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Each generator halves the number of runs required. A design with p such generators is a 1/(l p)=l −p fraction of the full factorial design. [3] For example, a 2 5 − 2 design is 1/4 of a two-level, five-factor factorial design.
If N is a power of 2, however, the resulting design is identical to a fractional factorial design, so Plackett–Burman designs are mostly used when N is a multiple of 4 but not a power of 2 (i.e. N = 12, 20, 24, 28, 36 …). [3]
In a fractional factorial design only a subset of treatment combinations are used. An orthogonal array can be used to design a fractional factorial experiment. The columns represent the various factors and the entries are the levels at which the factors are observed.
A full factorial design contains all possible combinations of low/high levels for all the factors. A fractional factorial design contains a carefully chosen subset of these combinations. The criterion for choosing the subsets is discussed in detail in the fractional factorial designs article. Formalized by Frank Yates, a Yates analysis exploits ...
A fractional factorial design is said to have resolution if every -factor effect [note 4] is unaliased with every effect having fewer than factors. For example, a design has resolution R = 3 {\displaystyle R=3} if main effects are unaliased with each other (taking p = 1 ) {\displaystyle p=1)} , though it allows main effects to be aliased with ...
Factorial experimental design software drastically simplifies previously laborious hand calculations needed before the use of computers. During World War II, a more sophisticated form of DOE, called factorial design, became a big weapon for speeding up industrial development for the Allied forces. These designs can be quite compact, involving a
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The design with 7 factors was found first while looking for a design having the desired property concerning estimation variance, and then similar designs were found for other numbers of factors. Each design can be thought of as a combination of a two-level (full or fractional) factorial design with an incomplete block design. In each block, a ...