Foldover a Fractional Factorial Design

DESCRIPTION:

Foldover a fractional factorial design, to create a design with twice as many rows which typically increases the resolution of the original design.

USAGE:

foldover(object) 

REQUIRED ARGUMENTS:

object
an object of class "design".

VALUE:

An object of class "design" which is the original design folded over, i.e., a design with twice the number of rows than the original design.

DETAILS:

The first half of the returned design is identical to the original design, the second half is the first half with the levels reversed (i.e. the first level of each factor substituted for the second, and vice versa).

BACKGROUND:

A foldover design is created by taking each of the runs in the original design and reversing the signs (levels). A foldover design is typically used to "unconfound" a Resolution III design; that is, if you fold over a resolution III design, it becomes a resolution IV design.

This can be useful when the results from a first small experiment indicate that there are possibly many interactions which can then be separated from the main effects by running the second half of the folded over design.

A foldover of a twelve-run Plackett-Burman design, is a Resolution IV design. The resulting design has the desirable property that all two-factors interactions with the first factor are estimable (although these two-factor interactions are confounded with other two-factor interactions). Such designs can be useful alternatives to 32-run designs.

REFERENCES:

Box, G.E.P., Hunter, W.G., and Hunter, J.S. (1978). Statistics for Experimenters. New York: Wiley.

Box, G.E.P. and Wilson, K.B. (1951). On the experimental attainment of optimum conditions. J. Royal Statistical Society, Series B, 13. 1.

Haaland, P. D. (1989). Experimental Design in Biotechnology. New York: Marcel Dekker.

SEE ALSO:

, , , , .

EXAMPLES:

# foldover a 7 factor 8 run design to get a resolution III 
# design 
alias(design.digest('ff0708')) 
alias(foldover(design.digest('ff0708'))) 
# create a foldover of a Placket-Burman design 
pb12.des <- design.digest('pb1112') 
alias(pb12.des) 
pb12.des.fo <- foldover(pb12.des) 
alias(pb12.des.fo)