5.3.3.3. Full factorial designs

5. Process Improvement
5.3. Choosing an experimental design
5.3.3. How do you select an experimental design?

5.3.3.3. Full factorial designs

A design where every setting of every factor appears with every setting of every other factor - is a full factorial design

Full-factorial designs in two levels

A basic experimental design is one with all input factors set at two levels each. These levels are called ‘high’ and ‘low’ or ‘+1’ and ‘-1’ respectively. A design with all possible high/low combinations of all the input factors is called a full factorial design in two levels.

If there are k factors, each at 2 levels, a full factorial design has 2^k runs.

**TABLE 3.2 Number of Runs for a 2^k Full Factorial**
Number of Factors	Number of Runs
2	4
3	8
4	16
5	32
6	64
7	128

As shown by the above table, when the number of factors is 5 or greater, a full factorial design requires a large number of runs and is not very efficient. As recommended in the Design Guideline Table, a fractional factorial design, or a Plackett-Burman design is a better choice for 5 or more factors.