• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.31-44
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• 1995

In fitting a model, there always exists a discrepancy between the fitted model and the true functional relationship. In measuring this discrepancy, Box and Drapper (1959) used the criterion dividing the discrepancy into two parts which are the bias error part and the variance error one in single response case. In this paper, an optimum design which makes these two types of errors as small as possible is found by extending the Box and Drapper criterion to multiple response situation. Especially, a design is found to meat rotatability conditions when we fit a quadratic model to each response fearing cubic bias. Using the central composite design, an application of general results to a specific case is shown to help understanding the material.

• Preventive Nutrition and Food Science
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• 제14권2호
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• pp.129-133
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• 2009

Salicornia herbacea is rich in natural minerals, dietary fibers, and potentially health-promoting phenolic compounds. In this paper, an experimental design was applied for the optimization of the ultrasound-assisted extraction of phenolic compounds from lyophilized Salicornia herbacea powder. The experiments were conducted in accordance with a five-level, three-variable central composite rotatable design (CCRD), and the effects of solvent concentration, extraction time, and extraction temperature were evaluated via response surface methodology (RSM). The optimal extraction conditions were as follows: ethanol concentration, 76.80%; extraction time, 20 min; and extraction temperature, $33.21^{\circ}C$; and the solvent concentration was the most significant parameter in this process, under which the predicted total phenolic content was 49.91 mg GAE/g sample.

• 한국연초학회지
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• 제11권1호
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• pp.93-102
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• 1989

The optimal condition was investigated to make for good quality of Burley tobacco during the toasting. A complete factorial design (3$\times$3) and rotatable central composite design were used in this study. Based on the results obtained, it would be possible that 1) methyl-pyrazine other than pyrazine compounds is assumed to play an important role in the improvement of smoke taste. 2) filling value of Burley 21 leaf can be increased by 5~10 % 3) fragility index can be increased by about 5%. 4) total volatile base can also be reduced by about 10% and 5) the aroma and favorable taste of the Burley tobacco can be Improved by toe optimization the amount of sugar added and the toasting time and temperature.

• 한국염색가공학회지
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• 제20권2호
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• pp.19-28
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• 2008

The objective of this study was to apply the statistical technique known as design of experiments to optimize the % exhaustion variables for phthalocyanine dyeing of nylon fiber. In this study, a three-factor Central Composite Rotatable Design (CCRD) was used to establish the optimum conditions for the phthalocyanine reactive dyeing of nylon fiber. Temperature, pH and liquor ratio were considered as the variable of interest. Acidic solution with higher temperature and lower liquor ratio were found to be suitable conditions for higher % exhaustion. These three variables were used as independent variables, whose effects on % exhaustion were evaluated. Significant polynomial regression models describing the changes on % exhaustion and % fixation with respect to independent variables were established with coefficient of determination, R2, greater than 0.90. Close agreement between experimental and predicted yields was obtained. Optimum conditions were obtained using surface plots and Monte Carlo simulation techniques where maximum dyeing efficiency is achieved. The significant level of both the main effects and interaction was observed by analysis of variance (ANOVA) approach. Based on the statistical analysis, the results have provided much valuable information on the relationship between response variables and independent variables. This study demonstrates that the CCRD could be efficiently applied for the empirical modeling of % exhaustion and % fixation in dyeing. It also shows that it is an economical way of obtaining the maximum amount of information in a short period of time with least number of experiments.

• Journal of Welding and Joining
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• 제34권3호
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• pp.23-30
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• 2016

This paper discusses the optimization of friction stir spot welding (FSSW) process parameters for joining Aluminum alloy (AA6061-T6) with Magnesium alloy (AZ31B) sheets. Prior to optimization an empirical relationship was developed to predict the Tensile Shear Fracture Load (TSFL) incorporating the four most important FSSW parameters, i.e., tool rotational speed, plunge rate, dwell time and tool diameter ratio, using response surface methodology (RSM). The experiments were conducted based on four factor, five levels central composite rotatable design (CCD) matrix. The maximum TSFL obtained was 3.61kN, with the tool rotation of 1000 rpm, plunge rate of 16 mm/min, dwell time of 5 sec and tool diameter ratio of 2.5.

• 한국축산식품학회:학술대회논문집
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• 한국축산식품학회 1997년도 제18차 정기총회 및 학술발표회
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• pp.19-39
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• 1997

Extrusion conditions were optimized for blends of ground lamb and starch using a single-screw extruder for the purpose of producing expanded snack-type products. A central composite rotatable response surface methodology(RSM) design was used with variation in feed moisture, process temperature, and screw speed. The three variables significantly affected one or more of the measured physical properties of extrudates. The optimum conditions for minimum shear force values were 26.5% feed moisture, $148^{\circ}C$ process temperature, and 134 rpm screw speed. Lean ground beef, chicken, goat, lamb or mutton was blended with corn starch, and extruded at the optimum condition established from RSM experiments. Physical/rheological properties were generally similar, water activity was low (<0.12) and total aerobic plate counts were <10 for all products. Extrudates containing chicken had the highest ratio of polyunsaturated fatty acids to saturated fatty acids, whereas those containing beef had the highest ratio of monounsaturated fatty acids to saturated fatty acids. Sensory data indicated that texture was acceptable and flavor characteristics were not different among the products.

