Optimal Three-Level Designs for Response Surfaces in Spherical Experimental Regions

摘要

Since 1960, Box-Behnken designs have been very popular with experimenters wishing to estimate a second-order model in three or four factors. This popularity is due to these three-level designs' simplicity and high efficiency. However, as the number of factors increases, the run size of Box-Behnken designs increases rapidly, making them less attractive. The purpose of this article is to recommend the use of D-optimal and I-optimal three-level designs for spherical design regions involving three or more factors. Using an optimal design algorithm offers flexibility of run size. In addition, optimal-design criteria permit construction of second-order designs for more complex response surface applications involving mixture or qualitative factors or requiring split-plot randomization. The restriction to three-level designs provides great practical convenience and often little loss in efficiency, provided the design is not nearly saturated.