• The Korean Journal of Applied Statistics
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• v.31 no.1
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• pp.97-108
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• 2018

It has been routine practice in regression analysis to check the validity of the assumed model by the use of regression diagnostics tools. Outliers and influential observations often distort the regression output in an undesired manner. Jang and Anderson-Cook (Quality and Reliability Engineering International, 30, 1409-1425, 2014) proposed a graphical method (called a firework plot) so that there could be an exploratory visualization of the trace of the impact of the possible outliers and influential observations on individual regression coefficients and the overall residual sum of the squares measure. This paper further extends a graphical approach to a multi-response surface methodology problem.

• Applied Biological Chemistry
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• v.40 no.3
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• pp.225-231
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• 1997

Optimization theory was applied to a native and two imported soybeans. Failure stress and stress relaxation curve was measured with rheometer, and color was measured by colorimeter. The effects of each soybean upon the tofu texture were expressed through a non-linear canonical regression model and trace plot. Compared to the other imported soybeans, native soybean produced a higher strength in tofu texture, and showed the positive increase in viscoelastic properties such as instantaneous stress, equilibrium stress and relaxation time, whereas it had no effect on whiteness from reference blend, represented that native soy-bean showed the individual strength upon the selected rheological texture properties. Higher soaking ability in native soybean was selected as a new response for the optimization mixture process, and it contributed positively to the rheological properties of tofu. New soaking process control system during processing and desirability for the mathematical model should be applied for a better mixture design in varieties of soybeans.

• Korean Journal of Food Science and Technology
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• v.31 no.2
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• pp.385-390
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• 1999

Noodle was made using a combination of yulmu, wheat and water through mixture design. Statistical models of yulmu noodle were shown by analysing tensile stress and color $(L^{*})$, and sensory evaluation with other constraints. Analysing the linear and non-linear model, the linearity in the values of tensile stress, lightness $(L^{*})$ and sensory evaluation showed that each component worked separately without interactions. In studying the component effect on the response by trace plot, the result indicated that the increase in the amount of yulmu enhanced tensile stress of noodle while degrading $L^{*}$ value and sensory evaluation score. In the range of satisfying the conditions of noodle in every tensile stress, $L^{*}$ value and sensory evaluation point, the optimum mixture ratio of yulmu : wheat : water was 2.27% : 66.28% : 28.45% based on least cost linear programming. In this calculation, the least cost was 9.924 and estimated potential results of the response for tensile stress was 2.234 N and those for $L^{*}$ was 82.39. Finally, the potential response results affected by mixture ratio of yulmu, wheat and water were screened using Excel.

• Proceedings of the Korean Radioactive Waste Society Conference
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• 2004.02a
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• pp.28-41
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• 2004

The study is aimed to assess the usefulness of the mixture design for spent resin immobilization in cement. Although a considerable amount of research has been carried out to determine the limits for the composition of an acceptable resin-cement mixture, no efficient experimental strategy exists that explores the full properties of waste form against composition relationship. In order to gain an overall view, this report introduces the method of mixture design and mixture analysis, and describes the design of experiment of the 5-component mixture with the constraint conditions. The mathematic models of 28-day compressive strength varying with the ingredients are fitted, and the main effect and interaction effect of two ingredients are identified quantitatively along with the graphical interpretation using the response trace plot and contour plots.

• IE interfaces
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• v.19 no.2
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• pp.117-123
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• 2006

Many products, such as gasoline, polymer plastics, alloys, and ceramics are manufactured by mixing two or more ingredients or components. When we are to develop new mixture products, we must deal with a long list of potentially important component variables. This paper introduces some mixture screening designs, analysis tools for screening important variables, and a guideline for applying these analysis tools. The results of this paper will be helpful to engineers who work in the research and development sector of mixture product industries.

• Korean journal of food and cookery science
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• v.25 no.2
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• pp.234-242
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• 2009

This study was performed to find the optimum ratio of ingredients for the manufacture of kiwifruit jam. The experiment was designed according to the D-optimal design of RSM (response surface methodology), which included 18 experimental points with 4 replicates for three independent variables (sugar $35{\sim}60%$, pectin $0.1{\sim}1.0.%$, kiwifruit paste $0.37{\sim}0.90%$). The compositional and functional properties of the prepared products were measured, and these values were applied to mathematical models. A canonical form and trace plot showed the influence of each variable on the quality attributes of the final product mixture. By use of the F-test, viscosity, color values (L, a, b), and sensory characteristics (color) were expressed by a linear model, while the L color value and select sensory characteristics (smell, taste, overall acceptance) were also expressed by a quadratic model. The optimum formulations by the numerical and graphical methods, were similar, and with the numerical method it presented as: sugar, pectin, and barley sproutling powder at 49.7%, 0.5%, and 0.6%, respectively. The above results demonstrate the feasibility of preparing kiwifruit jam added with barley sproutling powder, and therefore, the commercialization of a kiwifruit jam marketed as a functional food is deemed possible.

