Fractional factorial design generators
generators = fracfactgen(terms)
generators = fracfactgen(terms,k)
generators = fracfactgen(terms,k,R)
generators = fracfactgen(terms,k,R,basic)
generators = fracfactgen(terms) uses
the Franklin-Bailey algorithm to find generators for the smallest
two-level fractional-factorial design for estimating linear model
terms specified by
a string consisting of words formed from the
Z, separated by spaces.
'a'-'z' for the first 26 factors, and, if necessary,
the remaining factors. For example,
terms = 'a b c ab ac'.
Single-character words indicate main effects to be estimated; multiple-character
words indicate interactions. Alternatively,
an m-by-n matrix of
1s where m is the number
of model terms to be estimated and n is the number
of factors. For example, if
terms contains rows
1 0 0] and
[1 0 0 1], then the factor
the interaction between factors
included in the model.
generators is a cell array
of strings with one generator per cell. Pass
fracfact to produce the fractional-factorial
design and corresponding confounding pattern.
generators = fracfactgen(terms,k) returns
generators for a two-level fractional-factorial design with 2
if possible. If
the smallest design.
generators = fracfactgen(terms,k,R) finds
a design with resolution
R, if possible. The default
A design of resolution R is one in which no n-factor interaction is confounded with any other effect containing less than R – n factors. Thus a resolution III design does not confound main effects with one another but may confound them with two-way interactions, while a resolution IV design does not confound either main effects or two-way interactions but may confound two-way interactions with each other.
fracfactgen is unable to find a design
at the requested resolution, it tries to find a lower-resolution design
sufficient to calibrate the model. If it is successful, it returns
the generators for the lower-resolution design along with a warning.
If it fails, it returns an error.
generators = fracfactgen(terms,k,R,basic) also
accepts a vector
basic specifying the indices of
factors that are to be treated as basic. These factors receive full-factorial
treatments in the design. The default includes factors that are part
of the highest-order interaction in
Suppose you wish to determine the effects of four two-level
factors, for which there may be two-way interactions. A full-factorial
design would require 24 = 16 runs. The
finds generators for a resolution IV (separating main effects) fractional-factorial
design that requires only 23 = 8 runs:
generators = fracfactgen('a b c d',3,4) generators = 'a' 'b' 'c' 'abc'
The more economical design and the corresponding confounding
pattern are returned by
[dfF,confounding] = fracfact(generators) dfF = -1 -1 -1 -1 -1 -1 1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 1 -1 1 1 -1 -1 1 1 1 1 confounding = 'Term' 'Generator' 'Confounding' 'X1' 'a' 'X1' 'X2' 'b' 'X2' 'X3' 'c' 'X3' 'X4' 'abc' 'X4' 'X1*X2' 'ab' 'X1*X2 + X3*X4' 'X1*X3' 'ac' 'X1*X3 + X2*X4' 'X1*X4' 'bc' 'X1*X4 + X2*X3' 'X2*X3' 'bc' 'X1*X4 + X2*X3' 'X2*X4' 'ac' 'X1*X3 + X2*X4' 'X3*X4' 'ab' 'X1*X2 + X3*X4'
The confounding pattern shows, for example, that the two-way
confounded by the two-way interaction between
 Box, G. E. P., W. G. Hunter, and J. S. Hunter. Statistics for Experimenters. Hoboken, NJ: Wiley-Interscience, 1978.