Construction of Thirty Six Points Second Order Rotatable Design in Three Dimensions with a Practical Hypothetical Case Study

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.