Calculus Optimum Values Optimality Criteria for Twenty Four Points Specific Second Order Rotatable Design in Three Dimensions

Abstract

This study uses the existing second order rotatable design to obtain optimum design based on the known classical optimality criteria that is the determinant criterion, the average-variance criterion, the smallest-Eigen value criterion and the trace criterion. These criteria measure the desirability of a design, D-optimum design minimizes the content of the ellipsoidal confidence region for the parameters of the linear model, A-optimum design minimizes the sum (or average) of the variances of the parameter estimates, E-criterion reduces the variance of each individual parameter estimate and T-criterion is one that has not enjoyed much use because of the linearity aspect of T-criterion. This study considers the already existing twenty four points three dimensional specific rotatable design of order two. The information matrices C1, for this design is obtained from the moment matrix M, for the second order model for three factors using the relation C=(K1M-1K)-1, where M=1/N(X1X), is the moment matrix, K is the coefficient matrix of the parameter sub system of interest. Our parameter system of interest is that of the linear and pure quadratic factors only. The optimality criteria for the design with the corresponding information matrix C1, is determined as A-optimal.