Three classes of Central Composite Design: Central Composite Circumscribed Design (CCCD), Central Composite Inscribed Design (CCID) and Central Composite Face-Centered Design (CCFD) in Response Surface Methodology (RSM) were evaluated and compared using the A-, D-, and G-efficiencies for factors, k, ranging from 3 to 10, with 0-5 centre points, in other to determine the performances of the designs under consideration. The results show that the CCDs (CCCD, CCFD and CCID) are at their best when the G-efficiency is employed for all the factors considered while the CCID especially behaves poorly when using the A- and D-efficiencies.

Rotatability property for the Small Box-Behnken design is discussed in this paper. This paper aimed at applying a measure of obtaining percentage rotatability on the Small Box-Behnken designs to determine if the Small Box-behnken designs are rotatable or not and investigated the extent of rotatability in terms of percentage. The factors, q, considered range from 3 to 11. The results showed that for factors q, the Small Box-Behnken design is rotatable for q = 3 factors, near rotatable for q = 4, 7 factors and not rotatable for q = 5, 6, 8, 9, 10 and 11 factors.

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.