• Journal of Korean Society for Quality Management
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• v.39 no.3
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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 Korean Society for Quality Management
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• v.40 no.3
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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.

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.4
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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.

• Journal of Korean Society for Quality Management
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• v.13 no.2
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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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• v.21 no.2
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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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• v.28 no.3
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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.

• The Korean Journal of Applied Statistics
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• v.26 no.1
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• pp.201-208
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• 2013

In this paper, we consider the mixture components-process variables model and propose a model selection strategy using MTS. This strategy is illustrated using an example that involves three mixture components and two process variables in a bread making experiment that was studied in several literatures.

• IE interfaces
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• v.19 no.2
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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.

• Korean Journal of Human Ecology
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• v.16 no.5
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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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.7
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• pp.28-34
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• 2006

In general engineering problems, the purpose of an optimization is to get optimal design variables. It is the same problem to fix the total amount of the design variables and to judge the optimal mixing proportions of the design variables. That is to say, we can recompose the engineering problems in the concepts of the mixture amount experiments. The goal of mixture amount method is to get the response surfaces of varying both the mixing proportion of component and the total amount of the mixture. The solution of the aircraft fuselage optimization problem is obtained by the mixture amount method and genetic algorithm. In this study, it is shown that the mixture amount method can be utilized for the aircraft structural optimization problem. Also, this method in this study can be applied for the optimization problems over 12 design variables which is impossible for D-optimal design.