CONSTRUCTION OF A PRACTICAL OPTIMUM SECOND ORDER ROTATABLE DESIGN IN THREE DIMENSIONS
In this study, we find the specific coded and natural levels of some predictor variables coded and natural levels that optimize the expected value of a response variable starting from some best guess center and The experiment is performed by varying them in a region around this center point.
A specific optimum second order rotatable design of three factors in twenty points is constructed. This is achieved by estimation of the free parameters using calculus in an existing second order rotatable design of twenty points. Such a design permits a response surface to be fitted easily and provides spherical information contours which can best describe the region of interest. Such a response surface generated by the optimum combination of ingredients can be applied in agriculture, horticulture and allied sciences which result in economic use of scarce resources in relevant production processes. The expected second order rotatable design model in three dimensions will be available where the responses would then facilitate the estimation of the linear and quadratic coefficients. An example involving phosphate nitrogen and potassium is used to represent the three factors in the coded level and converted into natural levels. We shall then obtain the optimal values corresponding to the twenty points’ design with respect to the determinant criterion, the average-variance criterion, the smallest eigenvalue criterion and the trace criterion for all parameter systems of interest.
response surface methodology, second order design, optimality, coded levels, natural levels.