# How can I make DOE design?

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sewook on 27 Jan 2016
Answered: Tom Lane on 28 Jan 2016
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) ?

Tom Lane on 28 Jan 2016
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.

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