• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.745-755
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• 2007

The concept of slope rotatability introduced by Hader and Park(1978) is available when we are interested in the difference of the responses. Since there can be constraints on the factor levels in mixture experiments, there arises a need for adaptation of the concept of slope rotatability and the measure to assess it. In this article, measures of slope rotatability in mixture experiments are proposed to quantify the amount of slope rotatability for a given design. Measures for a restricted region design as well as for an unrestricted region design are presented. Then, the designs having different optimalities are compared with respect to these measures by some examples.

• Journal of the Korean Statistical Society
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• v.17 no.2
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• pp.121-133
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• 1988

In this paper a class of mixture designs for estimating the slope of second order Scheffe polynomial response surfaces for mixture experiments with q components is presented. The variance of the estimated directional slope at a point is a function of the direction of the slope and the design. If the variance is averaged over all possible directions in the (q-1)-dimensional simplex, the averaged variance is only a function of the point and the design. By choice of design, it is possible to make this variance constant for all points equidistant from the centroid point. This property is called "slope-rotatability over al directions in the simplex", and the necessary and sufficient conditions for mixture design to have this property are given and proved. The class of designs with this property is compared with other mixture designs and discussed.discussed.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.7
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• pp.28-34
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• 2006

In general engineering problems, the purpose of an optimization is to get optimal design variables. It is the same problem to fix the total amount of the design variables and to judge the optimal mixing proportions of the design variables. That is to say, we can recompose the engineering problems in the concepts of the mixture amount experiments. The goal of mixture amount method is to get the response surfaces of varying both the mixing proportion of component and the total amount of the mixture. The solution of the aircraft fuselage optimization problem is obtained by the mixture amount method and genetic algorithm. In this study, it is shown that the mixture amount method can be utilized for the aircraft structural optimization problem. Also, this method in this study can be applied for the optimization problems over 12 design variables which is impossible for D-optimal design.

• Korean Chemical Engineering Research
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• v.51 no.6
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• pp.677-684
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• 2013

A mixed refrigerant cycle (MRC) has been widely used in liquefaction of natural gas because it is simple and easily operable with reasonable equipment costs. One of the important techniques in MRC is selection of a refrigerant mixture and decision of its optimum mixing ratio. In this work, it is examined whether mixture components (refrigerants) and their mixing ratio influence performance of general MRC processes. In doing this, mixture design and response surface method, which are well-known statistical techniques, are used to find optimal mixture refrigerants and their optimal mixing ratio that minimize total energy consumption of the entire liquefaction process. A MRC process using several refrigerants and various mixing ratios is simulated by Aspen HYSYS and mixture design and response surface method are implemented using Minitab. According to the results, methane ($C_1$), ethane ($C_2$), propane ($C_3$) and nitrogen ($N_2$) are selected as best mixture refrigerants and the determined mixture ratio (mole ration) can reduce total energy consumption by up to 50%.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.6A
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• pp.561-572
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• 2010

This paper is a study about application of recently proposed Performance Based Mixture Design (PBMD) for design of high strength concrete (HSC) to obtain HSC mix proportion that satisfies required performances. The PBMD method which uses Satisfaction curve based on a Bayesian method is a performance oriented concrete mix proportion design procedure easily applicable to any condition and environment for a possible replacement to the current prescriptive design standards. Based on extensive experimental results obtained for various materials and performance parameters of HSC, the application feasibility of the developed PBMD procedure for HSC has been verified. Also, the proposed PBMD procedure has been used to perform application examples to obtain desired target performances of HSC with optimum concrete mixture proportions using locally available materials, local environmental conditions, and available concrete production technologies. The validity and precision of HSC mix proportion design obtained using the PBMD method is verified with the experimental and ACI presented results to check the feasibility for actual design usage.

• Korean Journal of Food Science and Technology
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• v.45 no.4
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• pp.473-477
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• 2013

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.

• IE interfaces
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• v.18 no.4
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• pp.402-411
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• 2005

Secondary batteries with high performance are essential in widespread use of modern portable devices such as cellular phones and laptop computers. High energy density, long cycle life, and safety are some of important requirements for secondary battery. To achieve such characteristics, a mixing proportion of electrolyte solution ingredients in the battery should be carefully chosen. In this paper, using statistical design of mixture experiments (DOME), we attempt to find an optimum condition of designing the secondary battery. DOME has a distinct feature in that the experimental region is represented by simplex, rather than hypercube, because the sum of blend proportions should be unity. Several designs based upon this point have been proposed for mixture experiments. Among them, an extreme vertices design is employed in this paper because there are a couple of blend constraints to be considered. In order to investigate how the mixing proportion interacts with other manufacturing factors, a fractional factorial design is also included across the extreme vertices design. As a result, we find that the blend proportion of solution ingredients has a significant effect on battery performances. By simultaneously optimizing two battery capacities, this paper proposes an optimum blend proportion according to process factor settings.

• Applied Chemistry for Engineering
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• v.32 no.5
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• pp.574-580
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• 2021

The main goal of this study was to find an optimal surfactant mixture composition for the development of the best performing cleansing products. Three different surfactants including sodium cocoyl alaninate (SCoA), cocamidopropyl betaine (CPB), and decyl glucoside (DG) were selected, which showed excellent properties in detergency, foaming height, and contamination rate through preliminary experiments. The experiments by simplex centroid design matrix for surfactant mixtures were performed, and the regression analysis was conducted with the experimental data. Surface response model equations, which is statistically significant (p < 0.05), were obtained. The optimal composition of the surfactant mixture was also determined as SCoA (0.22), CPB (0.78), and DG(0.00) from simultaneous optimization of three response variables.

• Advances in concrete construction
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• v.11 no.2
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• pp.99-109
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• 2021

Slag blended concrete is widely used as a mineral admixture in the modern concrete industry. This study shows an optimization process that determines the optimal mixture of air-entrained slag blended concrete considering carbonation durability, frost durability, CO2 emission, and materials cost. First, the aim of optimization is set as total cost, which equals material cost plus CO2 emission cost. The constraints of optimization consist of strength, workability, carbonation durability with climate change, frost durability, range of components and component ratio, and absolute volume. A genetic algorithm is used to determine optimal mixtures considering aim function and various constraints. Second, mixture design examples are shown considering four different cases, namely, mixtures without considering carbonation (Case 1), mixtures considering carbonation (Case 2), mixtures considering carbonation coupled with climate change (Case 3), and mixtures of high strength concrete (Case 4). The results show that the carbonization is the controlling factor of the mixture design of the concrete with ordinary strength (the designed strength is 30MPa). To meet the challenge of climate change, stronger concrete must be used. For high-strength slag blended concrete (design strength is 55MPa), strength is the control factor of mixture design.

• Journal of the Korea institute for structural maintenance and inspection
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• v.24 no.3
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• pp.26-38
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• 2020

Mixture design of self-compacting concrete is a typical multi-criteria decision making problem and conventional mixture designs are based on the low level engineering method like trials and errors through iteration method to satisfy the various requirements. This study concerns with performing the straightforward multiobjective design optimization of economic SCC mixture considering relative importances of the various requirements and cost-effectives of SCC. Total five requirements of 28day compressive strength, filling ability, segregation stability, material cost and mass were taken into consideration to prepare the objective function to be formulated in form of the weighted-multiobjective mixture design optimization problem. Economic SCC mixture computational design can be given in a rational way which considering material costs and the relative importances of the requiremets and from the result of this study it is expected that the development of SCC mixtue computational design and the consequent univeral concrete material design optimization methodology can be advanced.