A Sequential Third Order Rotatable Design of Eighty Points in Four Dimensions with an Hypothetical Case Study

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.