and machining accuracy.
Abstract: The purpose of this paper is to investigate the effects of assisted vibration cutting (VC) on the micro-milling quality of aluminum alloy Al 6061-T6. The desired vibration is proposed from the workpiece side by a two-dimensional vibrating worktable we developed. The slot produced by end milling is studied by examining its geometrical shape and machining accuracy. Through extensive experiments with end mills of diameter 1 mm, we found that slot oversize, displacement of slot center and slot surface roughness could be improved by imposing VC. The employment of VC increases the number of slots produced within the tolerance when high amplitude and proper frequency are imposed. With the help of Taguchi method and analysis of variance (ANOVA), we analyzed the effect of VC in end milling by investigating the slot-width accuracy. It is found that the use of second directional VC to minimize slot-width oversize in end milling is helpful.
TL;DR: In this article, the influence of the process parameters on surface roughness in squeeze casting of LM6 aluminium alloy using Taguchi method was analyzed and the results indicated that the squeeze pressure and the die preheating temperature are the recognized parameters to cause appreciable improvement in the surface finish of the squeeze cast components.
TL;DR: In this article, the authors presented an application of the Taguchi parameter design method to optimize the surface finish in a turning operation using a total of 36 experimental runs using an orthogonal array, and the ideal combination of control factor levels was determined for the optimal surface roughness and signal-to-noise ratio.
Abstract: This paper presents an application of the Taguchi parameter design method to optimizing the surface finish in a turning operation. The Taguchi parameter design method is an efficient experimental method in which a response variable can be optimized, given various control and noise factors, and using fewer experimental runs than a factorial design. The control parameters for this operation included: spindle speed, feed rate, depth of cut, and tool nose radius. Noise factors included varying room temperature, as well as the use of more than one insert of the same specification, which introduced tool dimension variability. A total of 36 experimental runs were conducted using an orthogonal array, and the ideal combination of control factor levels was determined for the optimal surface roughness and signal-to-noise ratio. A confirmation run was used to verify the results, which indicated that this method was both efficient and effective in determining the best turning parameters for the optimal surface roughness.
TL;DR: In this paper, a regression analysis was applied to determine the fitness of data used in the Taguchi optimization method using milling experiments based on a full factorial design, and a confirmation experiment with the optimal levels of process parameters was carried out in order to demonstrate the effectiveness of the taguchi method.
Abstract: The objective of this paper is to develop a Taguchi optimization method for low surface roughness in terms of process parameters when milling the mold surfaces of 7075-T6 aluminum material. Considering the process parameters of feed, cutting speed, axial-radial depth of cut, and machining tolerance, a series of milling experiments were performed to measure the roughness data. A regression analysis was applied to determine the fitness of data used in the Taguchi optimization method using milling experiments based on a full factorial design. Taguchi orthogonal arrays, signal-to-noise (S/N) ratio, and analysis of variance (ANOVA) are used to find the optimal levels and the effect of the process parameters on surface roughness. A confirmation experiment with the optimal levels of process parameters was carried out in order to demonstrate the effectiveness of the Taguchi method. It can be concluded that Taguchi method is very suitable in solving the surface quality problem of mold surfaces.
TL;DR: In this paper, an approach based on a Utility theory and Taguchi quality loss function (TQLF) has been applied to CFAAFM for simultaneous optimization of more than one response characteristics.
Abstract: Centrifugal force assisted abrasive flow machining (CFAAFM) process has recently been tried as a hybrid machining process with the aim towards the performance improvement of AFM process by applying centrifugal force on the abrasive laden media with a rotating centrifugal force generating (CFG) rod introduced in the work piece passage. For optimization of process parameters, an approach based on a Utility theory and Taguchi quality loss function (TQLF) has been applied to CFAAFM for simultaneous optimization of more than one response characteristics. Three potential response parameters i.e., material removal, % improvement of surface finish and scatter of surface roughness over the fine finished surface of a sleeve type work piece of brass are examined. Utility values based upon these response parameters have been analyzed for optimization by using Taguchi approach.
TL;DR: In this paper, the use of Taguchi's method and Pareto ANOVA analysis for optimizing the cutting parameters in turning glass fiber reinforced plastic composites using a poly crystalline diamond (PCD) tool for minimizing surface roughness.
Abstract: This article discusses the use of Taguchi’s method and Pareto ANOVA analysis for optimizing the cutting parameters in turning glass fiber reinforced plastic (GFRP) composites using a poly crystalline diamond (PCD) tool for minimizing surface roughness. The cutting parameters evaluated are cutting speed, feed rate, and depth of cut. An L27 orthogonal array, signal to noise ratio, and Pareto ANOVA analysis are used to analyze the effect of cutting parameters and its interactions. The experimental results suggest that the most significant process parameter is feed rate followed by cutting speed. The study shows that the Taguchi method and Pareto ANOVA are suitable for optimizing the cutting parameters with the minimum number of trials.
