Practical designs for mixture component-process experiments

Lim, Yong-B.

Journal of Korean Society for Quality Management > Volume 39(3); 2011 > Article

Journal of Korean Society for Quality Management 2011;39(3): 400-.

실용적인 혼합물 성분 공정변수 실험설계

임용빈

이화여자대학교 자연과학대학 통계학과

Practical designs for mixture component-process experiments

Yong-B. Lim

Department of Statistics, Ewha Womans University

ABSTRACT

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.

Key Words: Mixture Components-Process Variables Experiments;Combined Model;Robust Mixture Components-Process Variables Designs;Practical Mixture Components-Process Variables Designs;FDS(Fraction of Design Space) Plots;