| dc.description.abstract | The technique of response surface designs 1S not
new. Useful designs in this kind of technique are known
as rotatable designs1 Several authors have made contributions
in this area. Box [1 J gave the concept of
rotatability and he also gave the designs of first
degree. Box and Hunter [4J worked out second order
rotatable designs and Gardiner, Grandage and Hader[lS]
worked out the moment conditions and non-singularity
conditions for ~ set of experimental points to form a
third order rotatable design. Some rotatable designs
of second and third orders have been obtained by Bose
and Draper [7J and Norman Draper [11, 12, 13, 14J
respectively. This thesis deals with the fourth order
response surface designs.
Chapter 1 gives basic ideas in response surface
designs and describes briefly some relevant work that
has been done by various authors. The chapter also sets
out notations which,are used in the subsequent development
6f the theory in the later chapters. These
notations~are similar 10 those used by the authors
sited above.
In chapter 2, the moment conditions for a set of
experimental points to form a fourth order arrangement
are obtained. These are given in-s~ction 2.2.4. To
obtain these-conditions, a few ~nown results and definitions
have been given in the !lrs( sections. This is
done for clarity and easy reference.
In chapter 3, the non-singularity conditions for
a set of experimental points to form a fourth order
rotatable design have been obtained.To obtain these
conditions, the moment matrix for tile fourth order
response surface is obtained and hence its determinant
~ is worked out using the known methods. The determinant
is assumed, to be greater than zero and then the conditions | en |
