Three-level full factorial designs

The absorption spectra of Aspt, Ace-K, Caf and Na-Benz were recorded from 190 to 300 nm. The calibration set was generated by a three-level full factorial design (4).The absorbance valnes were recorded eveiy 5 nm. The calibration samples were measured in random order, so that experimental errors due to drift were not introduced. 

Three- or more-level response surface designs, such as three-level full factorial, central composite (CCD), and Box-Behnken designs, are applied in some case studies. 

A larger three-level full factorial design... 

Two-factor three-level full factorial designs. 

Three-Level, Full-Factorial Experiment Design, Interaction Model Between Pad A and Pad B... 

FIGURE 5.90. Concentration of component B versus concentration of component A in a three-level, full-factorial experimental design. 

It is obvious that to be able to estimate the quadratic coefficients, p, in equation (14), it is necessary to have at least three distinct levels or settings for the variables. This suggests that a suitable design for estimating the coefficients of the second-order model would be a single replicate of a three-level full factorial design in p variables. This design... 

If there are only p=2, or p=3 variables then a full factorial design is often feasible. However, the number of runs required becomes prohibitively large as the number of variables increases. For example, with p=5 variables, the second-order model requires the estimation of 21 coefficients the mean, five main effects, five pure quadratic terms, and ten two-factor interactions. The three-level full factorial design would require... 

Figure 5.5 shows a three level full factorial design for the HPLC example which tests three factors, centred around the method conditions. This design allows the testing of changes from the method conditions to extremes on either side. 

The design, which is illustrated in Figure 5.8, gives the most comprehensive evaluation of the response surface using a given number of experiments. It provides greater efficiency than a three level full factorial design yet essentially obtains the same information. However, as k increases the number of required experiments quickly becomes impractical [22]. 

The exact structure of each of the functions/ x),..., fk(x) depends on the transformation or factor coding used. For example, the F matrix for a three-level full factorial design for two process variables and a second-order model is shown in Table 8.4. 

Three-Level Full Factorial Designs. A three-level full factorial design contains all possible combinations between the /factors and their levels L = 3, and the number of experiments thus is A = = 3L These three-level... 

TABLE 2.13. Three-level full factorial design for two factors... 

ED (BGE optimization). Three-level full factorial design. Factors pH, sodium octanesuHonate concentration. Response migration time, peak width, resolntion. 

TABLE QS9.5b Eight Experiments Using Three-Level Full Factorial Design... 

Out of the many symmetric designs available, four are presented here that have widespread use the three-level full factorial designs, the central composite designs, the Doehlert designs and the Box Behnken designs. 

A three-level full factorial design contains all possible combinations of / factors at their 3 levels (-1,0, + 1). In total, f experiments will be required to examine the /factors (9 experiments for 2 factors 27 for 3 factors, etc.). 

Figure 3.18 displays the design matrix and the layout of a two-factor three-level full factorial design. The central point of the design [i.e. (0, 0)] is often replicated to estimate the experimental error for the subsequent calculations. 

A two level full factorial experimental design with three variables, F/P molar ratio, OH/P wt %, and reaction temperature was implemented to analyses the effect of variables on the synthesis reaction of PF resol resin. Based on the composition of 16 components of 10 samples, the effect of three independent variables on the chemical structure was anal3 ed by using 3 way ANOVA of SPSS. The present study provides that experimental design is a very valuable and capable tool for evaluating multiple variables in resin production. 

Figure 14.2 A three-factor two-level full factorial design in factors A, B, and C. The open circle locates the center of the design.

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