• 품질경영학회지
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• 제48권2호
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• pp.269-282
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• 2020

Purpose: The practical design for experiments with mixtures of q components is consisted in the four types of design points, vertex, center of edge, axial, and center points in a (q-1)-dimensional simplex space. We propose a sequential method for the successful construction of the design space in Quality by Design (QbD) by allowing the different number of replicates at the four types of design points in the practical design when the quadratic canonical polynomial model is assumed. Methods: To compare the mixture designs efficiency, fraction of design space (FDS) plot is used. We search for the practical mixture designs whose the minimal half-width of the tolerance interval per a standard deviation, which is denoted as d₂, is less than 4.5 at 0.8 fraction of the design space. They are found by adding the different number of replicates at the four types of the design points in the practical design. Results: The practical efficient mixture designs for the number of components between three and five are listed. The sequential method to establish a design space is illustrated with the two examples based on the simulated data. Conclusion: The designs with the center of edge points replications are more efficient than those with the vertex points replication. We propose the sample size of at least 23 for three components, 28 for four components, and 33 for the five components based on the list of efficient mixture designs.

• 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.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2004년도 추계 학술대회논문집
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• pp.173-176
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• 2004

In this study, the multidisciplinary aerodynamic-structural optimal design is carried out for the supersonic fighter wing. Through the aeroelastic analyses of the various candidate wings, the aerodynamic and structural performances are calculated such as the lift coefficient, the drag coefficient and the deformation of the wing. In general, the supersonic fighter is maneuvered under the various flight conditions and those conditions must be considered all together during the design process. The multi-point design, therefore, is deemed essential. For this purpose, supersonic dash, long cruise range and high angle of attack maneuver are selected as representative design points. Based on the calculated performances of the candidate wings, the response surfaces for the objectives and constraints are generated and the supersonic fighter wing is designed for better aerodynamic performances and less weights than the baseline. At each design point, the single-point design is performed to obtain better performances. Finally, the multi-point design is performed to improve the aerodynamic and structural performances for all design points. The optimization results of the multi-point design are compared with those of the single-point designs and analyzed in detail.

• 한국지하수토양환경학회지:지하수토양환경
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• 제15권1호
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• pp.9-18
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• 2010

In this study, Solid-phase micro-extraction (SPME) with Gas Chromatograph using Flame Ionization Detector (GC/FID) was studied as a possible alternative to liquid-liquid extraction for the analysis of Methyl tert-butyl ether (MTBE) and Tertiary-butyl ether (TBA) in water and an optimization condition of trace analysis of MTBE and TBA using the design of experiment (DOE) was described. The aim of our research was to apply experimental design methodology in the optimization condition of trace analysis of fuel oxygenated compounds in soil-phase microextraction with GC/FID. The reactions of SPME were mathematically described as a function of parameters of Temp ($X_1$), Volume ($X_2$), Time ($X_3$) and Salt ($X_4$) being modeled by the use of the partial factorial designs, which was used for fitting 2nd order response surface models and was alternative to central composite designs. The model predicted agreed with the experimentally observed result ($Y_1$(MTBE, $R^2$ = 0.96, $Y_2$ (TBA, $R^2$ = 0.98)). The estimated ridge of the expected maximum responses and optimal conditions for MTBE and TBA were 278.13 and (Temp ($X_1$) = $48.40^{\circ}C$, Volume ($X_2$) = 73.04 mL, Time ($X_3$) = 11.51 min and Salt ($X_4$) = 12,50 mg/L), and 127.89 and (Temp ($X_1$) = $52.12^{\circ}C$, Volume ($X_2$) = 88.88mL, Time ($X_3$) = 65.40 min and Salt ($X_4$) = 12,50 mg/L), respectively.

• 대한산업공학회지
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• 제33권3호
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• pp.349-354
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• 2007

A mixture experiment is a special type of the response surface experiment in which the factors are the components of a mixture, and the response variable is a function of the proportions of each component. When a new mixture product is developed, there are a large number of components, and the first objective of the experiment is to identify the ones that are most important by doing a screening experiment. We propose a method of screening mixture components using the correlation coefficients when t-tests cannot identify significant components.

