Indian Journal of Science and Technology

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