Indian Journal of Science and Technology
Year: 2019, Volume: 12, Issue: 8, Pages: 1-9
Zahra Rasooli Berardehi1 and Chongqi Zhang2*
1School of Mathematics and information Sciences, Guangzhou University, Guangzhou, China;
2School of Statistics and Economics, Guangzhou University , Guangzhou, China; [email protected]
*Author for correspondence
School of Statistics and Economics, Guangzhou University , Guangzhou, China.
Email: [email protected]
Objectives: To achieve an optimal approximation for two-degree Becker model in mixture design. Methods/Statistical Analysis: The problem of mixture design case, based on qualitative factors and finding A-optimal and D-optimal design for two-degree Becker model is investigated. With the aim of this issue, a generalization of Lee method is utilized. We proposed a new procedure of Lee method for approximation of Becker model. Moreover, simulation results are done in R software. Findings: There is a direct relation between qualitative factor and A-optimal and D-optimal design, such that, on the region of factors, if the qualitative factors have a uniform design then the trace of the inverse of information matrix is minimize for A-optimal design; and maximization of the determination of information matrix is essential for D-optimal design. Besides, for a product function, based on 3 sections corresponding to the 2-marginal design, the dispersion function can be detected. In addition, illustrated examples confirm the analytical results. Application/Improvements: The application of this work is to be used in engineering and manufacturing which need to an amount of convenient mixture design.
Keywords: Becker Model, Dispersion Function, Information Matrix, Mixture Experiment, Optimality
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