Fifth order rotatable designs

Abstract

This thesis deals with the fifth order rotatable designs. Many authors have made several contributions to the idea of rotatable designs. Box [1J gave the concept of rotatability and also rotatable designs of first order. Box and Hunter (4] worked out second order rotatable designs. Gardiner, Grandage and Hader [16J worked out the moment and non-singularity conditions for a set of experimental points to form a third order rotatable design. Some rotatable designs of second and third orders have been obtained by Dose and Draper [7J and Norman Draper [12J, [13J, [14J respectively. In Chapter 1, basic ideas in response surface designs have been ,given. It also briefly describes some relevant work that has been done by various author&, especially is first, second, third and fourth order response B-surface design~. The chapter also sets out notations which are used in the subsequent development of the theory in ~t-h8 later chapters. In Chapter 2, the moment conditions for a set of experiment points to form a fifth order arrangement are obtained. These are given in section 2.5. To obtain these conditions, a few known results and definitions have been given_ in the first sections , This is done for clarity and easy reference.