10 Two-level fractional factorial designs
As the number of factors grows, a full \(2^k\) design quickly becomes impractical, and most of its runs are spent estimating high-order interactions that the sparsity of effects principle says are negligible. A \(2^6\) design has \(64\) runs, but only \(6\) of its \(63\) degrees of freedom are for main effects and \(15\) for two-factor interactions. A fractional factorial design runs only a carefully chosen fraction of the combinations, and gives up information on the high-order interactions in exchange. These designs are the workhorse of screening experiments.
10.1 The one-half fraction
10.2 Resolution
10.3 Smaller fractions: the \(2^{k-p}\) design
10.4 Finding the generators of a given design
10.5 De-aliasing: the fold-over
10.6 Practice problems
10.2 Resolution
10.3 Smaller fractions: the \(2^{k-p}\) design
10.4 Finding the generators of a given design
10.5 De-aliasing: the fold-over
10.6 Practice problems
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