혼합물 반응표면분석에서 디자인 스페이스 구축을 위한 효율적인 실험계획

정종희,임용빈 한국품질경영학회 2020 품질경영학회지 Vol.48 No.2

Purpose: The practical design for experiments with mixtures of  components is consisted in the four types of design points, vertex, center of edge, axial, and center points in a    -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 , 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.

현대 니트패션에 나타난 공간 혼합의 디자인 특성

박문희(Moon Hee Park),김차현(Cha Hyun Kim) 한국디자인문화학회 2010 한국디자인문화학회지 Vol.16 No.2

현대 사회는 수많은 네트워크에 따른 문화 공유에 따라 ‘혼합’의 흐름 속에 놓여 있으며, 니트 패션에서도 수요의 증가에 따라 새로운 디자인이 요구되고 있어 이에 따른 전략적 방안이 절실히 요구 되고 있다. 본 연구는 2000∼2008년의 세계 4대 여성컬렉션의 횡편 니트 3∼8게이지의 자료를 선정, 현대 니트 패션에 나타난 공간의 혼합의 연도, 시즌별 출현빈도와 실루엣, 조직, 게이지와 색상의 시즌별 출현빈도 및 사례별로 디자인 특성을 분석하여 창의적인 니트디자인이 나올 수 있는 방안을 모색하는 것을 목적으로 하였다. 공간의 혼합의 출현빈도를 보면 2006년 이후 증가추세를 나타냈으며, F/W가 S/S에 비해 두 배 정도의 높은 빈도수를 나타냈다. 공간 혼합의 디자인 특성에서 실루엣은 여성스러움을 강조하는 특성으로 Hourglass실루엣이 가장 높은 빈도수를 나타냈으며. 게이지는 미들게이지와 하이게이지가 가장 높게 나타났다. 조직에서는 기본조직이 가장 높게 나타났으며, 북유럽의 전통적 아란 문양, 페어아일 등의 민속적 문양과 현대적인 디자인의 혼합과 관련되어 F/W에서 자카드 조직이 가장 높은 빈도수를 나타냈다. 색상의 빈도수를 살펴보면 S/S, F/W 두 시즌 모두 YR이 가장 높은 빈도수를 나타냈다. 현대 니트 패션에 나타난 공간의 혼합의 디자인 특성에서 중국 전통복식과 일본 전통 복식과의 혼합은 서양의 패턴 양식을 기본으로 트임, 컬러 모양, 여밈, 재단 등의 부분적 응용으로 전통복의 이미지를 혼합하는 특성을 나타냈다. 북유럽과 기타 지역의 혼합은 니트의 역사가 깊은 북유럽의 전통적 니트 문양의 단순화, 현대화로 혼합된 디자인 특성을 나타내고 있었다. 현대 니트패션에 나타난 공간의 혼합은 전통적인 상징성을 배재하고 모티프의 차용에 있어 오늘날의 특성에 어울리게 현대적인 해석을 통해 표현되고 있으며, 다문화 시대의 다채로운 문화의 특성, 이질적인 요소의 혼합으로 상상력이 더해져 그 표현 가능성의 범위가 점차 확대되어 가고 있음을 확인할 수 있었으며, 현대 니트패션의 새로운 디자인의 한 방향으로 활용될 수 있기를 기대한다. Modern society is placed amid a flow of `mixture` according to cultural sharing of resulting from numerous networks. Even in knit fashion, new design is being requested according to a rise in demand. Accordingly, a strategic plan is being desperately needed. This study selected materials of 3-8 gauges in flat knit for the world`s 4 Women Collections in 2000∼2008, The purpose of this study is to offer data that designers can utilize substantially, by developing creative materials in knit fashion through the appearance frequency and analysis relevant to design element, silhouette, structure, gauge and color in the mixture of space shown in modern knit fashion Given seeing the appearance frequency in mixture of space, the bullish trend has been indicated since 2006. F/W showed the higher frequency by about twice compared to S/S. As for silhouette, design elements in the spatial mixture, the Hourglass silhouette showed the highest frequency as the characteristic of emphasizing feminine nature. In gauge, the middle gauge and high gauge were shown most highly. In structure, the basic structure was indicated most highly. Jacquard structure in F/W is analyzed to have shown the highest frequency due to being related to traditional Aran pattern in Northern Europe, folk pattern such as fair Isle, and mixture of modern design. Given examining frequency in color, YR showed the highest frequency in both seasons of S/S, F/W. In the design characteristics of spatial mixture shown in modern knit fashion, the mixture of Chinese traditional costume and Japanese traditional costume indicated the characteristic of mixing image of traditional clothes with partial application such as opening, color shape, fastening, and cutting based on a pattern form in the West. The mixture of Northern Europe and other region was showing the design characteristic, which was mixed with simplification and modernization of traditional knit pattern in Northern Europe, which has deep history in knit. The spatial mixture, which was shown in modern knit fashion, is being expressed through modern interpretation suitably for today`s characteristics in borrowing motif with excluding traditional symbolism. And, the scope in possibility of its expression could be confirmed to proceed with being expanded gradually by being added imagination owing to the characteristic in the diversified culture of multi-cultural era and to the mixture of heterogeneous elements. And is expected to be likely to be possibly utilized as data necessary for developing design in the field of knit fashion.

