Response surface designs with four and six equi-spaced levels

Response surface methodology (RSM) is often used to determine and to quantify the relationship between the response and the levels of quantitative factors and to find the combination of the factor levels that gives optimum or best desired response(s) within experimental region of interest. In agricultural sciences, several experiments are conducted with equi-spaced four- and six-level factorial experiments. Construction of second order rotatable response surface designs with equi-spaced four- and six-level factorial experiments are not easy to obtain. Therefore, in this article nearly rotatable second order response surface designs with equi-spaced four and six levels have been obtained. Methods of construction available in literature for obtaining second order rotatable designs with four and six levels have been modified to obtain designs with equi-spaced levels. Construction methods developed are general in nature and can be used for obtaining designs with any number of factors. Rotatability measures and D-efficiency of second order response surface designs with four and six equi-spaced levels up to 6 factors have been computed.