Foldover design

The foldover design for the Plackett-Burman design in Table 14.9. 

An 11-factor Plackett-Burman design with foldover. 

Hint row 8 of this design and row 8 of the saturated fractional factorial design in Table 14.7 suggest that the reflection or foldover must be carried out first. Repetitions of switching one row with another, and switching one column with another, will eventually yield the desired result. Retain the identities of the rows and columns. 

In a classic reference, Box and Hunter (1961) noted that foldover designs comprised of pairs of runs that are mirror images of each other, for example ... 

Diamond, N. T. (1995). Some properties of a foldover design. Australian Journal of Statistics, 37, 345-352. 

Two-Factor Interactions and Foldover Designs in Sequential Bifurcation... 

The foldover design does not enable us to estimate individual interactions, but it does enable us to estimate whether interactions are important, as follows. We estimate the main effects from the original scenarios as in Section 2.3, ignoring the mirror scenarios. If the analyses of the foldover design and of the original ... 

This happens in two kinds of circumstances. The first may be involuntary, when the experiments are carried out sequentially, in two or several stages. This may be for reasons of economy, when a preliminary fractional factorial experiment has been carried out and a complementary design added some time later, to clarify the ambiguities in estimations of the main and interaction effects. The extrusion-spheronization experiment where a 2 design was followed by a second 2 foldover design is an example of this. 

Similarly, for the second part of the design, 6 is a generator, so we combine this with the defining relation already established for the 2 foldover design in section... 

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