### WHEN DO YOU USE A FACTORIAL DESIGN? 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.
2k design = k factors, each with 2 levels, 2k total runs

33 design = 3 factors, each with 3 levels, 33 = 27 total runs

Every factor effect can be estimated
Can include centre points, but not necessary
2k designs are the most popular
High Level (+1) and Low Level (-1)

Example: 22 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

213241 = 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. 2131 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

What is Design of Experiment