Fold-over design

Fold-over design to resolve main effects from confoundings with two-variable interactions... 

Mirror the first design in its bottom line. Switch the signs of the last row and write it as the first row in the fold-over design. Do the same with the last but one row and write it as the second row in the fold-over design etc. This gives the result shown on the next page. 

Example Fold-over design. Rearrangement of n-pentane in... 

The original paper [5] reports several responses. To show the principles of a fold-over design, only one response, the reported initial rate of formation of isopentane,... 

The experiments are summarized in Table 6.5. Experiments number 1-8 form the first design, and experiments number 9-16 form the fold-over design. 

The above method must be used to elucidate the confounding pattern of Plackett-Burman designs. It is seen, that a fold-over design would separate the main effects from confounding with the two-variable interactions. A fold-over design would switch the signs of the Xj matrix and hence switch the signs of the alias matrix... 

A modification of these coloring systems has recently been developed that leads to more sensitive detection. Chemiluminescent substrates have been designed that are converted by the enzymes to products that generate a light signal that can be captured on photographic film. This increases the level of sensitivity about 1000-fold over standard color detection methods. 

Miller, A. and Sitter, R. R. (2001). Using the folded-over 12-run Plackett-Burman designs to consider interactions. Technometrics, 43, 44—55. 

Resolution III designs can be constructed to accomodate three variables in four runs, up to seven variables in eight runs etc. Such designs can be augmented to Resolution IV designs by fold-over. Resolution IV designs are useful, since they make it possible to detect presence of strong interaction effects. 

With more than eight variables it is probably more practical to use a Resolution III design first, and run a complementary fraction by fold-over. 

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