• Journal of Microbiology and Biotechnology
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• 제21권7호
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• pp.739-745
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• 2011

During the production of grape wine, the formation of thick leathery pellicle/bacterial cellulose (BC) at the airliquid interface was due to the bacterium, which was isolated and identified as Gluconacetobacter hansenii UAC09. Cultural conditions for bacterial cellulose production from G. hansenii UAC09 were optimized by central composite rotatable experimental design. To economize the BC production, coffee cherry husk (CCH) extract and corn steep liquor (CSL) were used as less expensive sources of carbon and nitrogen, respectively. CCH and CSL are byproducts from the coffee processing and starch processing industry, respectively. The interactions between pH (4.5-8.5), CSL (2-10%), alcohol (0.5-2%), acetic acid (0.5-2%), and water dilution rate to CCH ratio (1:1 to 1:5) were studied using response surface methodology. The optimum conditions for maximum BC production were pH (6.64), CSL (10%), alcohol (0.5%), acetic acid (1.13%), and water to CCH ratio (1:1). After 2 weeks of fermentation, the amount of BC produced was 6.24 g/l. This yield was comparable to the predicted value of 6.09 g/l. This is the first report on the optimization of the fermentation medium by RSM using CCH extract as the carbon source for BC production by G. hansenii UAC09.

• 한국염색가공학회지
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• 제21권5호
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• pp.41-50
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• 2009

Design of experiments (DoE) concept was successfully applied to determine the optimum processing conditions that yield maximum % exhaustion for berberine interaction with synthetic tanning agent pretreated polyamide substrates. The potential of synthetic tanning agent to provide anionic sites on the polyamide for berberine interaction which is cationic in nature was tested to increase the % exhaustion of berberine in this article. Experiments were designed according to Central Composite Rotatable Design (CCRD). The three factors for synthetic tanning agent pretreatment and two factors for berberine interaction each at five different levels, including central and axial points were considered. Experiments were conducted in a laboratory scale infra-red treatment instrument according to CCRD. For each response, second order polynomial models were developed using multiple linear regression analysis incorporating linear, interactions and squared effects of all variables and then optimized. The significance of the mathematical model developed was ascertained using Excel regression (solver) analysis module. Analysis of variance (ANOVA) was performed to check the adequacy and accuracy of the fitted models. The response surfaces and contour maps showing the interaction of process variables were constructed. Applying Monte Carlo simulation, response surface and contour plots, optimum operating conditions were found and at this optimum point, % exhaustion of 81% and 74% respectively for synthetic tanning agent pretreatment and berberine interaction were observed and subsequently the results were experimentally investigated.

• 응용통계연구
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• 제25권1호
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• pp.215-223
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• 2012

반응표면 방법론은 어떤 공정을 개선하거나 최적화하는데 이용되는 아주 유용한 통계적방법이다. 이러한 최적조건을 추정하기 위하여 최적조건이 있으리라 예상되는 실험구역을 탐색하여 실험을 실시한다. 그런데 이 실험구역은 실험의 환경의 제약 그리고 연구자의 선택 등으로 그 모습이 다양하게 달라질 수 있다. 반응표면 설계는 실험구역의 모양에 따라 보통 둥그런 모양의 "구형설계"와 육면체 모양의 "입방형설계"로 구분한다. 구형설계는 회전성을 만족하거나 회전성에 상당히 근접하는 "유사회전성"을 갖는 특징이 있다. 반응표면 설계에서 가장 많이 사용되는 중심합성설계는 실험구역이 구형인 5수준 실험설계이다. 이 때, 축점의 ${\alpha}$값을 ${\alpha}=\sqrt{k}$ 대신 ${\alpha}=1$로 조정하면 5-수준이 아닌 3-수준 입방형 중심합성설계를 얻을 수 있다. 그러나 입방형 중심합성설계는 실험구역이 구형이 아니므로 회전성을 만족하지 못하는 문제가 있다. 이러한 이유로, 변수들의 수준 수를 3으로 제한하면서 실험구역은 구형인 실험설계가 필요할 때가 많다. 이에 대한 대표적 실험설계가 바로 박스-벤켄 실험설계이다. 이 실험설계는 구형의 실험구역으로 회전성을 만족하나 실험구역의 크기가 변수의 개수가 증가해도 제자리 수준으로 좁은 특징이 있다. 현실적으로 실험구역의 가상 자리 부분에 대한 예측에 관심이 있을 경우 변수의 개수가 많아지면 이에 비례하여 실험구역이 커지는 실험설계가 바람직하다. 본 논문은 3-수준 입방형설계에 비하여 실험구역이 유달리 좁은 박스-벤켄 실험설계를 보완하여 구형설계를 만족하면서도 다른 한편으로는 변수 수에 따라 실험반경이 커지는 3-수준 구형 반응표면 설계를 소개하고자 한다. 이 방법을 기존의 실험설계들과 비교한 결과 변수수가 비교적 작을 경우 실험횟수 등을 고려하여 응용가치가 있음을 확인하였다.

• Preventive Nutrition and Food Science
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• 제6권3호
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• pp.163-169
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• 2001

To produce expanded, minimally hard extrudates from blends of raw pork meat (20%), defatted soy flour (25%), and corn starch using a single-screw extruder, various combinations of feed moisture, process temperature, and screw speed were evaluated. First series of extrusion runs were conducted according to a central composite rotatable design/response surface methodology (RSM). Upon assessing the full model for each response, insignificant terms were eliminated to determine final response surface models. Screw speed within the range evaluated was found to have no significant effect on expansion ratio (ER) or shear force (SF) of extrudates. Since examinations of the response surfaces and their generated grids of predicted values indicated that maximum ER and minimum SF were likely to be attained with a moisture-temperature combination outside the RSM experimental range, the second series of extrusion runs were conducted with several selected combinations of moisture and temperature to determine a practical optimum extrusion condition. The combination of 22.78% feed moisture, 16$0^{\circ}C$ process temperature, and 170 rpm screw speed was chosen as such a condition, and used in the final extrusion. The final product required less force to break than did commercial pretzel sticks.