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 \(2^k\) runs.

TABLE 3.2 Number of Runs for a \(2^k\) Full Factorial

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. A fractional factorial design or a Plackett-Burman design is a better choice for 5 or more factors.