Factorial DOEs
Factorial and reduced factorial DOEs are a large family of techniques indispensable in order to perform a good statistical analysis of the problem.
Full Factorial is a classical DOE for studying interactions between variables. It is suited for statistical analysis, since it gives all the information related to the influence of each variable and each interaction.
Reduced Factorial is useful for evaluating only the main effects of each variable: in fact higher-order interactions are not provided. But the great advantage is that this can be done with only a fraction of the evaluations needed by the expensive Full Factorial scheme.
Cubic Face Centered allows the computation of second order interactions. It is less expensive than a three levels Full Factorial.
Box-Behnken is similar to intent to the Cubic Face Centered: only the points arrangement is different.
Latin Square can compute a DOE with more than two or three variable levels. The advantage of this algorithm is that the number of computed designs does not depend on the number of variables, but only on the number of levels.