Details of the FACTEX Procedure 
Example 15.11: Resolution IV Design with Minimum Aberration
See FACTEX14 in the SAS/QC Sample Library

If a design has resolution IV, then
you can simultaneously estimate all main effects
and some twofactor interactions. However, not all
resolution IV designs are equivalent; you may be able
to estimate more twofactor interactions with some than with others.
Among all resolution IV designs, a design that
allows you to estimate the maximum number of twofactor
interactions is said to have minimum aberration.
For example,
if you use the FACTEX procedure to generate a resolution IV twolevel
design in 32 runs for seven factors, you will be able to estimate all
main effects and 15 of the 21 twofactor interactions with the design
that is created by default. The following statements create this design
and display its alias structure in Output 15.11.1:
proc factex;
factors a b c d e f g;
model resolution=4;
size design=32;
examine aliasing;
run;
Output 15.11.1: Alias Structure for Default 2^{72}_{IV} Design
ALIAS 
a 
b 
c 
d 
e 
f 
g 
a*b = f*g 
a*c 
a*d 
a*e 
a*f = b*g 
a*g = b*f 
b*c 
b*d 
b*e 
c*d = e*g 
c*e = d*g 
c*f 
c*g = d*e 
d*f 
e*f 

In constrast, the resolution 4 design given in Table 12.15 of Box, Hunter,
and Hunter (1978) is a minimum aberration design that
allows estimation of 18 twofactor
interactions, three more than can be estimated with the default design.
The FACTEX procedure
constructs the minimum aberration
design if you specify the MINABS option to the MODEL statement, as in the
following statements:
proc factex;
factors a b c d e f g;
model resolution=4 / minab
size design=32;
examine aliasing;
run;
The alias structure for the resulting design is shown
in Output 15.11.2.
Output 15.11.2: Alias Structure for Minimum Aberration 2^{72}_{IV} Design
ALIAS 
a 
b 
c 
d 
e 
f 
g 
a*b 
a*c 
a*d 
a*e 
a*f 
a*g 
b*c 
b*d 
b*e 
b*f 
b*g 
c*d = e*f 
c*e = d*f 
c*f = d*e 
c*g 
d*g 
e*g 
f*g 

All of the designs listed in Table 12.15 of Box, Hunter, and Hunter
(1978) have minimum aberration. For most of these cases, the default
design constructed by the FACTEX procedure
has minimum aberration that is, the
MINABS option is not required. This is important because the MINABS
option forces the FACTEX procedure to check many more designs, and the search can,
therefore, take longer to run. You can limit the search time
with the TIME= option in the PROC FACTEX statement.
In five of the cases (2^{106}_{III}, 2^{72}_{IV}, 2^{83}_{IV},
2^{94}_{IV},
and 2^{103}_{V}), the MINABS option is required to construct a
design with minimum aberration, and in two cases (2^{95}_{III},
2^{93}_{IV}), the NOCHECK option is required as well.
If the FACTEX procedure is
given a sufficiently large amount of time to run, specifying both the MINABS and
the NOCHECK options will always result in a minimum aberration design.
However, with the default search time of 60 seconds, there are
three cases (2^{105}_{IV}, 2^{104}_{IV}, and 2^{115}_{IV})
for which the FACTEX procedure is unable to find the minimum aberration design, even
with both the MINABS and NOCHECK options specified.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.