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Details of the FACTEX Procedure
The factors of a design are variables that an experimenter can setat several values. In general, experiments are performed to study theeffects of different levels of the factors on the response ofinterest. For example, consider an experiment to maximize the percentageof raw material that responds to a chemical reaction. Thefactors might include the reaction temperature and the feedrate of the chemicals, while the response is the yield rate.Factors of different types are used in different ways in constructing adesign. This section defines the different types of factors.
Block factors are unavoidable factors that are known to affectthe response, but in a relatively uninteresting way. For example, in thechemical experiment, the technician operating the equipmentmight have a noticeable effect on the yield of the process. The operatoreffect might be unavoidable, but it is usually not very interesting. Onthe other hand, factors whose effects are directly of interest are calleddesign factors. One goal in designing an experiment is to avoidgetting the effects of the design factors mixed up, or confounded,with the effects of any block factors.
When constructing a design by orthogonal confounding, all factorsformally have the same number of levels q, where q is a primenumber or a power of a prime number. Usually, q is two,and the factor levels are chosen to representhigh and low values.
However, this does not mean, for example, that a design for two-levelfactors is restricted to no more than two blocks. Instead, the values ofseveral two-level factors can be used to index the values of a singlefactor with more than two levels. As an example, the values of threetwo-level factors (P1, P2, and P3)can be used to index the values of an eight-levelfactor(F), as follows:
| P1 | P2 | P3 | F |
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 2 |
| 0 | 1 | 1 | 3 |
| 1 | 0 | 0 | 4 |
| 1 | 0 | 1 | 5 |
| 1 | 1 | 0 | 6 |
| 1 | 1 | 1 | 7 |
The method for constructing an orthogonally confounded design forq-level factors in qm runs distinguishes between the first mfactors and the remaining factors. Each of the qm different combinations of thefirst m factors occurs once in the design in an order similar to thepreceding table. For this reason, the first m factors are called therun-indexing factors.
Table 15.7 summarizes the different types of factors discussedin this section.
Table 15.7: Types of Factors| Block factor | Unavoidable factor whose effect is not of direct interest |
| Block pseudo-factor | Pseudo-factor used to derive levels of a block factor |
| Derived factor | Factor whose levels are derived from pseudo-factors |
| Design factor | Factor whose effect is of direct interest |
| Pseudo-factor | Formal factor combined to derive the levels of a real factor |
| Run-indexing factors | The first m design factors, whose qm combinations |
| index the runs in the design |
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