Hexagonal rotatable design with

Figure 13.16 A hexagonal rotatable design with center point. DF = 1, DF = 3.

Figure 6. A hexagonal rotatable design with center point.

Reference [56] states that these are the smallest second-order rotatable designs, with a smaller number of trials than central composite rotatable designs. Of special use are designs that are made by vertices of hexagons with central points n0>l Fig. 2.58. 

To reach a second-order model by a mathematical theory of experiment, designs of second order experiments may be applied, as described in sects. 2.3.2, 2.3.3 and 2.3.4. Noncomposite designs such as simplex sum rotatable designs (SSRD) pentagonal or hexagonal types (k=2) with central points are analyzed in this case (Figs. 2.57 and 2.58.). 

The equiradial designs are rotatable. It is possible to adjust the number of center point experiments to achieve uniform precision as well as near-orthogonal properties. Uniform precision for the pentagon and the hexagon is obtained with three center point experiments. Orthogonal properties are obtained with five center point experiments for the pentagon, and with six center point experiments for the hexagon. 

The designs may be rotated by any angle and still retain the same properties. Certain orientations more commonly used than others are shown in figure 5.5 and table 5.8. We shall see later that the pentagonal and hexagonal design, with addition of centre points, may also be used with a second-order model (see sections V.B and D). 

The variables selected for use in optimization of the process were reaction ten erature and the molar ratio of dimethylamine to 4-chloroacetophenone. The experiments were run in sealed reactors. The initial design contained seven experiments (rotatable hexagonal design with center point). Six experiments were equally spaced around the center point that was set at 3 equivalents of dimethylamine and 230 C. The unit variation in the equivalents of dimethylamine was set to 1 molar equivalent, and the unit variation in temperature was set to 20 °C. At the conclusion of this series of experiments, it was determined that the optimum conditions were not within the experimental domain. Consequently, the original study was augmented with additional experiments. 

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