Computer Aided Generation of Linear Trend-free Response Surface Design

Abstract

ABSTRACT The treatment combinations of the ordinary full factorial need not be the best for fitting the relationship. Therefore, it is necessary to search for a suitable set of treatment combinations by using which a stipulated relation can be fitted. The special class of designed experiments for fitting the response surfaces is called response surface design. Response surface designs have wide applications in agricultural, biological and industrial experiments. Similar to factorial experiments, experimental units in response surface design may exhibit trend over space or time. Among response surface designs, Box-Behnken design has been studied and linear trend-free design has been obtained. The developed algorithm helps the experimenters who are conducting quantitative factors using response surface designs. There may be a trend in the experimental material and hence we need trend-free design. It provides a complete solution in the sense that it is capable of generating the trend free Box-Behnken design. Trend-free designs are quite useful for such experimental situations. But the construction for such design is not easily available. It is, therefore, required to give easy method of construction, possibly computer aided for the construction of these designs. Thus algorithms have been developed to generate complete factorial experiments each at two levels with any number of factors k ( ³ 4) that are linear trend-free for main effects using the criterion of component-wise product.