• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.215-223
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• 2012

Response surface methodology(RSM) is a very useful statistical techniques for improving and optimizing the product process. By this reason, RSM has been utilized extensively in the industrial world, particularly in the circumstances where several product variables potentially influence some quality characteristic of the product. In order to estimate the optimal condition of product variables, an experiment is being conducted defining appropriate experimental region. However, this experimental region can vary with the experimental circumstances and choice of a researcher. Response surface designs can be classified, according to the shape of the experimental region, into spherical and cuboidal. In the spherical case, the design is either rotatable or very near-rotatable. The central composite design(CCD)s widely used in RSM is an example of 5-level and spherical design. The cuboidal CCDs(CCDs with ${\alpha}=1$) is appropriate when an experimental region is cuboidal but this design dose not satisfy the rotatability as it is not spherical. Practically, a 3-level spherical design is often required in the industrial world where various level of experiments are not available. Box-Behnken design(BBD)s are a most popular 3-level spherical designs for fitting second-order response surfaces and satisfy the rotatability but the experimental region does not vary with the number of variables. The new experimental design with expanded experimental region can be considered if the predicting response at the extremes are interested. This paper proposes a new 3-level spherical RSM which are constructed to expand the experimental region together with number of product variables.

• KEPCO Journal on Electric Power and Energy
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• v.1 no.1
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• pp.181-188
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• 2015

The non-contact permanent magnet gear has advantages of high efficiency and improved reliability. It has other advantages of no mechanical friction loss, very little noise and vibration, and no need for lubricant. With these advantages, the non-contact permanent magnet gear that solves the physical contact problem of the mechanical gear has drawn attention. Due to this unique non-contact characteristic, the non-contact permanent magnet gear which is capable of non-contact torque transmission has replaced mechanical gear. The mechanical gears which is in many fields of the modern industry, is used mostly for power transmitting mechanical devices. However, it also has the problem of a low torque density, which requires improvement. In this paper, a novel pole piece shape is proposed in order to improve the problem of low torque density of the non-contact permanent magnet gear. The experiment data required for predicting the relationships among them are obtained using finiteelement Operating method based on two-dimensional (2-D) numerical analysis. Therefore, this paper derived an optimal model for thenon-contact permanent magnet gear with the novel pole piece using the Box-Behnken design, and the validity of the optimal design of the proposed pole piece shape through variance analysis and regression analysis demonstrated. In this paper, we performed the thransfer torque analysis in order to improve the torque density and power density, we have performed on optimal design of proposed pole piece shape using box-behnken.

• Journal of Korean Society of Environmental Engineers
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• v.32 no.1
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• pp.33-46
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• 2010

We investigated and estimated at the characteristics of decomposition and by-products of N-Nitrosodimethylamine (NDMA) using a design of experiment (DOE) based on the Box-Behken design in an UV process, and also the main factors (variables) with UV intensity($X_2$) (range: $1.5{\sim}4.5\;mW/cm^2$), NDMA concentration ($X_2$) (range: 100~300 uM) and pH ($X_2$) (rang: 3~9) which consisted of 3 levels in each factor and 4 responses ($Y_1$ (% of NDMA removal), $Y_2$ (dimethylamine (DMA) reformation (uM)), $Y_3$ (dimethylformamide (DMF) reformation (uM), $Y_4$ ($NO_2$-N reformation (uM)) were set up to estimate the prediction model and the optimization conditions. The results of prediction model and optimization point using the canonical analysis in order to obtain the optimal operation conditions were $Y_1$ [% of NDMA removal] = $117+21X_1-0.3X_2-17.2X_3+{2.43X_1}^2+{0.001X_2}^2+{3.2X_3}^2-0.08X_1X_2-1.6X_1X_3-0.05X_2X_3$ ($R^2$= 96%, Adjusted $R^2$ = 88%) and 99.3% ($X_1:\;4.5\;mW/cm^2$, $X_2:\;190\;uM$, $X_3:\;3.2$), $Y_2$ [DMA conc] = $-101+18.5X_1+0.4X_2+21X_3-{3.3X_1}^2-{0.01X_2}^2-{1.5X_3}^2-0.01X_1X_2+0.07X_1X_3-0.01X_2X_3$ ($R^2$= 99.4%, 수정 $R^2$ = 95.7%) and 35.2 uM ($X_1$: 3 $mW/cm^2$, $X_2$: 220 uM, $X_3$: 6.3), $Y_3$ [DMF conc] = $-6.2+0.2X_1+0.02X_2+2X_3-0.26X_1^2-0.01X_2^2-0.2X_3^2-0.004X_1X_2+0.1X_1X_3-0.02X_2X_3$ ($R^2$= 98%, Adjusted $R^2$ = 94.4%) and 3.7 uM ($X_1:\;4.5\;$mW/cm^2$, $X_2:\;290\;uM$, $X_3:\;6.2$) and $Y_4$ [$NO_2$-N conc] = $-25+12.2X_1+0.15X_2+7.8X_3+{1.1X_1}^2+{0.001X_2}^2-{0.34X_3}^2+0.01X_1X_2+0.08X_1X_3-3.4X_2X_3$ ($R^2$= 98.5%, Adjusted $R^2$ = 95.7%) and 74.5 uM ($X_1:\;4.5\;mW/cm^2$, $X_2:\;220\;uM$, $X_3:\;3.1$). This study has demonstrated that the response surface methodology and the Box-Behnken statistical experiment design can provide statistically reliable results for decomposition and by-products of NDMA by the UV photolysis and also for determination of optimum conditions. Predictions obtained from the response functions were in good agreement with the experimental results indicating the reliability of the methodology used.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2006.06a
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• pp.55-60
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• 2006

