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

Full factorial designs

Full factorial designs in two levels
A design in which every setting of every factor appears with every setting of every other factor is a full factorial design A common 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 2k runs.

TABLE 3.2  Number of Runs for a 2k Full Factorial
Number of Factors Number of Runs
2 4
3 8
4 16
5 32
6 64
7 128
Full factorial designs not recommended for 5 or more factors 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.
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