Example 15.11: Resolution IV Design with Minimum Aberration

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 two-factor interactions. However, not all resolution IV designs are equivalent; you may be able to estimate more two-factor interactions with some than with others. Among all resolution IV designs, a design that allows you to estimate the maximum number of two-factor interactions is said to have minimum aberration.

For example, if you use the FACTEX procedure to generate a resolution IV two-level design in 32 runs for seven factors, you will be able to estimate all main effects and 15 of the 21 two-factor 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 2^7-2_IV Design

Aliasing Structure

ALIAS
a
b
c
d
e
f
g
ab = fg
a*c
a*d
a*e
af = bg
ag = bf
b*c
b*d
b*e
cd = eg
ce = dg
c*f
cg = de
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 two-factor 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 2^7-2_IV Design

Aliasing Structure

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
cd = ef
ce = df
cf = de
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 (2^10-6_III, 2^7-2_IV, 2^8-3_IV, 2^9-4_IV, and 2^10-3_V), the MINABS option is required to construct a design with minimum aberration, and in two cases (2^9-5_III, 2^9-3_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 (2^10-5_IV, 2^10-4_IV, and 2^11-5_IV) for which the FACTEX procedure is unable to find the minimum aberration design, even with both the MINABS and NOCHECK options specified.

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