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Fractional designs are expressed using the notation l k − p, where l is the number of levels of each factor, k is the number of factors, and p describes the size of the fraction of the full factorial used. Formally, p is the number of generators; relationships that determine the intentionally confounded effects that reduce the number of runs ...
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 ...
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.
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
Designed experiments with full factorial design (left), response surface with second-degree polynomial (right) In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors.
Fractional factorial designs used in practice deliberately confound two-way and higher order interactions with lower order (typically main effects) estimates in order to make the design small: if the higher order interactions are non-zero then main effects are biased, with no way for the analyst to know or correct this ex post;