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fracfact

Fractional factorial design

Syntax

X = fracfact(gen)
[X,conf] = fracfact(gen)
[X,conf] = fracfact(gen,Name,Value)

Description

X = fracfact(gen) creates the two-level fractional factorial design defined by the generator string gen.

[X,conf] = fracfact(gen) returns a cell array of strings containing the confounding pattern for the design.

[X,conf] = fracfact(gen,Name,Value) creates a fractional factorial designs with additional options specified by one or more Name,Value pair arguments.

Input Arguments

gen

Either a cell array of strings where each cell contains one "word," or a string consisting of "words" separated by spaces. "Words" consist of case-sensitive letters or groups of letters, where 'a' represents string 1, 'b' represents string 2, ..., 'A' represents string 27, ..., 'Z' represents string 52.

Each word defines how the corresponding factor's levels are defined as products of generators from a 2^K full-factorial design. K is the number of letters of the alphabet in gen.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

'FactorNames'

Cell array specifying the name for each factor.

Default: {'X1','X2',...}

'MaxInt'

Positive integer setting the maximum level of interaction to include in the confounding output.

Default: 2

Output Arguments

X

The two-level fractional factorial design. X is a matrix of size N-by-P, where

  • N = 2^K, where K is the number of letters of the alphabet in gen.

  • P is the number of words in gen.

Because X is a two-level design, the components of X are ±1. For the meaning of X, see Fractional Factorial Designs.

conf

Cell array of strings containing the confounding pattern for the design.

Examples

Generate a fractional factorial design for four variables, where the fourth variable is the product of the first three:

x = fracfact('a b c abc')

x =
    -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
 

Find generators for a six-factor design that uses four factors and achieves resolution IV using fracfactgen. Use the result to specify the design:

generators = fracfactgen('a b c d e f',4, ... % 4 factors
    4) % resolution 4

generators = 
    'a'
    'b'
    'c'
    'd'
    'bcd'
    'acd'

x = fracfact(generators)

x =
    -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    -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     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

References

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

See Also

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