TL;DR: In this paper, an attempt has been made to obtain optimal settings of the green sand casting process in order to yield the optimum quality characteristics of the spheroidal graphite (SG) cast iron rigid coupling castings.
Abstract: This paper analyses various significant process parameters of the green sand casting process. An attempt has been made to obtain optimal settings of the green sand casting process in order to yield the optimum quality characteristics of the spheroidal graphite (SG) cast iron rigid coupling castings. The process parameters considered are: green strength, moisture content, permeability and mould hardness. The effect of selected process parameters and its levels on the casting defects and the subsequent optimal settings of the parameters have been accomplished using Taguchi’s parameter design approach. The result indicates that the selected process parameters significantly affect the casting defects of SG cast iron rigid coupling castings. The estimation of the optimum performance characteristics of green sand casting at the optimum levels of parameters is done in this paper and the results are verified by confirming with practical experiments.
TL;DR: In this paper, a pilot study for wastewater treatment in Exir pharmaceutical Co. (Borojerd, Iran) was conducted using a RO system with the capacity of 14.38m 3 /d.
TL;DR: In this article, the authors proposed an optimization method for a fin-tube heat exchanger of a household refrigerator under frosting conditions to improve its thermal performance and extend its operating time.
TL;DR: In this paper, the authors present an application of Taguchi method of experimental design for the development of an optical fiber sensor in a cost effective and timely manner, and illustrate a simple framework which provides guidance in the selection of a suitable DOE strategy.
Abstract: Purpose – The purpose of this paper is to present some fundamental and critical differences between the two methods of experimental design (i.e. Taguchi and classical design of experiments (DOE)). It also aims to present an application of Taguchi method of experimental design for the development of an optical fiber sensor in a cost effective and timely manner.Design/methodology/approach – The first part of the paper shows the differences between classical DOE and Taguchi methods from a practitioner's perspective. The second part of the paper illustrates a simple framework which provides guidance in the selection of a suitable DOE strategy. The last part is focused on a simple case study demonstrating the power of Taguchi methods of experimental design.Findings – One of the key questions from many quality and production related personnel in organisations are “when to use Taguchi and Classical DOE?”. The purpose of this paper is to make an attempt to address the above question from a practitioner's perspect...
TL;DR: In this article, a Grey relational analysis was used for the optimization of the machining parameters on machining GFRP composites using carbide (K10) tool and the results showed that machining performance in the composite machining process can be improved effectively by using this approach.
Abstract: The present investigation focuses on the multiple performance machining characteristics of GFRP composites produced through filament winding. Grey relational analysis was used for the optimization of the machining parameters on machining GFRP composites using carbide (K10) tool. According to the Taguchi quality concept, a L27, 3-level orthogonal array was chosen for the experiments. The machining parameters namely work piece fiber orientation, cutting speed, feed rate, depth of cut and machining time have been optimized based on the multiple performance characteristics including material removal rate, tool wear, surface roughness and specific cutting pressure. Experimental results have shown that machining performance in the composite machining process can be improved effectively by using this approach.
TL;DR: A parameter design approach that incorporates Taguchi’s robustness into the Genetic Algorithm search for optimal stochastic outputs of discrete event simulation (DES) to guide the GA selection scheme to converge to a near-optimal robust parameter design.
TL;DR: In this paper, an optimal setting of turning process parameters (cutting speed, feed rate and depth of cut) was obtained to obtain an optimal value of the feed force when machining EN24 steel with TiC-coated tungsten-carbide inserts.
Abstract: The objective of the paper is to obtain an optimal setting of turning process parameters (cutting speed, feed rate and depth of cut) resulting in an optimal value of the feed force when machining EN24 steel with TiC-coated tungsten-carbide inserts. The effects of the selected turning process parameters on feed force and the subsequent optimal settings of the parameters have been accomplished using Taguchi’s parameter design approach. The results indicate that the selected process parameters significantly affect the selected machining characteristics. The results are confirmed by further experiments.
TL;DR: The computational experiments show that the proposed TIA approach can obtain better digital IIR filters than the existing methods such as the genetic-algorithms-based method and the classic methods.
