FrF2 {FrF2}R Documentation

Function to provide regular Fractional Factorial 2-level designs

Description

Regular fractional factorial 2-level designs are provided. Apart from obtaining the usual minimum aberration designs in a fixed number of runs, it is possible to request highest number of free 2-factor interactions instead of minimum aberration or to request the smallest design that fulfills certain requirements (e.g. resolution V with 8 factors).

Usage

FrF2(nruns = NULL, nfactors = NULL, factor.names = if (!is.null(nfactors)) {
        if (nfactors <= 50) Letters[1:nfactors] else 
                             paste("F", 1:nfactors, sep = "")} else NULL, 
        default.levels = c(-1, 1), generators = NULL, resolution = NULL, 
        estimable = NULL, max.nfree2fis = FALSE, 
        randomize = TRUE, seed = NULL, ...)

Arguments

nruns Number of runs, must be a power of 2, if given.
The number of runs can also be omitted. In that case, the function looks for the smallest design of the requested resolution that accomodates nfactors factors.
nfactors The number of 2-level factors to be investigated. Can be omitted, if it is obvious from the factor.names or nruns together with generators.
factor.names a character vector of factor names (length up to nfactors) or a named list with names representing factor names and elements vectors of length 2 with factor levels for each factor. Elements can be empty strings. In this case, default levels are used for the respective factor.
default.levels default levels (vector of length 2) for all factors for which no specific levels are given
generators There are log2(nruns) basic factors the full factorial of which spans the design. The generators specify how the remaining factors are to be allocated to interactions of these.
Generators can be any of
a list of vectors with position numbers of basis factors (e.g. c(1,2,4) stands for the interaction between first, second and fourth basis factor)
a vector of character representations of these interactions (e.g. “ABD” stands for the same interaction as above)
a vector of columns numbers in Yates order (e.g. 11 stands for ABD)
resolution is the arabic numeral for the requested resolution of the design. FrF2 looks for a design with at least this resolution. A design with resolution III (resolution=3) confounds main effects with 2-factor interactions, a design with resolution IV confounds main effects with three-factor interactions or 2-factor interactions with each other, and designs with resolution V or higher are usually regarded as very strong, because all 2-factor interactions are unconfounded with each other and with main effects.
estimable Not yet implemented
max.nfree2fis logical, defaults to FALSE. If TRUE, maximizing the number of free 2-factor interactions takes precedence over minimizing aberration. Resolution is always considered first.
Most likely, features like this are going to change in the future.
randomize logical. If TRUE, the design is randomized. This is the default.
seed optional seed for the randomization process
... currently not used

Details

The function works on the basis of the catalogued designs by Chen, Sun and Wu (1993), which are available as catlg (a list object of class catlg). Various improvements are planned for the coming weeks and months, among others inclusion of replication / repeated measurement, blocking and split plot facilities (based on further catalogues), and inclusion of four-level factors. Also, it is planned to support specification of a model to be estimable, and input and output possibilities will be improved.

Please contact me with any suggestions you may have.

Value

Currently, value is a list with the following three elements

desnum Design matrix in -1/1 coding
design data frame with levels as requested
catentry list with one element, which is the entry of catlg on which the design is based

Author(s)

Ulrike Groemping

References

Chen, J., Sun, D.X. and Wu, C.F.J. (1993) A catalogue of 2-level and 3-level orthogonal arrays. International Statistical Review 61, 131-145.

See Also

See Also pb for non-regular fractional factorials according to Plackett-Burman and catlg for the Chen, Sun, Wu catalogue and some accessor functions.

Examples

## maximum resolution minimum aberration design with 4 factors in 8 runs
FrF2(8,4)
## the design with changed default level codes
FrF2(8,4, default.level=c("current","new"))
## the design with number of factors specified via factor names (standard level codes)
FrF2(8,factor.names=list(temp="",press="",material="",state=""))
## the design with changed factor names and factor-specific level codes
FrF2(8,4, factor.names=list(temp=c("min","max"),press=c("low","normal"),
     material=c("current","new"),state=c("new","aged")))
## three ways for custom specification of the same design
FrF2(8, generators = "ABC")
FrF2(8, generators = 7)
FrF2(8, generators = list(c(1,2,3)))
## more than one generator
FrF2(8, generators = c("ABC","BC"))
FrF2(8, generators = c(7,6))
FrF2(8, generators = list(c(1,2,3),c(2,3)))
## finding smallest design with resolution 5 in 7 factors
FrF2(nfactors=7, resolution=5)

## maximum resolution minimum aberration design with 9 factors in 32 runs
FrF2(32,9)[3]
## maximum number of free 2-factor interactions instead of minimum aberration
FrF2(32,9,max.nfree2fis=TRUE)[3]

[Package FrF2 version 0.9-1 Index]