Central composite rotatable designs

Central composite rotatable designs Quantitative Regression models of second order... 

Design matrices of central composite rotatable designs (CCRD) for k=2, k=3 and k=5 are shown in Tables 2.138 - 2.140. By using relation (2.59), which connects coded and real factor values, we switch from design matrix to operational matrix, Table 2.138. 

Basic Experiment-Mathematical Modeling 327 Table 2.140 Central composite rotatable design 25 1 +2x5 + 6... 

The central composite rotatable design of experiment with outcomes is shown in Table 2.147. 

To optimize the process of isomerization of sulphanylamide from Problem 2.6, a screening experiment has been done by the random balance method. Factors X1 X2 and X3 have been selected for this experiment. Optimization of the process is done by the given three factors at fixed values of other factors. To obtain the second-order model, a central composite rotatable design has been set up. Factor-variation levels are shown in Table 2.148. The design of the experiment and the outcomes of design points are in Table 2.149. 

A process having properties dependent on four factors has been tested. A full factorial experiment and optimization by the method of steepest ascent have brought about the experiment in factor space where only two factors are significant and where an inadequate linear model has been obtained. To analyze the given factor space in detail, a central composite rotatable design has been set up, as shown in Table 2.152. 

For designs of experiments where we have replications in null point, we determine the value fAD from Eq. (2.162) with reference to expression (2.164). This is valid for cases of application of central composite rotatable designs. The value of residual sum of squares in Eq. (2.156) is determined in this way ... 

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. 

The experimental domain is given in Table 12.4. A uniform precision central composite rotatable design (5 center point experiments) was used. The design and the yields of enamine obtained after 15 minutes are given in Table 12.5. 

An equiradial design with m = 8 defines an octagon. This is also the distribution which is obtained by a central composite rotatable design. 

These principles are illustrated by a central composite rotatable design in two variables. This design will be orthogonal with eight experiments at the center point... 

Central composite rotatable design and experimental results... 

A screening of the variables was carried out using a Plackett-Burman design. Then, a set of two sequential factorial designs was carried out to optimise the conditions of the extraction process. A complete 2 factorial was used, followed by a central composite rotatable design. 

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