현재의 공정조건을 향상시키기 위한 혼합물 반응표면 방법론

임용빈 ( Yong B. Lim ) 한국품질경영학회 2010 품질경영학회지 Vol.38 No.3

Mixture experiments involve combining ingredients or components of a mixture and the response is a function of the proportions of ingredients which is independent of the total amount of a mixture. The purpose of the mixture experiments is to find the optimum blending at which responses such as the flavor and acceptability are maximized. We assume the quadratic or special cubic canonical polynomial model over the experimental region for a mixture since the current mixture is assumed to be located in the neighborhood of the optimal mixture. The cost of the mixture is proportional to the cost of the ingredients of the mixture and is the linear function of the proportions of the ingredients. In this paper, we propose mixture response surface methods to develop a mixture such that the cost is down more than ten percent as well as mean responses are as good as those from the current mixture. The proposed methods are illustrated with the well known the flare experimental data described by McLean and Anderson(1966).

An efficient methodology for constructing optimal foldover designs in terms of mixture discrepancy

A.M. Elsawah,Hong Qin 한국통계학회 2016 Journal of the Korean Statistical Society Vol.45 No.1

Mixture discrepancy criterion (Zhou et al., 2013) is more reasonable than other discrepancies criteria for measuring the uniformity of experimental designs. In this paper,wetake the mixture discrepancy criterion as the optimality measure to assess optimal foldover plans, which serve as benchmarks for constructing optimal foldover and combined designs (see Definition 2). New analytical expressions as well as new lower bounds of the mixture discrepancy criterion for both symmetric two-level and three-level combined designs under general foldover plans are obtained. We also describe necessary conditions for the existence of optimal combined designs meeting these lower bounds. An algorithm for searching the optimal foldover plans is also developed. Illustrative examples are provided, where numerical studies lend further support to our theoretical results. These results may help to provide some powerful and efficient algorithms for searching the optimal foldover and combined designs.

Optimal Mixture Design of Low-CO₂ High-Volume Slag Concrete Considering Climate Change and CO₂ Uptake

Han-Seung Lee,Seung-Min Lim,Xiao-Yong Wang 한국콘크리트학회 2019 International Journal of Concrete Structures and M Vol.13 No.6

High-volume slag (HVS) can reduce the CO₂ emissions of concrete, but increase the carbonation depth of concrete. In particular, because of the effects of climate change, carbonation will accelerate. However, the uptake of CO₂ as a result of carbonation can mitigate the harm of CO₂ emissions. This study proposes an optimal mixture design method of low-CO₂ HVS concrete considering climate change, carbonation, and CO₂ uptake. Firstly, net CO₂ emissions are calculated by subtracting the CO₂ emitted by the material from the uptake of CO₂ by carbonation. The strength and depth of carbonation are evaluated by a comprehensive model based on hydration. Secondly, a genetic algorithm (GA) is used to find the optimal mixture. The objective function of the GA is net CO₂ emissions. The constraints of the GA include the strength, carbonation, workability, and range of concrete components. Thirdly, the results show that carbonation durability is a control factor of the mixture design of low-strength HVS concrete, while strength is a control factor of the mixture design of high-strength HVS concrete. After considering climate change, the threshold of strength control increases. With the increase of strength, the net CO₂ emissions increase, while the CO₂ uptake ratio decreases.

