Factorial designs disadvantages

In order to overcome one of the main disadvantages of SFE, Salafranca et al. [322] have proposed the use of full-factorial design with the objective of attaining optimum extraction conditions. It was considered that... 

The disadvantage of full factorial designs is that the number of experiments increases rapidly when the number of factors increases. For 6 factors 64 experiments are required and for 7 factors 128. In practice it is usually not possible to perform such a large number of experiments in a reasonable span of time. For this reason often only a fraction of a full factorial design is performed. This kind of design is called fractional (or partial) factorial design. 

A first possibility is the use of full factorial designs with three levels [31]. The disadvantage of the three-level factorial designs is that the number of experiments increase very rapidly for a larger number of factors. 

This model allows us to estimate a response inside the experimental domain defined by the levels of the factors and so we can search for a maximum, a minimum or a zone of interest of the response. There are two main disadvantages of the complete factorial designs. First, when many factors were defined or when each factor has many levels, a large number of experiments is required. Remember the expression number of experiments = replicates x Oevels) " (e.g. with 2 replicates, 3 levels for each factor and 3 factors we would need 2 x 3 = 54 experiments). The second disadvantage is the need to use ANOVA and the least-squares method to analyse the responses, two techniques involving no simple calculi. Of course, this is not a problem if proper statistical software is available, but it may be cumbersome otherwise. 

When the seven differences for factors A-G have all been calculated in this way, it is easy to identify any factors that have a worryingly large effect on the results. It may be shown that any difference that is more than twice the standard deviation of replicate measurements is significant and should be further studied. This simple set of experiments, technically known as an incomplete factorial design, has the disadvantage that interactions between the factors cannot be detected. This point is further discussed in Chapter 7. 

A disadvantage of Plackett-Burman designs is that the relations between the calculated contrasts and the effects of a complete factorial are quite complex. This makes it difficult to choose the additional runs necessary to unconfound the effects. 

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