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3.2 Theory
The main goal of any experimental study is to fi nd the relationships
between independent variables (factors) and dependent variables (results,
outcomes) within the experimental framework. Even though it sounds
easy to accomplish, this task can be cumbersome when it is not organized
correctly. In the fi eld of pharmaceutical technology, independent variables
are usually formulation factors (ingredients amount, materials attributes,
etc.) or processing parameters, whereas dependent variables are product
properties or parameters indicating process performance. Experimental
design is, in general, used to simultaneously study the effects of multiple
independent variables (factors) on response variable(s); therefore, it is a
multivariate analysis technique. DoE requires defi nition of levels (values)
of analyzed factors and often this phase uses knowledge from previous
experience about the problem being studied.
In the simplest screening experimental design, a relatively large number
of factors can be studied in a small number of experiments. In this way,
the most infl uencial factors are identifi ed and further examined in more
detail using full factorial or response surface designs. The screening
design usually varies the factors on two levels and only a few of all
possible combinations of different factors on different levels are used.
Response surface design enables optimization of the most infl uential
factors. In this design, factors are varied on at least three levels, and many
more combinations of factors on different levels are used (in comparison
to screening designs). A mixture design is used for studies where examined
factors are mixture related, such as in the amounts of formulation
ingredients. There is a constraint that the total sum of ingredient masses
must remain the same and the factors represent a fraction of the given
ingredients in the formulation.
The reader is advised to consult relevant textbooks in the fi eld of
pharmaceutical experimental design for further explanations of
experimental design concepts (Montgomery, 1997; Lewis et al., 1999;
Armstrong, 2006).
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3.2.1 Screening designs
Screening designs are used to identify the most infl uential factors from
those that potentially have an effect on studied responses. A huge number
of factors, f , can be screened by varying them on two levels in a relatively
small number of experiments N ≥ f + 1. Typical two-level screening
 
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