Mixture Design 분석을 이용한 여주음료 조성 최적화 연구

김명희(Kim, Myung-Hee) 한국식공간학회 2020 식공간연구 Vol.15 No.3

본 연구의 목적은 Mixture Design의 이론적 연구와 실험의 계획, 분석 및 결과를 도출하는 과정을 제시하는 연구로 여주를 사용한 음료 조성의 최적화로 실험을 진행하였다. Mixture Design의 실험 계획은 Simplex 공간에 설계한다. 본 연구에서는 여주, 옥수수, 보리를 요인으로 10개의 샘플과 중복된 4개의 샘플로 총 14개의 샘플을 만들어 관능 실험을 하였다. 추정을 위해 회귀식을 구하고, 회귀식의 적합성을 확인하기 위해 수치적인 방법과 모형적인 방법으로 검정을 하였다. 모든 회귀식에서 유의 수준, 정규성, 신뢰성을 확인 하고, 반응표면을 분석하였다. 맛의 만족도는 여주보다는 옥수수와 보리가 많은 경우 높게 나왔다. 향의 만족도는 여주는 적고, 보리는 많을수록 좋았고, 옥수수는 영향을 미치지 않았다. 색의 만족도는 보리가 많은 경우 좋았다. 전반적인 선호도는 여주와 옥수수는 적게, 보리는 많을수록 좋았다. 즉, 맛과 향을 위해서는 여주의 비율을 낮추고, 색과 전반적인 선호도를 높이기 위해 보리의 비율을 높여야 한다. 모든 반응 값을 최대로 하는 최적의 조성비는 여주: 옥수수: 보리 = 0.2: 0.1: 0.7로 반응 값은 맛 5.71, 향 5.12, 색 5.25, 전반적인 선호도 5.55이었고, Desirability는 맛 0.85, 향 0.97, 색 0.83, 전반적인 선호도 0.91로 최적 조성비의 전체 Desirability는 0.89로 높은 수렴성을 보였다. This study was carried out for the purpose of optimizing the creation of a beverage using bitter melon, as a study presenting the process of deriving the planning, analysis, and results of the theoretical study and experiment of Mixture Design. The plan for the experiment of Mixture Design is made in a simplex space. In this study, a total of 14 samples were made from 10 with the main factors of bitter melon, corn, and barley, including 4 overlapping ones to carry out a sensory experiment. Regression equations were obtained for estimation, and the verification process was done in numerical and model ways to confirm the suitability of the regression equations. The significance level, normality, and reliability were checked in all regression equations, and the response-surface was analyzed. The optimum composition ratio to make all response values maximum was bitter melon: corn: barley = 0.2: 0.1: 0.7, in which the response values were 5.71 for taste, 5.12 for flavor, 5.25 for color, and 5.55 for overall preference, and the desirability was 0.85 for taste, 0.97 for flavor, 0.83 for color, and 0.91 for overall preference, in which the overall desirability of the optimum composition ratio was 0.89 to show a high astringency.

Experimental Designs for Computer Experiments and for Industrial Experiments with Model Unknown

Fang, Kai-Tai The Korean Statistical Society 2002 Journal of the Korean Statistical Society Vol.31 No.3

Most statistical designs, such as orthogonal designs and optimal designs, are based on a specific statistical model. It is very often that the experimenter does not completely know the underlying model between the response and the factors. In computer experiments, the underlying model is known, but too complicated. In this case we can treat the model as a black box, or model to be unknown. Both cases need a space filling design. The uniform design is one of space filling designs and seeks experimental points to be uniformly scattered on the domain. The uniform design can be used for computer experiments and also for industrial experiments when the underlying model is unknown. In this paper we shall introduce the theory and method of the uniform design and related data analysis and modelling methods. Applications of the uniform design to industry and other areas are discussed.

The Effect of Aggregate Gradation Limits Consideration on Performance Properties and Mixture Design Parameters of Hot Mix Asphalt

Ebrahim Sangsefidi,Hasan Ziari,Maryam Sangsefidi 대한토목학회 2016 KSCE JOURNAL OF CIVIL ENGINEERING Vol.20 No.1

The main aim of mixture design is to select the best configuration of material in order to achieve mixture fabricating purposes. Aggregate make up a high proportion of volume and mass of mixtures, hence it considered as an important constituent of asphalt concrete. It has been hypothesised that the gradation is an important feature of the aggregate in adoption of optimum mixture. Three gradations are used to manufacture Hot Mix Asphalt (HMA) within special specification band of local code. Rutting resistance was evaluated using the Flow Number (FN) parameter and in order to determine the moisture sensitivity mechanism, a mechanical and visual inspection tests are carried out. The main conclusion of this study is that contrary to customary belief, middle gradation of select band does not produce the best results. Eventually some proposed factors, such as determining “sensitive mixtures” to binder content variation, have been determined for mixture design process.

