A Sequential Third Order Rotatable Design in Four Dimensions

Abstract

In research, experiments must be performed at pre-determined levels of the controllable factors, meaning that an experimental design must be selected prior to experimentation. 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 previously available mineral elements necessitating a sequential appendage of the mineral elements which become deficient in the soil over time. In this study, a fifty six points third order rotatable design is constructed by adding a set of factors to a second order  rotatable design in four dimensions and a practical hypothetical example is given by converting coded level to natural levels.  This design permits a response surface to be fitted easily and provide spherical information contours besides the economic use of scarce resources in relevant production processes.