To illustrate a fraction, consider an experiment with six factors and suppose that the
engineer is interested primarily in main effects but would also like to get some information
about the two-factor interactions. A 26−1 design would require 32 runs and would have 31
degrees of freedom for estimation of effects. Since there are only 6 main effects and 15 twofactor
interactions, the one-half fraction is inefficient—it requires too many runs. Suppose we
consider a fraction, or a 26−2 design. This design contains 16 runs and with 15 degrees of
freedom will allow estimation of all six main effects, with some capability for examination of
the two-factor interactions. To generate this design we would write down a 24 design in the
factors A, B, C, and D, and then add two columns for E and F. Refer to Table 13.22. To find
the new columns, we would select the two design generators I = ABCE and I = BCDF. Thus,
column E would be found from E = ABC and column F would be F = BCD. Thus, columns
ABCE and BCDF are equal to the identity column. However, we know that the product of any
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