Abstract
Objectives: To obtain a reliable approximation for the K-model in mixture experiments and design. Methods/Statistical Analysis: Here, the problem of mixture experiments, according to qualitative factors and finding A-optimal and D-optimal design for K-model is taking into account. Also, an improvement of Lee method is used to aim of this goal. In addition, a new procedure of Lee method for approximation of K-model is proposed. Moreover, illustrated examples are simulated in R software. Findings: It is demonstrated that the qualitative factor has a directly relation with A-optimal and D-optimal design. Such that, firstly, if the qualitative factor, on the region of factors, be a uniform design, then for A-optimal design, the trace of the inverse of the information matrix should be minimized. Secondly, for D-optimal design, maximization of the determination of information matrix is necessary. Moreover, in a product function, the dispersion function can be detached into 3 sections corresponding to the 2 marginal design. Application/Improvements: This research is using of an amount of convenient mixture design in engineering and manufacturing can be detached into 3 sections corresponding to the 2 marginal design. Keywords: Information Matrix, K-model, Mixture Experiment, Optimality, Qualitative Factors
Highlights
Mixture experiments have found a special importance in science and application
It is demonstrated that the qualitative factor has a directly relation with A-optimal and D-optimal design
At the first step, on the region of factors, if the qualitative factors have a uniform design the trace of the inverse of information matrix is minimize for A-optimal design
Summary
Mixture experiments have found a special importance in science and application. Almost all of the cakes, are combined by alot of materials such as, flour, water, eggs, oil and etc The amount of this material is very important to set the best product sometime due to increase or decrease of the materials. The model is presented as follows: E[ y( j,τ )]. Where, it shows the j-th level of a r-level qualitative factor and and f1(x) is the part of the regression function having disruption with the qualitative property, and.
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