• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.267-280
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• 2007

Various single-valued design optimality criteria such as D-, G-, and V-optimality are used often in constructing optimal experimental designs for mixture experiments in a constrained region R where lower and upper bound constraints are imposed on the ingredients proportions. Even though they are optimal in the strict sense of particular optimality criterion used, it is known that their performance is unsatisfactory with respect to the prediction capability over a constrained region. (Vining et at., 1993; Khuri et at., 1999) We assume the quadratic polynomial model as the mixture response surface model and are interested in finding efficient designs in the constrained design space for a mixture. In this paper, we make an expanded list of candidate design points by adding interior points to the extreme vertices, edge midpoints, constrained face centroids and the overall centroid. Then, we want to propose a robust design with respect to D-optimality, G-optimality, V-optimality and distance-based U-optimality. Comparing scaled prediction variance quantile plots (SPVQP) of robust designs with that of recommended designs in Khuri et al. (1999) and Vining et al. (1993) in the well-known examples of a four-component fertilizer experiment as well as McLean and Anderson's Railroad Flare Experiment, robust designs turned out to be superior to those recommended designs.

• Journal of Industrial Technology
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• v.22 no.A
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• pp.83-87
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• 2002

Many industrial products such as paints, ink and adhesives are composed of the ingredients of a mixture. In mixture experiments, the characteristics of quality(response) depends only on the proportions of the ingredients and does not depend on the total amount of the mixture. This article discusses the constrained mixture experimental design, the data analysis, and the optimum formulation of ingredients based on the two quality characteristics - taste and flavor. It IS shown that efficient designs can be constructed from D-optimal criterion. Special cubic models were selected as the final mixture response surfaces for both reponses. The desirability function was used for the optimization of the two responses.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2001.11a
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• pp.117-126
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• 2001

Tribological properties of high temperature fade were investigated by changing relative amounts of ingredients in the brake friction material. Based on a simple experimental formulation containing 10 ingredients, friction materials were tested using a pad-on-disk type friction tester. Twenty-five friction material specimens with different relative amounts of the ingredients were manufactured according to the constrained mixture design .The difference ($\Delta$${\mu}$=${\mu}$$\sub$max/. -${\mu}$$\sub$min/. ) of friction coefficients was measured to represent the high temperature fade. Results from elevated temperature tests showed that five ingredients including cashew, graphite, Sb$_2$S$_3$, ZrSiO$_4$, and Cu fibers played important roles on $\Delta$${\mu}$. In order to find relative importance on fade phenomena among these ingredients, ANOVA(analysis of variance) was performed in this investigation. Thirty-two friction material specimens by changing ${\pm}$50vol.％ of these five ingredients were tested to examine the relative importance. Results showed that cashew, graphite '||'&'||' Sb$_2$S$_3$, and cashew '||'&'||' graphite aggravated the fade behavior and Cu fibers improved on fade resistance.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.33 no.1
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• pp.1-9
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• 2010

Quality design methodologies have received constituent attention from a number of researchers and practitioners for more than twenty years. Specially, the quality design for drug products must be carefully considered because of the hazards involved in the pharmaceutical industry. Conventional pharmaceutical formulation design problems with mixture experiments have been typically studied under the assumption of an unconstrained experimental region with a single quality characteristic. However, real-world pharmaceutical industrial situations have many physical limitations. We are often faced with multiple quality characteristics with constrained experimental regions. ln order to address these issues, the main objective of this paper is to propose a robust desirability function (RDF) model using a desirability function (DF) and mean square error (MSE) to simultaneously consider a number of multiple quality characteristics. This paper then present L-pseudocomponents and U-pseudocomponents to handle physical constraints. Finally, a numerical example shows that the proposed RDF can efficiently be applied to a pharmaceutical process design.

• KSTLE International Journal
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• v.10 no.1_2
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• pp.43-47
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• 2009

Influences of carbonaceous ingredient as a solid lubricant in automotive friction materials on friction properties were studied. Three types of carbonaceous ingredients such as natural graphite, artificial graphite, and cokes were mixed using a constrained mixture design. A 1/5 scale brake dynamometer was used to obtain tribological properties. Results showed that cokes substantially increased the friction coefficient, and natural graphite effectively reduced stick-slip phenomena. This significant difference was attributed to the formation of the friction film on the brake pad which was shown to be strongly dependent on the graphite types. The different crystal structures of the carbonaceous solid lubricants played a significant role in the formation of friction film at the interface.

• Tribology and Lubricants
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• v.25 no.1
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• pp.31-37
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• 2009

상용화 마찰재를 사용하여 고온 열화에 대한 원료들의 영향을 연구하였다. 제한된 영역에서의 실험계획법에 의해 25개의 마찰재가 제작되었으며, 축소 마찰 시험기로 마찰, 마모특성을 조사하였다. 아라미드 섬유, 흑연, 구리섬유는 열화에 대한 저항성을 향상시켰으며, 반면 삼황화 안티몬, 지르콘은 열화현상을 가속시키는 것으로 나타났다. 이러한 결과는 각 원료들이 계면에 미치는 영향이 각기 다르기 때문으로 사료된다. 아라미드 섬유, 흑연, 구리섬유등은 계면을 안정화 시켰으며, 삼황화 안티몬, 지르콘등은 고온에서 불안정한 계면을 형성시키는 것으로 나타났다.

• Tribology and Lubricants
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• v.23 no.6
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• pp.278-282
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• 2007

Friction characteristics of a low-steel friction material were examined to investigate creep groan phenomena. The amount of three ingredients (steel fiber, $ZrSiO_4$, cashew) were changed to produce test specimens using a constrained mixture design. Tribological properties of the friction material specimens were obtained by using a 1/5 scale dynamometer. Results showed that the amount of three different ingredients strongly affected the level of friction coefficient and the difference between the static friction coefficient and the kinetic friction coefficient $({\Delta}{\mu}).\;ZrSiO_4$ and steel fiber tended to increase the average friction coefficient and aggravated the stick-slip phenomena suggesting high creep groan propensity. On the other hand, cashew tended to decrease average friction coefficient and ${\Delta}{\mu}$.

• Journal of the Korea Concrete Institute
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• v.20 no.5
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• pp.627-634
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• 2008

This paper presents an optimum mixture design method for proportioning a concrete. In the proposed method, the search space is constrained as the domain defined by the minimal convex region of a database, instead of the available range of each component and the ratio composed of several components. The model for defining the search space which is expressed by the effective region is proposed. The effective region model evaluates whether a mix-proportion is effective on processing for optimization, yielding highly reliable results. Three concepts are adopted to realize the proposed methodology: A genetic algorithm for the optimization; an artificial neural network for predicting material properties; and a convex hull for evaluating the effective region. And then, it was applied to an optimization problem wherein the minimum cost should be obtained under a given strength requirement. Experimental test results show that the mix-proportion obtained from the proposed methodology using convex hulls is found to be more accurate and feasible than that obtained from a general optimum technique that does not consider this aspect.