Full factorial designs problem

Consider the screening problem of table 2.20. Here we want to know the effect of various diluents, disintegrants, lubricants etc. on the stability of the drug substance. We have not imposed any restraint whatsoever on the numbers of levels for each variable. We could of course test all possible combinations with the full factorial design, which consists of 384 experiments (4 x 2 x 3 x 4 x 2 x 2) Reference to the general additive screening model for different numbers of levels will show that the model contains 12 independent terms. Therefore the minimum number of experiments needed is also 12. 

Any of the problems that we have looked at in this chapter can be investigated using a full factorial design - that is by doing an experiment at each possible combination of levels. 

Assume first of all that we have solved the problem We call the 3 selected variables A, B, and C. The full factorial design is therefore the design whose model matrix as shown below in table 3.26. AB, AC, BC, ABC represent the interactions. 

Finally, the problem was resolved by irradiating standards and mixtures of standards in a factorial experiment. The experiment design was a full factorial experiment with three variables, mercury, selenium, and ytterbium, at two levels with replication and with a center point added to test higher order effects. The pertinent information on treatments and levels of variables are shown in Table VII. 

The full factorial 4 3 2 design, of 384 experiments (4 x 4 x 3 x 2 x 2 x 2), consisting of all possible combinations of the levels of the different variables, is a solution to the problem. This set of experiments is therefore used as candidates, from which we extract exhaustively a representative sub-set, of 12 to 20 experiments. 

Full-factorial three-level designs are sometimes used for investigating few factors (two or three) although their statistical properties with respect to symmetry or confounding of parameter estimates are less favorable than those known for the two-level designs. In the case of many factors, the same problem as with... 

A second related problem is how to compare the quality of libraries that were designed in different property spaces. Imagine that a worker develops a property space of three dimensions and manages to obtain a set of molecules, one at each corner of the property cube, thereby achieving a full factorial,... 

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