Central Composite Designs Within A Split-Plot Structure

Central composite designs and split-plot experiments are two important components of classical statistical experimental designs, both of which have their advantages and disadvantages. Central composite designs are the most frequently used in second-order response surface analysis; but central composite designs requires complete randomization which can not be always guaranteed in practice. Split-plot experiments break through the constraint of complete randomization; however, those experiments are limited to analysis of variance, and have their limitations in prediction, control and optimization. As a result, in recent years, how to modify the standard central composite design to accommodate a split-plot structure has been greatly concerned in the field of design of experiments.Based on the newly studying achievements and wide reference of related literature, this dissertation firstly reviews the traditional central composite design theories, especially in constructing orthogonal and rotatable experimental designing methods; then the split-spot experimental model from a regression analysis point of view is addressed as well as the generalized least squares theory and the robustness of ordinary least squares estimate; with the theories demonstrated above, this dissertation, through mathematically deducing a special variance-covariance matrix in split-spot central composite designs, has established the relationship between the former theory and new issue; the issues of orthogonal and rotatable realization as well as combination of the two are further studied in the dissertation.The innovation through this dissertation is that it constructs a split-spot orthogonal central composite design with one and two subplot factors respectively, as well as a split-spot rotatable central composite design with one subplot factor and a split-spot orthogonal rotatable central composite design with one subplot factor. Those academic results above are theoretically innovative and practical in application.