General factorial designs


This menu covers full factorial designs orthogonal main effects designs for cases for which not all factors are at two levels. Furthermore, Taguchi-parameter designs are covered. This help file is about how and when to apply these.

Quantitative or Qualitative

Both types of design are suitable for quantitative and qualitative factors alike. If you have quantitative factors only, you may want to consider the special menu for these.

Full factorial designs

Full factorial designs are straight-forward to generate and are generated by function from package DoE.base. The number of runs needed for a full factorial experiment is the product of the numbers of levels of all factors. This may be more than is feasible. In such situations, the orthogonal main effects plans may be helpful. If interactions are also of interest, it may be useful to combine several plans or to pay attention to specific properties of orthogonal arrays (automatic support for such possibilities is currently poor and will be improved in the future).
Full factorial designs can be run in blocks. This is advisable, whenever the experimental units are not homogeneous, but smaller groups of units (the blocks) can be made reasonably homogeneous (e.g., batches of material, etc.).

Orthogonal main effects plans

If a full factorial experiment is too large, an orthogonal main effects plan may be useful. As long as there are no interactions between the factors represented by columns of the array, all such arrays work well, provided they are large enough for stable estimation. Some arrays also work well in the presence of interactions or even allow estimation of interactions for special subsets of variables. However, there is no automated support for selection of an array that has desirable properties. It may therefore be useful to specifically select an array the properties of which are known to the experimenter.


Important: For all factorial designs, the experiment must conduct all experimental runs as determined in the design, because the design properties will deteriorate in ways not easily foreseeable, if some combinations are omitted.

It must be carefully considered in the planning phase, whether it is possible to conduct all experimental runs, or whether there might be restrictions that do not permit all combinations to be run (e.g.: three factors, each with levels “small” and “large”, where the combination with all three factors at level “large” is not doable because of space restrictions). If such restrictions are encountered, the design should be devised in a different way from the beginning. If possible, reasonable adjustments to levels should ensure that a factorial design becomes feasible again. Alternatively, a non-orthogonal D-optimal design can take the restrictions into account. Unfortunately, this functionality is not yet implemented in this GUI.

Taguchi inner-outer array designs - also called parameter designs

With the menu item Create Taguchi inner-outer array, two existing designs can be combined into a crossed inner-outer array design. For more detail, see the literature and the help in the Taguchi design menu.


Ulrike Groemping


Box G. E. P, Hunter, W. C. and Hunter, J. S. (2005) Statistics for Experimenters, 2nd edition. New York: Wiley.

See Also

See Also pb for the function behind the screening designs, FrF2 for the function behind the regular fractional factorial designs, and catlg for a catalogue of regular fractional factorial designs, and DoEGlossary for a glossary of terms relevant in connection with orthogonal 2-level factorial designs.

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