• 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.

• 품질경영학회지
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• 제40권3호
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• pp.347-358
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• 2012

Purpose: Given the mixture components - process variables experimental data, we propose the strategy to find the proper combined model. Methods: 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. Results: First we choose the reasonable starting models among the class of admissible product models and practical combined models suggested by Lim(2011) based on the model selection criteria and then, search for candidate models which are subset models of the starting model by the sequential variables selection method or all possible regressions procedure. Conclusion: Good candidate models are screened by the evaluation of model selection criteria and checking the residual plots for the validity of the model assumption. The strategy to find the proper combined model is illustrated with examples in this paper.

• 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.

• 응용통계연구
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• 제26권1호
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• pp.201-208
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• 2013

이 논문에서는 공정변수를 갖는 혼합물 실험에 대하여 적절한 모형을 선택하는 한 방법으로 혼합물 성분의 공선성에 로버스트한 성질을 갖는 마할라노비스-다구찌 시스템을 활용한 전략을 소개한다. 여러 문헌에서 언급된 3개의 혼합물 성분과 2개의 공정변수를 갖는 제빵 실험 사례를 대상으로 이 전략적 방법을 적용하여 적절한 모형을 선택하였다.

• 한국환경과학회지
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• 제25권5호
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• pp.737-744
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• 2016

For electrolysis process using an insoluble electrode, electrochemical performance was greatly affected by the manufacturing method and procedure, such as the firing temperature, pre-treatment, type of precursor solution, coating method, electrode material, etc. Components of the electrode therein is one of the most important factors in electrochemical reaction. To achieve such characteristics, a appropriate ratio of the electrode material should be carefully chosen. The aim of this research was to apply experimental design method in the optimization of electrode component for the maximum generation of oxidants in electrochemical oxidation process. Mixture design, especially expanded simplex lattice design, in DOME (design of mixture experiments) with Design Expert - commercial software - was used to analyze the data. Analysis of variance (ANOVA) showed a high coefficient of determination ($R^2$) value of 0.9470, thus ensuring a satisfactory adjustment of the $3^{rd}$ order special cubic regression model with the experimental data. The application of response surface methodology (RSM) yielded the following regression equation, which is an empirical relationship between the TRO generation concentration and independent variables(mol ratio of 3 electrode components) in a real unit: TRO generation concentration $(mg/L)=TRO\;conc.=98.25{\times}[Ir]+49.71{\times}[Sn]+95.29{\times}[Sb]-16.91{\times}[Ir]{\times}[Sn]-29.47{\times}[Ir]{\times}[Sb]-22.65{\times}[Sn]{\times}[Sb]+703.19{\times}[Ir]{\times}[Sn]{\times}[Sb]$. The optimized formulation of the 3 component electrode for an high TRO (total residual oxidants) generation was acquired at mol ratio of Ir 0.406, Sn 0.210, Sb 0.384 (desirability d value, 1).