Appropriate Number of Center Points for Response Surface Exploration Using Small Box Behnken Design

Abstract

Industrial exploration using the Box Behnken Design (BBD) has been faced with a serious setback due to the swift upsurge in the runs size as the number of factors increase. This, therefore, dissuades researchers and affects the application of the design. The Small Box Behnken Designs (SBBD) which achieve the research goal of BBD were proposed to overcome the setback. This paper aimed at recommending an appropriate number of center points suitable for response surface exploration and its applications in industries using the SBBD. The method adopted for assessing the center points is the prediction variance-based G-efficiency optimality criterion. The range of design factors, k, considered is 3 to 11, while comparing the designs at 0 - 5 number of center points. For each of the design factors considered, the result showed that increasing the center point, decreases the G-efficiency value. Hence, increasing the center point does not contribute significantly to the prediction variance capability of the designs considered. However, in other to test the model lack of fit and estimate pure error which are very important in experimental design analysis, this study recommends that at most two runs (center points) be replicated at the center. Since with this number, approximately 90% G-efficiency can be achieved for response surface exploration using the SBBD.