공정변수를 갖는 혼합물 실험 자료의 분석
Analysis of mixture experimental data with process variables
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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 seletion 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.
Abstract
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 seletion 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.
참고문헌 (7)
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- 임용빈, "실용적인 혼합물 성분 공정변수 실험설계", 품질경영학회지, 39(3), pp.400~411 (2011), 한국품질경영학회
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- Cornell, J. A., "Fractional design plans for process variables in mixture ex periments", Journal of Quality Technology, 16, pp.20~38 (1984)
- Kowalski S., "A new model and class of designs for mixture experiments with process variables", Commun. Statist. -Theory Meth, 29, pp.2255~2280 (2000)
- Myers, R. H., "Response Surface Methodology, 3rd ed." (2009), Wiley
- Nas, T., "A comparison of methods for analyzing data from a three component mixture experiment in the presence of variation created by two process variables", Chemometrics and Intelligent Laboratory Systems, 41, pp.221~235 (1998)