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 gen.

[X,conf] = fracfact(gen) also returns the confounding pattern for the design.

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

Examples

Fractional Factorial Design for Four Variables

Create 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 = 8×4

    -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

Six-Factor Design with Resolution IV

Find generators for a six-factor design that uses four factors and achieves resolution IV by using the fracfactgen function.

res = 4;
gen = fracfactgen("a b c d e f",4,res)

gen = 6×1 cell
    {'a'  }
    {'b'  }
    {'c'  }
    {'d'  }
    {'bcd'}
    {'acd'}

Create the two-level fractional factorial design defined by the generators.

x = fracfact(gen)

x = 16×6

    -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
      ⋮

Input Arguments

gen — Generators

string array | cell array of character vectors | string scalar | character vector

Generators for the smallest two-level fractional-factorial design, specified as one of the following values.

• A string array or a cell array of character vectors in which each element contains one word.

• A string scalar or character vector consisting of words separated by spaces.

Words are case-sensitive letters or groups of letters, where "a" represents value 1, "b" represents value 2, ..., "A" represents value 27, ..., and "Z" represents value 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.

Example: ["a" "b" "c" "abc"]

Example: {'a' 'b' 'c' 'abc'}

Example: "a b c abc"

Example: 'a b c abc'

Data Types: string | char

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: X = fracfact(gen,MaxInt=3) specifies the maximum level of interaction as 3.

FactorNames — Name for each factor

string array | cell array of character vectors

Name for each factor, specified as a string array or cell array of character vectors. By default, the factor names are {'X1','X2',...}.

Data Types: string | char

MaxInt — Maximum level of interaction

2 (default) | positive integer

Maximum level of interaction to include in the confounding output, specified as a positive integer.

Output Arguments

X — Two-level fractional factorial design

matrix

Two-level fractional factorial design, returned as 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 — Confounding pattern for the design

cell array of character vectors

Confounding pattern for the design, returned as a cell array of character vectors.

Alternative Functionality

Instead of using fracfact, you can create a fractionalFactorialDOE object by using the fractionalFactorialDOE function. The fractionalFactorialDOE function provides these advantages:

• The function allows you to specify the factor names, number of factors, categorical factors, experiment model, and number and values of the levels for each factor.

• In addition to returning the design runs, the function stores your specifications in the fractionalFactorialDOE object properties.

• After you create a fractionalFactorialDOE object, you can fit a linear model to the design runs using the fitlm function.

References

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

Version History

Introduced before R2006a