Abstract:
In research, experiments must be performed at pre determined levels of the controllable factors, meaning
that an experimental design must be selected before the experiment takes place. Once an experimenter has
chosen a polynomial model of suitable order, the problem arises on how best to choose the settings for the
independent variables over which he has control. A particular selection of settings or factor levels at
which observations are to be taken is called a design. A design may become inappropriate under special
circumstances requiring an increase in factors or levels to make it more desirable. In agriculture for
instance, continuous cultivation of crops may exhaust the previously available mineral elements
necessitating a sequential appendage of the mineral elements which become deficient in the soil over
time.
In current study, an eighty points four dimensional third order rotatable design is constructed by
combining two, four dimensional second order rotatable designs and a practical hypothetical case study
is given by converting coded levels to natural levels. We present an illustration on how to obtain the
mathematical parameters of the coded values and its corresponding natural levels for a third order rotatable design in four dimensions by utilizing response surface methodology to approximate the
functional relationship between the performance characteristics and the design variables. This design
permits a response surface to be fitted easily and provides spherical information contours besides the
economic use of scarce resources in relevant production processes.