• 한국생물공학회:학술대회논문집
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• 한국생물공학회 2005년도 생물공학의 동향(XVI)
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• pp.68-72
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• 2005

Leuconostoc citreum is one of the representative strains of Leuconostoc spp. that show fast growth rates in fermented vegetables. Sequential experimental designs including the Plackett-Burman design, fractional factorial design, steepest ascent analysis, central composite design and response surface methodology were introduced tooptimize and improve the medium for Leuconostoc citreum. Fifteen medium ingredients were examined and glucose (20 g/l), yeast extract (12.5 g/l), sodium acetate trihydrate (6.12 g/l), potassium phosphate (42.55 g/l) and dibasic ammonium citrate (4.12 g/l)were chosen as the best components to give a critical and positive effect for cell-growth. The biomass was increased to 2.79 g/l (169%), compared to the 1.65 g/l in MRS medium.

• Biotechnology and Bioprocess Engineering:BBE
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• 제9권4호
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• pp.278-284
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• 2004

Leuconostoc citreum is one of the representative strains of Leuconostoc spp. that show fast growth rates in fermented vegetables. Sequential experimental designs including the Plackett-Burman design, fractional factorial design, steepest ascent analysis, central composite design and response surface methodology were introduced to optimize and improve the medium for L. citreum. Fifteen medium ingredients were examined and glucose ($20 g/\ell$), yeast extract ($12.5g/\ell$), sodium acetate trihydrate ($6.12g/\ell$), potassium phosphate ($42.55g/\ell$), and dibasic ammonium citrate ($4.12g/\ell$), were chosen as the best components to give a critical and positive effect for cell-growth. The biomass was increased to ($2.79g/\ell$), (169%), compared to the $1.65g/\ell$ in MRS medium.

• 한국산학기술학회논문지
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• 제16권3호
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• pp.1630-1638
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• 2015

많은 산업분야에서 구조설계 시 구조성능을 검토하기 위한 유한요소해석은 필수적인 과정이 되었다. 이와 함께, 컴퓨터의 성능도 급속도로 개선되고 있지만 대형 문제의 경우에는 최적설계기법을 적용하는데 한계가 있다. 이러한 대형 문제의 최적화를 위하여 메타모델을 이용한 근사모델을 이용하고 있다. 근사모델을 생성하는 방법은 곡선맞춤법과 내삽법으로 분류할 수 있는데, 반응표면모델과 크리깅 모델이 대표적인 것이다. 그러나 각 모델은 오버피팅이나 언더피팅이 될 수 있는 단점이 있다. 본 연구에서는 반응표면과 크리깅으로 구성되는 혼합모델에 의한 메타모델을 이용하여 구조설계에 적용하고자 한다. 제안된 방법을 2부재 구조물과 자동차용 아우터타이로드의 구조설계에 적용하였다.

• International Journal of Precision Engineering and Manufacturing
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• 제5권4호
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• pp.61-68
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• 2004

Necessity to address engineering system uncertainties in design processes has long been acknowledged. To obtain quality of product, a safety factor is traditionally used by many design engineers due to its easy of use and comprehension. However, the safety factor approach often yields either conservative or unreliable designs, since it ignores the type of probability distribution and the mechanism of uncertainty propagation from the input to the output. For a consistent reliability-based design, two fundamental issues must be investigated thoroughly. First, the design-decision process that clearly identifies a mechanism of uncertainty propagation under system uncertainties needs to be developed, which must be an efficient and accurate process. To identify the mechanism more effectively, an adaptive probability analysis is proposed by adaptively setting probability levels through a posteriori error estimation. The second is to develop the design process that not only yields a high quality design but also a cost-effective optimum design from manufacturing point of view. As a result, a response surface methodology is specially developed for RBDO, thus enhancing numerical challenges of efficiency and complicatedness. Side crashworthiness application is used to demonstrate the integrated design process for product and manufacturing process design.

• 품질경영학회지
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• 제30권4호
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• pp.58-67
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• 2002

Since the inception of off-line quality control, it has drawn a particular attention from research community and it has been implemented in a wide variety of industries mainly due to its extensive applicability to numerous real situations. Emphasizing design issues rather than control issues related to manufacturing processes, off-line quality control has been recognized as a cost-effective approach to quality improvement. It mainly consists of three design stages: system design, parameter design, and tolerance design which are implemented in a sequential manner. Utilizing experimental designs and optimization techniques, off-line quality control is aimed at achieving product performance insensitive to external noises by reducing process variability. In spite of its conceptual soundness and practical significance, however, off-line quality control has also been criticized to a great extent due to its heuristic nature of investigation. In addition, it has also been pointed out that the process optimization procedures are inefficient. To enhance the current practice of off-line quality control, this study proposes an integrated optimization model by utilizing a well-established statistical tool, so called response surface methodology (RSM), and a tolerance - cost relationship.