Abstract: In this paper, based on both the features of a biological immune system and the systematic reasoning ability of the Taguchi method, an improved immune algorithm, named the Taguchi-immune algorithm (TIA), is proposed to solve the problem of designing the optimal digital infinite impulse response (IIR) filters. In the TIA, the clonal proliferation within hypermutation for several antibody diversifications and the recombination by using the Taguchi method for the local search are integrated to improve the capabilities of exploration and exploitation. The systematic reasoning ability of the Taguchi method is executed in the recombination operations to select the better antibody genes to achieve the potential recombination, and consequently enhance the TIA. Based on minimizing the Lp-norm approximation error and minimizing the ripple magnitudes of both passband and stopband, a multicriterion combination is employed as the design criterion to obtain the optimal IIR filter that can fit different performance requirements. The proposed TIA approach is effectively applied to solve the multiparameter and multicriterion optimization problems of designing the digital low-pass, high-pass, bandpass, and bandstop filters. In these studied problems, there are many parameters and numerous local optima so that these studied problems are challenging enough for evaluating the performances of any proposed evolutionary approaches. The computational experiments show that the proposed TIA approach can obtain better digital IIR filters than the existing methods such as the genetic-algorithms-based method and the classic methods
TL;DR: In this article, a four-step procedure is proposed to resolve the parameter design problem involving multiple responses, where multiple signal-to-noise ratios are mapped into a single performance statistic through neuro-fuzzy based model, to identify the optimal level settings for each parameter.
Abstract: Purpose – To provide a good insight into solving a multi-response optimization problem using neuro-fuzzy model and Taguchi method of experimental design.
Design/methodology/approach – Over the last few years in many manufacturing organizations, multiple response optimization problems were resolved using the past experience and engineering judgment, which leads to increase in uncertainty during the decision-making process. In this paper, a four-step procedure is proposed to resolve the parameter design problem involving multiple responses. This approach employs the advantage of both artificial intelligence tool (neuro-fuzzy model) and Taguchi method of experimental design to tackle problems involving multiple responses optimization.
Findings – The proposed methodology is validated by revisiting a case study to optimize the three responses for a double-sided surface mount technology of an electronic assembly. Multiple signal-to-noise ratios are mapped into a single performance statistic through neuro-fuzzy based model, to identify the optimal level settings for each parameter. Analysis of variance is finally performed to identify parameters significant to the process.
Research limitations/implications – The proposed model will be validated in future by conducting a real life case study, where multiple responses need to be optimized simultaneously.
Practical implications – It is believed that the proposed procedure in this study can resolve a complex parameter design problem with multiple responses. It can be applied to those areas where there are large data sets and a number of responses are to be optimized simultaneously. In addition, the proposed procedure is relatively simple and can be implemented easily by using ready-made neural and statistical software like Neuro Work II professional and Minitab.
Originality/value – This study adds to the literature of multi-optimization problem, where a combination of the neuro-fuzzy model and Taguchi method is utilized hand-in-hand.
TL;DR: In this paper, a multi-response performance index (MRPI) was used for optimization of machining parameters of GFRP composites with multiple performance characteristics, such as metal removal rate, tool wear, and surface roughness.
Abstract: Glass fiber reinforced polymer (GFRP) composite materials are finding increased applications in a variety of engineering fields. Subsequently, the need for accurate, machining of composites has increased enormously. This paper discusses the application of the Taguchi method with fuzzy logic to optimize the machining parameters for machining of GFRP composites with multiple characteristics. A multi-response performance index (MRPI) was used for optimization. The machining parameters viz., work piece (fiber orientation), cutting speed, feed rate, depth of cut and machining time were optimized with consideration of multiple performance characteristics viz., metal removal rate, tool wear, and surface roughness. The results from confirmation runs indicated that the determined optimal combination of machining parameters improved the performance of the machining process.
TL;DR: In this paper, a multi-objective optimization approach is proposed by simultaneously maximizing the bulge ratio and minimizing the thinning ratio, which is solved by using a goal attainment method.
Abstract: Tube hydroforming is an attractive manufacturing technology which is now widely used in many industries, especially the automobile industry. The purpose of this study is to develop a method to analyze the effects of the forming parameters on the quality of part formability and determine the optimal combination of the forming parameters for the process. The effects of the forming parameters on the tube hydroforming process are studied by finite element analysis and the Taguchi method. The Taguchi method is applied to design an orthogonal experimental array, and the virtual experiments are analyzed by the use of the finite element method (FEM). The predicted results are then analyzed by the use of the Taguchi method from which the effect of each parameter on the hydroformed tube is given. In this work, a free bulging tube hydroforming process is employed to find the optimal forming parameters combination for the highest bulge ratio and the lowest thinning ratio. A multi-objective optimization approach is proposed by simultaneously maximizing the bulge ratio and minimizing the thinning ratio. The optimization problem is solved by using a goal attainment method. An example is given to illustrate the practicality of this approach and ease of use by the designers and process engineers.