Design of experiments (DOE)
Steps
Define problem
Define experimental objectives
Select factors that influence quality
Select control & noise factors
Select levels for factors
Select orthogonal arrays
Select interactions
Conduct tests
Analyze results
Design of experiments (DOE)
Breadmaking problem:
Level
Factor
1
2
1.
flour21/3 cups all-purpose
2.
sugar
2 Tsp
21/2 Tsp
3.
salt
1 tsp
1/2
4.
butter
1 Tsp
1 Tsp margarine
5.
milk 1 cup homogenized
6.
dry yeast
1 tsp brand A
21/3 cups special
tsp
1 cup low-fat
1 tsp brand B
Design of experiments (DOE)
How many loaves of bread to get "best" set of
ingredients?
6 factors, each w/ 2 levels ––> 26 = 64!
Taguchi method (Genechi Taguchi) says only a
few needed
Design of experiments (DOE)
Testing methods
Factors and factor levels
Trial
A
B
C
D
1.
1
1
1
1
2.
2
1
1
1
3.
1
2
1
1
4.
1
1
2
1
5.
1
1
1
2
Design of experiments (DOE)
Testing methods
Factors and factor levels
Trial
A
B
C
1.
1
1
1
2.
1
2
2
3.
2
1
2
4.
2
2
1
Better…….."orthogonal"
Standard L4 orthogonal array
Design of experiments (DOE)
Which OA to use? Depends on:
# of factors & interactions
# of levels for each factor
Use L4, L8(7 factors), L12(11 factors), L16(15
factors),…..OAs - determined by # trials to be
run
# of levels usually 2 or 3
Design of experiments (DOE)
Some factors may interact. Then:
Factors and factor levels
Trial
A
B
C(=AxB)
1.
1
1
1
2.
1
2
2
3.
2
1
2
4.
2
2
1