Robustness studies typically utilise fractional factorial designs to meet validation requirements - although sometimes Plackett
Burman designs are used.14 These designs help to estimate the effects of individual method parameters and all their interactions with each other. 15,16 Each parameter is varied over two levels: high or “level +1” and low or “level -1”, and the two levels of each parameter
are then systematically combined to create the set of experiments. Full two-level factorial designs permit estimation of the
effect of individual parameters and all their interactions. Although the maximum amount of information is be obtained, full
factorial designs are not practical because of the elevated number of experiments to be performed. In fractional factorial
designs, only a fraction of the full design is studied, which decreases the overall number of experiments and the statistical
resolution because not all the single parameter effects or interactions are estimated independently. It is desirable to further
reduce the number of experiments used for two reasons:
- To enable the use of such studies to provide an early indication of robustness and a direction for further method improvement
- To most effectively use resources for the demonstration of robustness.
The number of experiments in fractional factorial designs can be reduced in two ways, which can be combined:
- Reducing the number of factors
- Reducing the statistical resolution of the design.
Figure 1, taken from the DoE software Design-Expert (DX7), shows how many experiments (runs, vertical axis) are required for various
numbers of factors (horizontal axis) and for different statistical resolutions (explained later). It illustrates the two ways
of reducing the number of experiments.
Figure 1: Two ways of reducing the number of experiments (runs); illustration from DX7 software.
Reducing the number of factors
Prior to building the statistical design, a risk assessment is performed to help determine whether the number of factors and
the resolution of the design can be reduced. A prioritisation matrix tabulates the method parameters and the method performance
characteristics, and the impact of each parameter over these characteristics is assessed and scored. Different scoring scales
can be used; in this paper, the following scale has been used: 1=very low impact, 3=slight impact, 5=possible impact, 7=likely
impact and 9=strong impact.
The scores for each method parameter are then summed to give an importance score, which is used to rank each parameter with
respect to risk.
The outcome of this prioritisation exercise determines whether any method parameters can be removed from the design, combined
with other parameters, or should be included as a single factor. It also helps decide appropriate design resolution. An example
of the prioritisation matrix is shown in the case study that follows.
The acceptability of removing a parameter partly depends on whether it is an early or final robustness assessment. If doubts
remain as to whether or not a parameter should be removed, the parameter can be combined with other low‑risk parameters to
determine whether these parameters studied together produce an effect (e.g., instrument‑related parameters with narrow ranges).