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The Full Factorial algorithm generates every possible combination of all the parameters.
A common Full Factoriall is one with all input variables set at two levels each (lower bound and upper bound). A design with all possible lower and upper combinations of all the input variables is called a "full factorial design in two levels".
The number of total experiments is given by:
where ni is the number of levels for ith variable and k the number of variables.
Figure 6.11. Full Factorial of 3 levels of 3 variables (27 experiments).This full factorial allows the computation of 2nd order interactions
For each variable The Number of Levels has to be defined.
The level must be an integer equal or greater than 2.
Even if the number of total designs is greater, the maximum number of experiments generated with this algorithm is limited to 64000.
This algorithm allows the estimation of how each variable affects the responses.
The disadvantage of this method is that the number of experiments grows dramatically with the number of variables. A full factorial is practical when less than five or six input variables are being analyzed. With more than five or six input variables, testing all combinations becomes too hard.
There are three ways to solve the above problem:
Reduce the number of levels for each variable, e.g., reduce ni to 2 levels.
Reduce the number of variables.
Use Section 6.1.7, "Reduced Factorial (Fractional Factorial)"reduced factorial design.
