fracfact - Fractional factorial design

Syntax

dfF = fracfact(generators) [dfF,confounding] = fracfact(generators)

Description

dfF = fracfact(generators) gives factor settings dfF for a two-level Box-Hunter-Hunter fractional factorial design specified by the generators in generators. generators is a string consisting of words formed from the letters a-z, separated by spaces. For example, generators = 'a b c ab ac'. Alternatively, generators is a cell array of strings with one word per cell, as returned by fracfactgen. Single-character words indicate basic factors, for which the design includes all full-factorial treatments. Multiple-character words indicate factors whose levels are limited by the design to products of the levels of component basic factors. dfF is m-by-n, where m is the number of treatments in the design and n is the number factors specified by generators.

[dfF,confounding] = fracfact(generators) also returns a cell array confounding that shows the confounding pattern among the main effects and the two-factor interactions.

Examples

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 fracfactgen function 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 fracfact:

[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 interaction between X1 and X2 is confounded by the two-way interaction between X3 and X4.

References

[1] Box, G. E. P., W. G. Hunter, and J. S. Hunter. Statistics for Experimenters. Hoboken, NJ: Wiley-Interscience, 1978.

fracfact - Fractional factorial design

Syntax

Description

Examples

References

See Also

Recommended Products