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L1592_Frame_C29 Page 268 Tuesday, December 18, 2001 2:48 PM

TABLE 29.6
Some Fractional Factorial Designs
Main Effects Second-Order
No. of Factors Design No. of Runs Resolution Interactions
3
3 2 8 OK OK
4–1
4 2 8 IV OK Confounded
5–2
5 2 8 III Confounded Confounded
6–3
6 2 8 III Confounded Confounded
7–4
7 2 8 III Confounded Confounded
4
4 2 16 OK OK
5–1
5 2 16 V OK OK
6–2
6 2 16 IV OK Confounded
7−3
7 2 16 IV OK Confounded
8–4
8 2 16 IV OK Confounded
9–5
9 2 16 III Confounded Confounded
10–6
10 2 16 III Confounded Confounded
9−4
9 2 32 IV OK Confounded
10−5
10 2 32 IV OK Confounded
11−6
11 2 32 IV OK Confounded
11−7
11 2 16 III Confounded Confounded
Note: Resolution V: All main effects and two-factor interactions can be estimated. No two-factor interactions
are confounded with other two-factor interactions or main effects. No main effects are confounded
with each other.
Resolution IV: No main effects are confounded with two-factor interactions or other main effects. Two-
factor interactions may be confounded with other two-factor interactions.
Resolution III: No main effects are confounded with other main effects. Main effects may be con-
founded with two-factor interactions.
The resolution of the design, indicated by roman numerals, describes the extent of confounding among
the main effects and the two-factor interactions. The higher the resolution, the better the main effects
and two-factor interactions can be estimated. The definitions are:
Main Effects are Two-Factor Interactions are
Design Resolution Confounded with: Confounded with:
III Two-factor interactions Main effects
IV Three-factor interactions Other two-factor interactions
V Four-factor interactions Three-factor interactions
VI Five-factor interactions Four-factor interactions
5−1
4−1
The 2 design used in the fly ash case study is a resolution V design. The 2 design used in Chapter 28
is a resolution IV design.
This chapter presented only the main ideas about confounding in fractional experimental designs. A
great deal more is worth knowing and Box et al. (1978) is worth careful study. “A Practical Aid for
Experimenters” (Bisgaard, 1987) summarizes more than 40 factorial and fractional designs and gives
the effects that can be estimated and their confounding arrangement.

References

Bisgaard, S. (1987). A Practical Aid for Experimenters, Madison, WI, Center for Quality and Productivity
Improvement, University of Wisconsin–Madison.
k–p
Box, G. E. P. and J. S. Hunter (1961). “The 2 Fractional Factorial Designs. Part I,” Technometrics, 3(3),
311–351.
© 2002 By CRC Press LLC