Multi-factorial experiments

There is no logical reason why we need to stop at two experimental factors. When trying to optimize a drug synthesis we might need to define the best  

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The reader will have noticed that we have discussed two difTerent techniques for the investigation of multi-variable systems, namely multiple correlation and the factorial experiment. 

In the previous chapters it was seen that the linear coefficients, Bj, and the rectangular (interaction) coefficients. By, can be efficiently estimated by a two-level factorial or fractional factorial design. To determine also the square coefficients, Bjj, it will, however, be necessary to explore the variations of the experimental variables on more than two levels. One possibility would be to use a multi-level factorial design to define a grid of experimental points in the domain. However, with r levels and k variables, the number of experiments, increases rapidly and becomes prohibitively large when the number of levels and the number of variables increase. 

Multi-parameter study Analysis of optimum conditions using factorial experimental design and response surface experiments. 31... 

We may take the results of the 2 factorial study of an effervescent table formulation reported earlier, and select the data corresponding to the 12 experiments of table 3.31. Estimates of the coefficients obtained either by contrasts or by the usual method of multi-linear regression are very close to those estimated from the... 

For the experiment array, I prefer an orthogonal central-composite design (2), (3), which consists of three main parts, as shown in Table I. The first is a conventional 16-experiment fractional factorial design for five variables at two levels. The second comprises three identical experiments at the average, or center-point, conditions for the first 16 experiments. The final part comprises two out-lier experiments for each variable. These augment the basic two level design to provide an estimate of curvature for the response to each variable. The overall effect of the design is to saturate effectively the multi-dimensional variable space. It is more effective than the conventional "one-variable-at-a-time" approa.ch. 

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