Abstract:
In many experimental situations, the researchers are concerned with explaining certain aspects of a functional relationship
( ) ( )
( )
where is the response,
are the levels of quantitative variables or factors and is the
random error. Response surface methodology is a statistical technique which is very useful in analysis of scientific experiments
where several independent variables influence a dependent variable. The response is assumed to be a random variable while the
independent variables are assumed to be continuous and are controlled by the experimenter. For example if a farmer wishes to find
the Potash ( ), Nitrogen( ) and Phosphate ( ) ferlizer levels that maximizes the yield, the observed response may be written
(
)
as a function of the levels of potash, nitrogen and phosphate fertilizers as
. The concept of rotatability
which is very important in response surface methodology was introduced by Box and Hunter [3]. They developed second order
rotatable designs through geometrical configurations. Bose and Draper [9] point out that the technique of fitting a response
surface is one widely used to aid in the statistical analysis of experimental work in which the response of the product depends in
some unknown fashion ,on one or more controllable variables. Mutiso [8] constructed specific optimal second order rotatable
designs in three dimensions. Koske et al. [6, 7] and Keny et al [10] constructed optimal second order rotatable designs and gave
practical hypothetical examples. Cheruiyot[1] evaluated the efficiencies of the six second order rotatable designs in three
dimensions that were constructed by Mutiso[8]. Cornelious[2, 3, 4 and 5]Constructed optimal sequential third order rotatable
designs, and a second order rotatable design of 39 points using trigonometric functions, with a practical hypothetical example. The
current study gives yet another new second order rotatable design in three dimensions of thirty six points constructed using
trigonometric functions with a practical hypothetical example.
