Central composite design error

Error, 4,5,6,7 Error of first kind, 14 Error of second kind, 14 Error, Measurement of, 7,8 Evolutionary operation, 64 Experimental designs, 48—63 central composite designs, 52,53,54... 

Table 3.17 presents the results from an analysis of the standard errors of each effect. Dividing the coefficient value by the standard error for each effect gives the t ratio. The critical t ratio is given by f i, = VF ritlP/ h DPR) ratio. Here we see that 022 exceeds while flu does not. This method is not foolproof since fly and 022 are mutually biased. However, for central composite designs the degree of bias is often slight. 

To estimate the experimental error, replications of factor combinations are necessary. Usually, the center point is run thrice. The total number of runs in a central composite design with three factors amounts then to 17. 

Central composite designs (CCD) are the most frequently applied response surface designs. They consist of a two-level full factorial design (2 experiments), a star design (2/ experiments) and a central point. As a consequence the CCD requires 2 + 2/+ 1 experiments to examine / factors (9 experiments for two factors 15 experiments for three factors, etc.). The experiments of the full factorial are situated at levels -1 and +1, those of the star designs at levels -a and +a for each factor, and the central point has all levels at 0 (see Figure 3.19). The central point of the design (0, 0) is replicated commonly to estimate the experimental error. 

In the framework of each program 16 various compositions have been prepared in accordance with the experimental design. Moreover 4 additional replications have been done in the central point of the experimental domain to estimate the experimental error variances. 

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