• Korean journal of food and cookery science
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• v.28 no.1
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• pp.67-76
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• 2012

This study examined the optimal ingredient mixing ratio for the preparation of steamed cake containing mugwort (Artemisia princeps var. orientalis) powder. After preliminary studies, the following ingredient ranges were determined; 110~129% sugar, 3~8% mugwort powder, 10~25% oil. Among the different mixture designs, the D-optimal design was chosen for analysis. The results of F-test, specific gravity, viscosity, volume and color values (L, a, b), hardness decided a linear model, while the sensory characteristics (color, taste, texture and overall acceptance) decided a quadratic model. The fitness analysis results showed that in all characteristic, the probabilities were significant within 0.05%; thus, the models were accepted as appropriate. The response surface and trace plot results showed that increasing amounts of mugwort powder decreased the brightness, and increased redness and yellowness. As the level of added oil increased, the softness of the cake increased. Cake samples received low sensory evaluation scores when sugar, mugwort powder, and oil were added above their optimal levels. The optimum formulations by the numerical and graphical methods, were similar, and with the numerical method presented as: sugar, mugwort powder, and oil at 120.7%, 5.1%, and 16.2%, respectively(flour weight basis). The above results demonstrate the feasibility of adding mugwort powder to sponge cake, and therefore, the commercialization of mugwort powder cake marketed as a functional food is deemed possible.

• Korean journal of food and cookery science
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• v.25 no.3
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• pp.317-329
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• 2009

In the study, we determined the optimal ingredient mixing ratio for the preparation of sponge cake containing bamboo (Pseudosasa japonica Makino) leaves. This experiment was designed in according with the D-optimal design of mixture design, which involved 14 experimental points including 4 replicates for three independent variables (sugar 110${\sim}$129%, bamboo leaves 3${\sim}$8%, oil 10${\sim}$25%). The results the F-test, specific gravity, volume and color values (L, a, b) decided a linear model, while the viscosity, hardness and sensory characteristics (color, smell, taste, texture and overall acceptance) decided a quadratic model. The results of our fitness analysis demonstrated that in all characteristic, the probabilities were significant within 0.05%; thus, the models were accepted as appropriate. The response surface and trace plot results demonstrated that increasing amounts of added bamboo leaves induced a reduction in brightness, and increasing redness and yellowness. In addition, increasing amounts of bamboo leaves caused increases in hardness, and thus the softness of the cake decreased. And as the level of added oil increased, softness increased. Cake samples received low sensory evaluation scores when sugar, bamboo leaves, and oil were added above their optimal levels. In the numeric optimization, the optimal ingredient amounts were 121.36% sugar, 4.96% bamboo leaves, and 15.69% oil. The above results demonstrate the feasibility of adding bamboo leaves to sponge cake, and therefore, a bamboo leaves as a functional food.

• Journal of the East Asian Society of Dietary Life
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• v.23 no.2
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• pp.218-226
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• 2013

This study examined the optimal mixture ratio of rice gruel supplemented with puffed rice by mixture design. The quality characteristics of rice gruel samples were examined according to mixture ratios at eleven experimental points. The high soluble solid content and viscosity of gruel samples were significantly dependent on rice (short grain) content instead of glutinous rice. The viscosity ranged from $2,891{\sim}9,153\;cP{\cdot}s$ and soluble solid content ranged from $8.23{\sim}10.13^{\circ}Brix$ at the eleven experimental points. The mixture with the highest solid content and viscosity, 12% rice gruel sample was $10.10{\sim}10.13^{\circ}Brix$ and $9,150{\sim}9,153\;cP{\cdot}s$. The L color of sample decreased with decreasing rice content, while "a" (redness) and "b" (yellowness) values slightly increased. In the sensory evaluation, samples with higher amount of puffed rice and glutinous rice scored higher for brown color, flavor and sweetness than high-content rice samples. The response surface and trace plot results showed that increasing of puffed rice increased the brown color, sweet taste and sticky aftertaste. From the results of the F-test, viscosity, "a" (redness) and "b" (yellowness) values fit a quadratic model with significant probabilities within 0.05%. The optimum predicted formulations of rice gruel containing puffed rice were 1.69% of puffed rice, 0.47% of glutinous rice and 9.84% of rice, respectively.

• Journal of Life Science
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• v.25 no.3
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• pp.329-335
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• 2015

This study was performed to determine the optimal ratio of Petasites japonicus, Luffa cylindrica, and Houttuynia cordata, all of which are supposed to have anti-respiratory disease effects, such as against rhinitis. The experiment incorporated a mixture design and included 12 experimental points with center replicates for three different independent variables (Petasites japonicus 30~70%; Luffa cylindrica 10~30%; and Houttuynia cordata 10~30%). Based on this design, the mixture was extracted in hot water at 121℃ for 45 min and anti-allergy and anti-microbial activities were observed. The response surface and trace plot described for the anti-allergy activity showed Petasites japonicas was a relatively important factor. The correlation coefficient (R²) value 82.10% for the inhibition effect of degranulation was analyzed by the regression equation. The analysis of variance showed the model fit was statistically significant (p<0.05). The optimal ratio of the mixture was Petasites japonicus 0.75%, Luffa cylindrica 0.11%, and Houttuynia cordata 0.14%. The anti-microbial activity for each extraction of the mixture was valid on gram-positive, such as Staphylococcus aureus (KCCM 40881) and Staphylococcus epidermidis (KCCM 35494), while it was less effective on gram-negative, such as Escherichia coli (KCCM 11234) and Pseudomonas aeruginosa (KCCM 11328).