• 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.

• 대한산업공학회지
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• 제29권4호
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• pp.334-344
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• 2003

A mixture experiment is a special type of response surface experiment in which factors are the ingredients or components of a mixture, and the response is a function of the proportions of each ingredient. Evolutionary operation is useful to improve on-line full-scale manufacturing process by systematically changing the levels of the process variables without jeopardizing the product. This paper presents an evolutionary operation procedure with mixture variables for large-scale mixture production process which can be beneficial to practitioners who should improve on-line mixture quality while maintaining the production amount of the mixture product.

• 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.

• Communications for Statistical Applications and Methods
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• 제21권2호
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• pp.161-168
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• 2014

In mixture experiments with process variables, we consider the case that some of process variables are either uncontrollable or hard to control, which are called noise variables. Given the such mixture experimental data with process variables, first we study how to search for candidate models. Good candidate models are screened by the sequential variables selection method and checking the residual plots for the validity of the model assumption. Two methods, which use numerical optimization methods proposed by Derringer and Suich (1980) and minimization of the weighted expected loss, are proposed to find a cost-effective robust optimal condition in which the performance of the mean as well as the variance of the response for each of the candidate models is well-behaved under the cost restriction of the mixture. The proposed methods are illustrated with the well known fish patties texture example described by Cornell (2002).

• 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.

• 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.

• 산업공학
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• 제19권2호
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• pp.117-123
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• 2006

Many products, such as gasoline, polymer plastics, alloys, and ceramics are manufactured by mixing two or more ingredients or components. When we are to develop new mixture products, we must deal with a long list of potentially important component variables. This paper introduces some mixture screening designs, analysis tools for screening important variables, and a guideline for applying these analysis tools. The results of this paper will be helpful to engineers who work in the research and development sector of mixture product industries.

• 한국생활과학회지
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• 제16권5호
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• pp.899-908
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• 2007

Clusters of parental and peer variables associated with adolescent risk behaviors are explored using the mixture model. Questionnaires were completed by 917 high school freshmen in the Daegu Kyungpook area and included measures of risk behaviors, parental attachment, autonomy, parental monitoring, and peers' risk behaviors and desirable behaviors. As a result of the mixture model, five clusters were produced. Two of the subgroups were consistent with the literature of showing linear relationships among adolescent risk behaviors and above variables; a group of higher parental attachment and autonomy as well as parental monitoring, lower friends' risk behaviors, and lower adolescent risk behaviors, and a group of lower parental attachment and autonomy as well as parental monitoring, higher friends' risk behaviors, and higher adolescent risk behaviors. Two other subgroups were similar in parental attachment and autonomy, but differed in parental monitoring, friends' risk behaviors, and adolescent risk behaviors. The last subgroup was characterized by scoring the lowest parental attachment and autonomy, parental monitoring, friends' risk behaviors, and lower adolescent risk behaviors compared to other subgroups. The utility of the mixture model in research on adolescent risk behaviors is discussed in the conclusion.

• 한국항공우주학회지
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• 제34권7호
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• pp.28-34
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• 2006

일반적인 엔지니어링 문제에 대한 최적화는 최적의 설계변수를 구하는 문제이다. 이는 설계변수의 총합을 얼마로 하며, 총합을 설계변수들이 어떠한 비율로 차지하는 것이 최적인가를 판단하는 문제가 된다. 즉, 혼합물 총량법의 개념에 맞추어 문제를 재구성할 수 있다. 혼합물 총량법의 목적은 각 성분의 혼합비율과 혼합물의 총량을 동시에 고려하여 반응면을 구하는 것이다. 항공기 동체 최적화 문제에 혼합물 총량법과 유전자 알고리즘을 적용하였다. 이번 연구를 통해서 항공기 구조물 최적화 문제에 대한 혼합물 총량법의 유용성을 확인하였다. 또한 본 연구에서 제시된 혼합물 총량법은 D-optimal에서는 불가능한 설계변수 12개 이상의 최적화 문제에도 적용이 가능하다.