Consider a specific example where there are 7 parameters to be evaluated and there is considered to be some risk of an interaction
between two parameters, here allocated to factors A and F. Ideally the design would estimate AF separately from main effects.
Table 1 illustrates some of the considerations and choices to be made for a specific example as follows:
- Design A is a resolution IV design that separates all main effects from 2 factor interactions, but requires 16 runs (ignoring
centre points).
- Design B is a resolution III (so AF will be aliased with a main effect), but only requires 8 runs. If this design is used,
AF should be aliased with the lowest risk parameter (letter G in this case).
- If it is appropriate to group two parameters, this leads to 6 factors and design C which, despite being resolution III, separates
AF from main effects.
Table 1: Example of resolution and aliasing considerations.
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If no two parameter interactions were of particular risk, then design B rather than design C should be used because there
would only be disadvantages from grouping parameters.
The literature has suggested the use of supersaturated designs, that is designs where the number of main effects exceeds the
number of runs in process development.19 This approach is a group factor screening type designs. Risk assessment combined with scientific understanding is used to
provide the grouping scheme, an aspect that Lin20 suggests is seldom discussed, but crucial. Whilst supersaturated designs have been suggested for analytical methods,21,22 these focus on designs, which have factors partially correlated in the design rather than using grouping. Consequently, the
statistical analysis is not straightforward and Dejaegher and Heyden22 even suggest it should not be used for estimating effects in analytical method robustness testing. Whilst there may be situations
where those designs are useful, the approach of grouping factors used in this paper has the following advantages:
- Easy for analysts to use existing knowledge of fractional factorial design and software.
- Careful grouping of parameters reduces ambiguities relating to cause of effects and any additional experimentation (e.g.,
folding over the original design) required to de‑alias effects or separate out effects of grouped parameters will be familiar
to many analysts using fractional factorial design.
Case study: application of RMR to GC-FID analysis of N‑acetyl piperazine (NAP)
Table 2: NAP method conditions.
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A gas chromatographic (GC) method with flame ionisation detection (FID) for the analysis of a starting material (N-acetyl
piperazine; NAP) had been observed in the past to sometimes produce variable results although the cause for this variation
was unknown.
Figure 3: Example chromatogram from NAP method.
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Therefore, it was deemed necessary to conduct robustness testing to identify and control any parameters that were responsible
for this variation. The robustness testing was planned and conducted using the reduced method robustness principals outlined
above. Details of the chromatographic conditions and a typical sample chromatogram are shown in Table 2 and Figure 3, respectively.
Parameter risk assessment and prioritisation
Figure 4: Fishbone for GC-FID method parameters (with enlarged method section).
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Parameters for the method were brainstormed and categorised on a fishbone using mind-mapping software as in Figure 4.
Table 3: Risk scoring of X parameters and RMR decision based upon risk scoring for GC-FID method parameters.
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The fishbone categories were as follows: equipment; environment; measurement; method; materials; and people. The parameters
were then given a variable classification - C, N or X (as described by Borman et al.,).4 The X (experimental) parameters are the parameters that will be considered for inclusion in the robustness study. These include
instrumental parameters, such as flow rate and temperature, which are given a set point in the method, but will vary in line
with the precision of the instrument. These parameters could also be related to the sample preparation (e.g., heating of NAP
or sonication time) where variability is derived from how the operator follows the method procedure. To establish which parameters
were most important to the method, GC experts scored and prioritised the X parameters using a prioritisation matrix. The method
characteristics were: resolution of impurity A and impurity B; % area impurity A; % area impurity B; % area impurity C; limit
of quantitation (LOQ), retention time (Rt) for impurity C; and Rt for NAP. Each parameter was assigned a score in the range
1-9 for each method characteristic, as described in the RMR approach section, and the overall importance score was calculated.
Results are detailed in Table 3.
Parameters were grouped primarily based on those that are low risk and/or likely to affect different responses. This makes
the analysis of the data at the end of the study simpler because there is less ambiguity around assigning significant factors.
Parameters such as column flow and column loading affect signal‑to‑noise ratio and are in the same group. Since the direction
of their effects was thought to be the same, this combination was deemed acceptable. It will, however, be impossible to determine
which of the two parameters is responsible for any effect observed (only the total effect can be assessed and whether it is
large enough to cause concern).
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