__WHEN DO YOU USE A FACTORIAL DESIGN?__

Factorial designs are good preliminary experiments

- A type of factorial design, known as the fractional factorial design, are often used to find the “vital few” significant factors out of a large group of potential factors.
- This is also known as a screening experiment
- ¢Also used to determine curvature of the response surface

__FULL FACTORIAL DESIGNS__

- Every combination of factor levels (i.e., every possible treatment) is measured.

2^{k} design = k factors, each with 2 levels, 2^{k }total runs

3^{3} design = 3 factors, each with 3 levels, 3^{3} = 27 total runs

- Every factor effect can be estimated
- Can include centre points, but not necessary
- 2
^{k}designs are the most popular

High Level (+1) and Low Level (-1)

Example: 2^{2 }design = 4 runs

Run Factor A Level Factor B Level

1 -1 -1

2 -1 +1

3 +1 -1

4 +1 +1

FULL FACTORIAL DESIGNS

Full factorials can also allow factors to have different number of levels

2^{1}3^{2}4^{1} = 4 factors total (sum of exponents) One factor has 2 levels, two have 3 levels, one has 4 levels Total of 2*3*3*4 = 72 runs

Ex. 2^{1}3^{1} design = 6 runs

Run Factor A Level Factor B Level

1 1 1

2 1 2

3 1 3

4 2 1

5 2 2

6 2 3

For previous DOE Definition you can click