An "experiment" tests a theory or guides to a solution to a question. For example, "why are some products defective"?
Onefactor experiments test only one variable at a time. Onefactor experiments are much simpler than multifactor experiments; but they miss interactions and may require many cycles.
A simple onefactor experiment might be formalized in Example #1:
Onefactor design is least helpful if interactions cause the defects. For example: most people may consume from 1 to 3 standard drinks of alcohol without risking death. We might observe that people who have had no alcohol for several days may take a halfdose, full dose, or double dose of a specific medication and survive with no ill effects. However, people who had 2 or 3 drinks plus a double dose of the medication might die as a result.
Twolevel experiments have multiple variables. These are more complex than onefactor experiments.
Example #2:
One problem with twolevel experiments is "confounding" the test. From example #2, we have #2A:
Fullfactorial orthogonal design avoids the "confounding" problem: test all variables against all other variables. In example #2B, both operators use materials from both suppliers:
Test 
Operator 
Supplier 
Defect Rate 
1 
Adam 
1 
3% 
2 
Betty 
1 
4% 
3 
Adam 
2 
3% 
4 
Betty 
2 
2% 
5 
Adam 
3 
7% 
6 
Betty 
3 
6% 
It is clear that Supplier 3 is the major source of the defects.
An interaction would be indicated if the final row of the table were:
Test 
Operator 
Supplier 
Defect Rate 
~ 
~ 
~ 
~ 
6 
Betty 
3 
15% 
Here it seems that Betty has problems with Supplier 3's materials – an example of an interaction which cannot be found using a onefactor experiment.
Full factorial design tests all combinations of all expected factors. This may be expensive or timeconsuming. For example, a full factorial 3factor table, where factors a, b and c each have 2 values, would have 8 tests :
Test# 
Fa 
Fb 
Fc 
Result 
1 
a1 
b1 
c1 
R1 
2 
a2 
b1 
c1 
R2 
3 
a1 
b2 
c1 
R3 
4 
a2 
b2 
c1 
R4 
5 
a1 
b1 
c2 
R5 
6 
a2 
b1 
c2 
R6 
7 
a1 
b2 
c2 
R7 
8 
a2 
b2 
c2 
R8 
Twolevel fractional factorial design tests fewer combinations, usually to save on cost or time. For example, say that the above table represents too much testing. A full fractional 3factor table might be limited to 4 tests, where we limit interactions for factors a and b:
T# 
Fa 
Fb 
Fc 

Result 
1 
a1 
b1 
c1 

R1 

a2 
b1 
c1 
Ignore 
N/A 

a1 
b2 
c1 
Ignore 
N/A 
2 
a2 
b2 
c1 

R2 
3 
a1 
b1 
c2 

R3 

a2 
b1 
c2 
Ignore 
N/A 

a1 
b2 
c2 
Ignore 
N/A 
4 
a2 
b2 
c2 

R4 
In this example, there may be a known reason to avoid testing the (a1, b2) and (a2, b1) combinations. If time or cost constrains an experiment, there is no way to avoid missing some combinations.
The first experiment for an injection molding process might test three variables: temperature; pressure; and cooldown time. Set a "low", "medium" and "high" value to each variable. Run 3X3X3 = 27 experiments. The best results come from, let's say, the 4 tests with medium or high temperature and medium or long cooldown time.
This would indicate that a second experiment should focus on temperature and cooldown time with a different set of medium/high values.
The concept is to structure experiments to control the variables and use Analysis of Variance (ANOVA) techniques to determine which variables contribute most to the results. It permits multivariate experiments so that any interaction among variables might be observed.
Problems with obvious causes should have been resolved already.
To solve the harder problems, or to make other factbased improvements, it is vital to plan, perform and analyze tests in a systematic way. Design of Experiments (DOE) provides this methodology.
By Oskar Olofsson