The single factors are high‑risk factors that cannot be easily combined with other factors. The excluded factors are those
with low risk, or, in the case of split time, their effect will be accounted by another factor (split ratio).
The 19 parameters detailed in Table 3 were risk assessed and a study containing only 7 instrumental factors were created; this was achieved by eliminating some
parameters, combining other low risk parameters and combining parameters that were thought to have similar effects or affect
different responses. The combination of parameters was quite aggressive to obtain a 7‑factor study where the number of experiments
required was reduced. The resolution of the design was also kept to the minimum resolution (III) to reduce the resources required
to run the experiment. Taking these steps cuts the total number of experiments required by at least 50% (i.e., 16 experiments;
8 for the instrument factors study and 8 for a further sample preparation factors study) instead of 32 (19 parameter resolution
III design) or typically 40 (as sample preparation is usually evaluated separately, ignoring centre points). See Figure 5 for a visual representation of how this resource was reduced.
Figure 5: Reduction of factors reduces resource required by 50%.
In a resolution III study, the two factor interactions are aliased with single factors. Therefore, it is important to allocate
the factors carefully to minimise the confusion this can cause during the analysis of the study if the factor is seen to have
an effect. It is advisable to review the alias list prior to the finalisation of the design and assess whether the two‑factor
interactions aliased with each single factor could have the same effect on any of the responses that are assessed in the study.
If the same effect is likely, then factors should be re-allocated to avoid these situations as far as possible, which will
make the analysis of the study easier and lower the likelihood of having to perform further experimentation to de-alias factors.
The alias list for this study is shown in Figure 6.
Figure 6: Alias list for 7 factors resolution III design.
Given the symmetry of the aliasing pattern, there is little opportunity for smart allocation of factors. However, from the
risk assessment, it is known that some parameters have a higher risk than others; also, as a rule, three-factor interactions
are less likely than two-factor interactions (which are less likely than single factors). The factors were allocated as in
Table 4 to reduce the complexity of the analysis of the study.
Table 4: Allocation of factors.
A, B and D are low risk groups, making it easy to discard any two‑factor interaction containing any of these factors.
C, F and G are high risk and all the two‑factor interactions they are aliased with contain either A, B or D; therefore, there
should not be any ambiguity in determining the cause of an effect.
Had A, B and C been allocated to the low risk parameters, on the other hand, then D, E and F would have been aliased with
one two-factor interaction that did not contain any of these low risk parameters, and is therefore more likely (Figure 6). In this later example, the complexity of the analysis of the study would not have been reduced.
The statistical design used in the case study had additional complications to that outlined because of the need to block runs
(i.e., to reduce the number of column and liner changes) and missing results in the data. For these reasons, modelling of
the data was complicated and has therefore not been included in this article because the main focus is the design setup. However,
a brief summary of the conclusions from the study is given.