5. Process Improvement
5.3. Choosing an experimental design
5.3.3. How do you select an experimental design?
5.3.3.4. Fractional factorial designs

## Summary tables of useful fractional factorial designs

Useful fractional factorial designs for up to 10 factors are summarized here There are very useful summaries of two-level fractional factorial designs for up to 11 factors, originally published in the book Statistics for Experimenters by G.E.P. Box, W.G. Hunter, and J.S. Hunter (New York, John Wiley & Sons, 1978) and also given in the book Design and Analysis of Experiments, 5th edition by Douglas C. Montgomery (New York, John Wiley & Sons, 2000).
Generator column notation can use either numbers or letters for the factor columns They differ in the notation for the design generators. Box, Hunter, and Hunter use numbers (as we did in our earlier discussion) and Montgomery uses capital letters according to the following scheme:
Notice the absence of the letter I. This is usually reserved for the intercept column that is identically 1. As an example of the letter notation, note that the design generator "6 = 12345" is equivalent to "F = ABCDE".
Details of the design generators, the defining relation, the confounding structure, and the design matrix TABLE 3.17 catalogs these useful fractional factorial designs using the notation previously described in FIGURE 3.7.

Clicking on the $$2_{R}^{k-p}$$ specification for a given design provides details (courtesy of Dataplot files) of the design generators, the defining relation, the confounding structure (as far as main effects and two-level interactions are concerned), and the design matrix. The notation used follows our previous labeling of factors with numbers, not letters.

Click on the design specification in the table below and a text file with details about the design can be viewed or saved
TABLE 3.17: Summary of Useful Fractional Factorial Designs
 Number of Factors, k Design Specification Number of Runs  N 3 2III3-1 4 4 2IV4-1 8 5 2V5-1 16 5 2III5-2 8 6 2VI6-1 32 6 2IV6-2 16 6 2III6-3 8 7 2VII7-1 64 7 2IV7-2 32 7 2IV7-3 16 7 2III7-4 8 8 2VIII8-1 128 8 2V8-2 64 8 2IV8-3 32 8 2IV8-4 16 9 2VI9-2 128 9 2IV9-3 64 9 2IV9-4 32 9 2III9-5 16 10 2V10-3 128 10 2IV10-4 64 10 2IV10-5 32 10 2III10-6 16 11 2V11-4 128 11 2IV11-5 64 11 2IV11-6 32 11 2III11-7 16 15 2III15-11 16 31 2III31-26 32