How can I make DOE design?

I have a question at statistics toolbox I would like to make DOE using fracfactgen and fracfact

For example, with 5 parameters (generator? I don't know the meaning of generator) under the 2 lever condition. To observe main effect (each a b c d e ) and interaction of 2 parameters(ab, ac, ad, ae, bc, bd, be, cd, ce ,de ) (I think it is okay to omit interaction of 3 parameters) How can I make DOE design using these functions (fracfactgen and fracfact) ?

Answer 1

[Tom Lane]

Here are two ways to do it. First, specify that you have 5 factors a-e and you want a resolution 5 design. Resolution 5 means you can estimate pairwise interactions as long as you are willing to assume the effects of three-way interactions are zero. This attempts to find the smallest design that meets these criteria.

>> fracfactgen('a b c d e', [], 5)
ans = 
    'a'
    'b'
    'c'
    'd'
    'abcd'

Alternatively you could request the specific model terms:

>> fracfactgen('a b c d e ab ac ad ae bc bd be cd ce de')
ans = 
    'a'
    'b'
    'c'
    'd'
    'abcd'

These "generators" define how the final design is created. In this case the first four factors a-d are generated in a full factorial fashion, so the entire design has 2^4=16 rows. The fifth factor is generated by multiplying together the other four, e=abcd.

>> fracfact(ans)
ans =
    -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

This design is only half as big as the 2^5=32 row full factorial, but is capable of estimating all of the terms listed as long as the effects of higher-order terms are zero.