THE MIXTURE MODELS WITH LOGARITHMIC TERMS AND THEIR D-OPTIMALITY

In this paper a type of mixture models with logarithmic terms is given. These models are extensions of Scheffé’s canonical models and alternatives of Draper and St. John’s mi xturemodels wish inverse terms. Using computer-aided design method which consists of Kiefer-Wolfowitz’s equivalence theorm, Fedorov’s and Wynn’s iteration processes, and combinatorial searching suggested by authors, we prove and construct the approximate D-optimal measure and D_n-optimal exact designs for use with first and second order mixtures regression models with logarithmic terms in three and four components. To illustrate our new model’s viability and ease of use with real data, we give in this paper anapplication of this new model to industrial ceramic material. Moreover, Using published data from Mclean and Anderson, we show the model fitting wish logarithmic term mixture model and compare it with Draper and St. John’s model.