Chemistry Reference
In-Depth Information
tAble 5.1
plackett-burman design in twelve runs for up to eleven Factors
run
pattern
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
1
++++++++++++
1
1
1
1
1
1
1
1
1
1
1
2
−+−+++−−−+−
−1
1
−1
1
1
1
−1
−1
−1
1
−1
3
−−+−+++−−−+
−1
−1
1
−1
1
1
1
−1
−1
−1
1
4
+−−+−+++−−−
1
−1
−1
1
−1
1
1
1
−1
−1
−1
5
−+−−+−+++−−
−1
1
−1
−1
1
−1
1
1
1
−1
−1
6
−−+−−+−+++−
−1
−1
1
−1
−1
1
−1
1
1
1
−1
7
−−−+−−+−+++
−1
−1
−1
1
−1
−1
1
−1
1
1
1
8
++−−−+−−+−+
1
1
−1
−1
−1
1
−1
−1
1
−1
1
9
+++−−−+−−+−
1
1
1
−1
−1
−1
1
−1
−1
1
−1
10
+++−−−+−−+−
1
1
1
−1
−1
−1
1
−1
−1
1
−1
11
−+++−−−+−−+
−1
1
1
1
−1
−1
−1
1
−1
−1
1
12
+−+++−−−+−−
1
−1
1
1
1
−1
−1
−1
1
−1
−1
Note:
High (1) and low (−1) values correspond to chromatographic variables or factors.
5.3.1.3 plackett-burman designs
For robustness testing, it usually is sufficient to determine whether a method is robust
to many changes, rather than to determine the value of each individual effect, and
Plackett-Burman (PB) designs are very efficient screening designs where only main
effects are of interest. Plackett and Burman published their now-famous paperback
in 1946 describing their economical experimental designs in multiples of four rather
than a power of two [8], and PB designs have been frequently reported in the lit-
erature for chromatographic robustness studies (see, for example, References 9-12).
Table 5.1 shows a generic PB design for the twelve runs needed to evaluate eleven
factors, according to the general formula N-1 factors. Figures 5.3a and 5.3b illus-
trate an example of some actual experimental conditions that might be used for a
PB design for an eight-factor HPLC experiment. A PB design is a type of resolution
3 two-level fractional factorial design where main effects are aliased with two-way
interactions. PB designs also exist for 20 (19 factors), 24 (23 factors), and 28 (27 fac-
tors) run designs, but these are seldom used in chromatography as there is rarely the
need to evaluate so many factors. In instances where N-1 factors do not result in a
multiple of four, “dummy” factors are used.
5.3.2 d
etermInIng
the
f
ActorS
, m
eASurIng
the
r
eSultS
A typical HPLC method consists of many different parameters that can affect the
results. Various instrument, mobile phase, and even sample parameters must be
taken into account. Even the type of method (isocratic versus gradient) can dictate
the numbers and importance of various factors.
Typically, factors are chosen symmetrically around a nominal value, or the value
specified in the method, forming an interval that slightly exceeds the variations
