Chemistry Reference
In-Depth Information
% Organic
Wave
length
Wave
length
Flow
Flow
pH
pH
% Organic
Column
Temp
Wave
length
Wave
length
Flow
Flow
pH
pH
FIgure 5.2
Fractional factorial design robustness study for a five-factor experiment: pH,
flow rate, wavelength, percent organic, and temperature. Runs are indicated by the dots.
and experiments are usually dominated by main effects; not every variable interacts
with every other variable. The scarcity of effects principle is further based on the
probability that it is rare (low probability) for every factor to be low or high at the
same time. Therefore, the most critical issue in fractional factorial design is selec-
tion of the proper fraction of the full factorial to study. There is, of course, a price
to be paid for reducing the number of runs, and that is that not all factors can be
determined “free and clear,” but are aliased or confounded with other factors, and
the design resolution refers to the degree of confounding. Full factorial designs have
no confounding, and have a resolution of infinity. Fractional factorial designs can be
resolution 3 (some main effects confounded with some two-level interactions), reso-
lution 4 (some main effects confounded with three-level interactions), and resolution
5 (some main effects are confounded with four-level interactions). In general, the
resolution of a design is one more than the smallest order interaction with which a
main effect is confounded (aliased). Where possible, important factors should not be
aliased with each other. Chromatographic knowledge and the lessons learned during
method development (e.g., what affects the separation the most?) are very important
for selecting the proper factors and fraction. But do not worry; runs can always be
added to fractional factorial studies if ambiguities result.