Draw-bead is applied to control the material flow in a stamping process and improve the product quality by controlling the draw-bead restraining force (DBRF). Actual die design depends mostly on the trial-and-error method without calculating the optimum DBRF. Die design with the predicted value of DBRF can be utilized at the tryout stage effectively reducing the cost of the product development. For the prediction of DBRF, a simulation-based prediction model of the circular draw-bead is developed using the Box-Behnken design with selected shape parameters such as the bead height, the shoulder radius and the sheet thickness. The value of DBRF obtained from each design case by analysis is approximated by a second order regression equation. This equation can be utilized to the calculation of the restraining force and the determination of the draw-bead shape as a prediction model. For the evaluation of the prediction model, the optimum design of DBRF in sheet metal forming is carried out using response surface methodology. The suitable type of the draw-bead is suggested based on the optimum values of DBRF. The prediction model of the circular draw-bead proposes the design method of the draw-bead shape. The present procedure provides a guideline in the tool design stage for sheet metal forming to reduce the cost of the product development.

• Applied Chemistry for Engineering
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• v.32 no.6
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• pp.621-626
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• 2021

A sequential design of experiments was used to optimize MOF-801 synthesis process. For the initial screening, a general 2^k factorial design was selected followed by the central composition design, one of the response surface methods. A 2³ factorial design based on the molar ratio of fumaric acid, dimethylformamide (DMF), and formic acid was performed to select the more suitable response variable for the design of experimental method among the crystallinity and BET specific surface area of MOF-801. After performing 8 synthesis experiments designed by MINITAB 19 software, the characteristic analysis was performed using XRD analysis and nitrogen adsorption method. The crystallinity with R² = 0.999 was found to be more suitable for the experimental method than that of BET specific surface area. Based on analysis of variance (ANOVA), it was confirmed that the molar ratio of fumaric acid and formic acid was a major factor in determining the crystallinity of MOF-801. Through the response optimization and contour plot of two factors, the optimal molar ratio of ZrOCl₂·8H₂O : fumaric acid : DMF : formic acid was 1 : 1 : 39 : 35. In order to optimize the synthesis process, the central composition design on synthesis time and temperature was performed under the identical molar ratio of precursors. The results derived through the designed 9 synthesis experiments were calculated using the quadratic model equation. Thus, the maximum crystallinity of MOF-801 predicted under the synthesis time and temperature of 7.8 h and 123 ℃, respectively.

• Korean Chemical Engineering Research
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• v.56 no.4
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• pp.568-576
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• 2018

In order to investigate the adsorption characteristics of the antibiotics trimethoprim (TMP) by activated carbon (WCAC) prepared from waste citrus peel, the effects of operating parameters on the TMP adsorption were investigated by using a response surface methodology (RSM). Batch experiments were carried out according to a four-factor Box-Behnken experimental design with four input parameters : concentration ($X_1$: 50-150 mg/L), pH ($X_2$: 4-10), temperature ($X_3$: 293-323 K), adsorbent dose ($X_4$: 0.05-0.15 g). The experimental data were fitted to a second-order polynomial equation by the multiple regression analysis and examined using statistical methods. The significance of the independent variables and their interactions was assessed by ANOVA and t-test statistical techniques. Statistical results showed that concentration of TMP was the most effective parameter in comparison with others. The adsorption process can be well described by the pseudo-second order kinetic model. The experimental data of isotherm followed the Langmuir isotherm model. The maximum adsorption amount of TMP by WCAC calculated from the Langmuir isotherm model was 144.9 mg/g at 293 K.

• Journal of Energy Engineering
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• v.23 no.2
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• pp.62-73
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• 2014

This research was focused to apply response surface methodology for optimization of bio-methane production by biogas upgrading process. Methane concentration(Y1) and methane efficiency(Y2) on biogas upgrading process were mathematically described as being modeled by the use of the Box-Behnken design on response surface methodology. The results of ANOVA(analysis of variance) about models, the probability value of the methane concentration and methane recovery response surface model are 0.0001 and 0.0001, respectively and coefficient of determination($R^2$) are 0.9788 and 0.9710, respectively. The response surface model is proved of high reliability and suitability. The operation pressure had the greatest influence to methane concentration than other operation parameters and the PSA rotary valve velocity had the greatest influence to methane recovery than other operation parameters. Optimal condition of biogas upgrading process for production of $100Nm^3/hr$ bio-methane were operation pressure 8.0bar and outlet flow rate 31.55RPM, respectively. At that operation condition the methane concentration of bio-methane was 97.13% and methane recovery in biogas upgrading process was 75.89%.

• Food Engineering Progress
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• v.21 no.2
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• pp.132-137
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• 2017

The purpose of this study was to optimize dough properties using response surface methodology (RSM) and to demonstrate the performances of dough prepared under optimized conditions. Dough mixed with yeast, margarine, salt, sugar and wheat flour was prepared by fermentation process. Hardness, cohesiveness and springiness of dough were selected as critical quality attributes. The critical formulations (yeast and water) and process (fermentation time) variables were selected as critical input variables based on preliminary experiment. Box-Behnken design (BBD) was used as RSM. As a result, the quardratic, the squared and the linear model respectively provided the most appropriate fit ($R^2$>90) and had no significant lack of fit (p>0.05) on critical quality attributes (hardness, cohesiveness and springiness). The accurate prediction of dough characteristics was possible from the selected models. It was confirmed by validation that a good correlation was obtained between the actual and predicted values. In conclusion, the methodologies using RSM in this study might be applicable to the optimization of fermented foods containing various wheat flour and yeast.