• Communications for Statistical Applications and Methods
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• 제6권1호
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• pp.1-10
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• 1999

When the component proportions in mixture experiments are restricted by lower and upper bounds multicollinearity appears all too frequently. The ridge regression can be used to stabilize the coefficient estimates in the fitted model. I propose a graphical method for evaluating the mixture component effects of ridge regression estimator with respect to the prediction variance and the prediction bias.

• 품질경영학회지
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• 제13권2호
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• pp.66-72
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• 1985

The objective of mixture experiments with process variables is to find experimental blends and conditions that produce the product of highest quality. In this paper, designs for mixture experiments with process variables are presented, where the emphasis is on using only a fraction of the total number of possible design points and the fitting of reduced models for measuring the effects of the mixture components and process variables.

• 품질경영학회지
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• 제34권3호
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• pp.62-65
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• 2006

We can use the ridge regression as a means for stabilizing the coefficient estimators in the fitted model when performing experiments in highly constrained regions causes collinearity problems in mixture experiments. But there is no theory available on which to base statistical inference of ridge estimators. The bootstrap could be used to seek the confidence intervals of ridge estimators.

• 품질경영학회지
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• 제38권3호
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• pp.413-424
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• 2010

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).

• Journal of the Korean Data and Information Science Society
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• 제28권5호
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• pp.1021-1026
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• 2017

화학, 제약, 식품 등 여러 분야에서 활용되는 혼합물 실험은 반응변수가 설명변수들의 절대량이 아닌 상대적인 혼합비율에 의해 영향을 받고 구조상 공선성이 존재하게 되는 성질이 있으며 양적인 반응변수들에 대한 실험이 많아 대부분 정규분포를 가정하고 선형모형을 적용하여 분석하고 있다. 이 논문에서는 반응변수가 계수형인 혼합물 실험의 사례로 Chen 등(1996)에 소개된 종양 억제 효과에 대한 실험에 나타난 지방, 탄수화물, 섬유질과 같은 식이요법 관련 혼합물 성분들과 종양 발현 여부인 계수형 방응변수를 갖는 자료를 대상으로 셰페의 2차 다항모형과 성분들간의 비선형적 관계를 보완하기 위해 대안으로 제시된 베커의 수정 모형들, 그리고 공선성을 완화하기 위해 제시된 Akay와 Tez(2011)의 성분비 변환 모형을 설명변수들의 선형결합으로 활용하여 설정한 로지스틱회귀모형들을 분류 정확도 기준을 적용하여 비교하고 결과를 설명하였다.

• 품질경영학회지
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• 제39권3호
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• pp.400-411
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• 2011

Process variables are factors in an experiment that are not mixture components but could affect the blending properties of the mixture ingredients. For example, the effectiveness of an etching solution which is measured as an etch rate is not only a function of the proportions of the three acids that are combined to form the mixture, but also depends on the temperature of the solution and the agitation rate. Efficient designs for the mixture components-process variables experiments depend on the mixture components-process variables model which is called a combined model. We often use the product model between the canonical polynomial model for the mixture and process variables model as a combined model. In this paper we propose three starting models for the mixture components-process variables experiments. One of the starting model we are considering is the model which includes product terms up to cubic order interactions between mixture effects and the linear & pure quadratic effect of the process variables from the product model. In this paper, we propose a method for finding robust designs and practical designs with respect to D-, G-, and I-optimality for the various starting combined models and then, we find practically efficient and robust designs for estimating the regression coefficients for those models. We find the prediction capability of those recommended designs in the case of three components and three process variables to be good by checking FDS(Fraction of Design Space) plots.

• Journal of the Korean Statistical Society
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• 제28권3호
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• pp.325-336
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• 1999

Collinearity among independent variables can have severe effects on the precision of response estimation for some region of interest in the experiments with mixture. A method of finding optimal linear restriction on regression parameter in linear model for mixture experiments in the sense of minimizing integrated mean squared error is studied. We use the formulation of optimal restrictions on regression parameters for estimating responses proposed by Park(1981) by transforming mixture components to mathematically independent variables.

• Communications for Statistical Applications and Methods
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• 제3권1호
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• pp.51-59
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• 1996

A measure that quantifies the amount of slope retatability for the second degree Scheffe polynomial model for mixture experiments is proposed and used to compare the several mixture designs which met the symmetric momemts conditions in this article.

• 품질경영학회지
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• 제24권4호
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• pp.156-167
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• 1996

D-optimality is used often in design augmentation of mixture experiments. Although such alphabetic criteria provide a valuable foundation for generating designs, they often fail to convey the true nature of the design's support of the fitted model in terms of prediction variance over a region of interest. Thus, a graphical method is proposed to evaluate augmented designs in mixture experiments. This method can be used to evaluate the effect of missing observation and outlier in mixture experiments.

• 한국지하수토양환경학회지:지하수토양환경
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• 제19권2호
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• pp.1-6
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• 2014

The objective of this study was to find the effect of the mixture of the nonionic surfactant and bioactive agent that solubilizes trichlorobenzene (TCB) present as a contaminant for surfactant-enhanced soil flushing (SESF). Three different nonionic surfactants and two different bioactive agents were obtained from four companies. Separate funnel experiments and shaker table agitation / centrifugation experiments were used for the test. Based on the separate funnel experimental results, three suitable mixture agents (APG + OSE, Brij 35 + MOSE, T-Maz 60 + MOSE) were selected. In the shaker table agitation / centrifugation experiments, these three different mixture agents were reduced to one (T-Maz 60 +MOSE). The maximum removal (95%) of TCB was obtained using a mixture of the nonionic surfactant and bioactive agent. Therefore, the used test methods and results can be used for SESF.