f_p{phi_p}-optimal designs for a linear log contrast model for experiments with mixtures

摘要

A mixture experiment is an experiment in which the k ingredients are nonnegative and subject to the simplex restriction on the (k − 1)-dimensional probability simplex S k-1. In this work, an essentially complete class of designs under the Kiefer ordering for a linear log contrast model with a mixture experiment is presented. Based on the completeness result, -optimal designs for all p,−∞ ≤ p ≤ 1 including D- and A-optimal are obtained, where the eigenvalues of the design moment matrix are used. By using the approach presented here, we gain insight on how these -optimal designs behave. Keywords A-optimal - Complete class - D-optimal - Kiefer ordering Mong-Na Lo Huang was supported in part by the National Science Council of Taiwan, ROC under grant NSC 93-2118-M-110-001.