• 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.

• 응용통계연구
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• 제20권2호
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• pp.267-280
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• 2007

혼합물 성분들의 비율의 상한과 하한에 대한제한조건이 부과된 제한된 혼합물 실험 공간 R에서의 혼합물 실험을 위한 최적 설계를 찾는 데에 D-, G-, V- 최적기준 등과 같은 다양한 최적 설계 기준이 사용된다. 각각의 실험 설계는 선택된 최적 기준에 대해서는 최적이지만, 제한된 혼합물 실험 공간에서의 예측력에 대해서는 만족스럽지 못하다는 것은 잘 알려진 사실이다. (Vining 등, 1993; Khuri 등, 1999). 우리의 관심사는 2차 혼합물 반응표면모형을 가정한 경우에 제한된 혼합물 공간에서의 효율적인 실험 설계를 찾는 것이다. 이 논문에서는 꼭지점, 선중심점, 면중심점, 중앙점과 내부점으로 구성된 확장된 후보 실험점 그룹을 구성한 다음에, D-최적기준, G-최적기준, V-최적기준과 실험점들 간의 거리에 근거한 U-최적기준에 강건한 실험 설계를 제안한다. Khuri 등(1999)에서 분석된 비료 혼합물 실험과Vining과 Cornell(1993)이 분석한 조명탄 혼합물 실험의 사례에서 강건한 실험설계들과 두 논문에서 추천된 실험 설계들에 대한 예측치의 표준화된 분산의 분위수의 그림(SVPQP)을 비교한 결과 강건한 설계가 상대적으로 우월함이 판명되었다.

• 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).