혼합실험계획법에 의한 율무와 밀가루의 압출성형 최적 배합 조건 설정

조석철(Seok-Cheol Cho),강병선(Byung-Sun Kang) 한국식품과학회 2013 한국식품과학회지 Vol.45 No.4

혼합디자인에 의해 설정된 조건하에서 압출성형한 율무와 밀가루의 압출성형물은 율무 첨가에 대해 여러 반응 요인들이 압출성형물의 특성에 영향을 끼치는 것으로 나타났다. 실험조건은 율무 함량 5-75%, 밀가루 25-95%로 결정하였으며, 수분함량은 20.55%로 고정하여 modified distance based mixture design으로 실험설계 및 분석하였다. Bending 파손강도, WAI, a값 등은 유의성이 없는 것으로 나타났으나, 팽화물의 직경, WSI, L값, b값은 율무와 밀가루의 혼합에 의해 유의성이 존재하는 것으로 나타났다. 팽화물의 직경, L값, b값은 선형 모델로 분석할 수 있었으나 WSI는 quadratic 모델로만 설정이 가능한 것으로 나타났다. 율무의 함량이 많아질수록 외관적으로 팽창되어지는 정도가 적어졌으며, 색상도 어두워지는 것으로 나타났다. 율무의 함량이 증가할수록 L값은 77.84에서 72.73, a값은 1.37에서 1.77로, b값은 19.42에서 17.64로 이동되었다. WSI는 율무와 밀가루가 40%:60% 로 혼합되어 압출성형되었을 때 가장 낮게 나타났으며, WAI는 율무와 밀가루 혼합 비율에 대해서는 유의성이 없는 것으로 나타났다. 혼합디자인 계획법은 시리얼류 제품 생산에 적합한 조직형성과 반응량에 유의한 영향을 미치는 요인 등에 대해 적절한 혼합 비율과 가공 조건 등을 제시할 수 있음을 알 수 있었다. Modified distance based mixture design에 의해, 일반 시중 제품과 유사한 조직감을 나타낼 수 있는 율무와 밀가루, 물의 적정 배합비율은 60.12:19.42:20.46으로 나타났다. The aim of this study was to identify the optimal ingredient-mixing ratio of Job’s-tear and wheat flour subjected to extrusion. A modified distance-based mixture design analysis was chosen for the experimental design. The results showed that the bending failure force, the a-value, and the water absorbtion index (WAI) value had no correlation with the mixture ratio of Job’s-tear and wheat flour. However, the diameter of the extrudates, the L- and b-values, and the water solubility index (WSI) value were all found to be correlated to the mixture ratio. While the first three values were determined using a linear model, the WSI value was determined using a quadratic model. The diameter and color had an inverse correlation to the mixture ratio: the higher the ratio of Job’s-tear to wheat flour, the lower the diameter and darker the color. The L- and b-values were found to change in accordance with the mixture ratio of Job’s-tear to wheat flour. The lowest WSI value was obtained at a 40:60 ratio of Job’s-tear to wheat.

한국형 기포 아스팔트 혼합물의 품질 평가에 관한 기초연구

강성일,이강훈,김용주,이재준 한국도로학회 2020 한국도로학회논문집 Vol.22 No.6

PURPOSES : This paper presents a quality evaluation of Korean foamed asphalt, which uses the maximum expansion ratio and half-life method. The maximum expansion ratio and half-life method are used to determine the optimum water content to produce a foamed asphalt mixture. The foamed asphalt mixture according to determine an optimum water content with this method; the mixture quality was compared with hot mix asphalt mixture. METHODS : For the foamed asphalt mixed design, the water content was determined in addition to the Marshall mixing design method. The water content was determined using the ratio of the maximum to minimum volume and the time for the volume to decrease to half of the maximum volume. We conducted stability, indirect tensile strength, tensile strength ratio, dynamic immersion, and absorption rate tests to compare the foamed and hot mixed asphalt mixtures. RESULTS : The foam asphalt mixture exhibited less performance reduction due to temperature change than the hot mixed asphalt mixture. Most of the two mixture types exhibited similar performance. In addition, both mixtures should use an anti-stripping agent to improve water resistance. CONCLUSIONS : As a result of the laboratory test, the foamed asphalt mixture was able to ensure a similar performance to the hot-mixed asphalt mixture.