K-model Based Mixture Design Using D-optimal And A-optimal With Qualitative Factors

The fundamental objective is to obtain a reliable approximation for the K-model in mixture experiments design.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.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 uniform design,then for A-optimal design,the trace of the inverse of information matrix should be minimized.Secondly,for D-optimal design,maximization of the determination of information matrix is necessary.The main application of this research is using of an amount of convenient mixture design in engineering and manufacturing.It can be detached in to 3 sections corresponding to the 2-marginal design.