CatalogueAccessors {FrF2}

Catalogue file and accessor functions

Description

Functions to select elements or extract information from design catalogues of class catlg

Usage

res(catlg)
## S3 method for class 'catlg'
res(catlg)
## S3 method for class 'character'
res(catlg)
nruns(catlg)
## S3 method for class 'catlg'
nruns(catlg)
## S3 method for class 'character'
nruns(catlg)
nfac(catlg)
## S3 method for class 'catlg'
nfac(catlg)
## S3 method for class 'character'
nfac(catlg)
WLP(catlg)
## S3 method for class 'catlg'
WLP(catlg)
## S3 method for class 'character'
WLP(catlg)
nclear.2fis(catlg)
## S3 method for class 'catlg'
nclear.2fis(catlg)
## S3 method for class 'character'
nclear.2fis(catlg)
clear.2fis(catlg)
## S3 method for class 'catlg'
clear.2fis(catlg)
## S3 method for class 'character'
clear.2fis(catlg)
all.2fis.clear.catlg(catlg)
dominating(catlg)
## S3 method for class 'catlg'
dominating(catlg)
## S3 method for class 'character'
dominating(catlg)
catlg
## S3 method for class 'catlg'
catlg[i]
## S3 method for class 'catlg'
print(x, name="all", nruns="all", nfactors="all", 
                        res.min=3, MaxC2=FALSE, show=10, 
                        gen.letters=FALSE, show.alias=FALSE, ...)
block.catlg

Arguments

catlg

Catalogue of designs of class catlg (cf. details section), or character vector with name(s) of catlg element(s) in case of accessor functions

i

vector of index positions or logical vector that can be used for indexing a catlg object

x

an object of class catlg

name

character vector of entry names from x; default “all” means: no selection made

nruns

numeric integer (vector), giving the run size(s) for entries of x to be shown; default “all” means: no selection made

nfactors

numeric integer (vector), giving the factor number(s) for entries of x to be shown; default “all” means: no selection made

res.min

numeric integer giving the minimum resolution for entries of x to be shown

MaxC2

logical indicating whether designs are ordered by minimum aberration (default, MaxC2=FALSE) or by maximum number of clear 2fis (MaxC2=TRUE)

show

integer number indicating maximum number of designs to be shown; default is 10

gen.letters

logical indicating whether the generators should be shown as column numbers (default, gen.letters=FALSE) or as generators with factor letters (e.g. E=ABCD, gen.letters=TRUE)

show.alias

logical indicating whether the alias structure (up to 2fis) is to be printed

...

further arguments to function print

block.catlg

data frame with block generators for full factorial designs up to 256~runs, taken from Sun, Wu and Chen (1997)

Details

The class catlg is a named list of design entries. Each design entry is again a list with the following items:

res

resolution, numeric, i.e. 3 denotes resolution III and so forth

nfac

number of factors

nruns

number of runs

gen

column numbers of additional factors in Yates order

WLP

word length pattern (starting with words of length 1, i.e. the first two entries are 0 for all designs in catlg)

nclear.2fis

number of clear 2-factor interactions (i.e. free of aliasing with main effects or other 2-factor interactions)

clear.2fis

2xnclear.2fis matrix of clear 2-factor interactions (clear to be understood in the above sense); this matrix represents each designs clear interaction graph, which can be used in automated searches for designs that can accomodate (i.e. clearly) a certain requirement set of 2-factor interactions; cf. also estimable.2fis

all.2fis.clear

vector of factors with all 2-factor interactions clear in the above sense

dominating

logical that indicates whether the current design adds a CIG structure that has not been seen for a design with less aberration (cf. Wu, Mee and Tang 2012 p.196 for dominating designs); TRUE, if so; FALSE, if current CIG is isomorphic to previous one or has no edges (IMPORTANT: the dominance assessment refers to the current catalogue; for designs with more than 64 runs, it is possible that a design marked dominating in catalogue catlg is not dominating when considering ALL non-isomorphic designs).
This element is helpful in omitting non-promising designs from a search for a clear design.
This element may be missing. In that case, all catalogue entries are assumed dominating.

Reference to factors in components clear.2fis and all.2fis.clear is via their position number (element of (1:nfac)).

The print function for class catlg gives a concise overview of selected designs in any design catalogue of class catlg. It is possible to restrict attention to designs with certain run sizes, numbers of factors, and/or to request a minimum resolutions. Designs are ordered in decreasing quality, where the default is aberration order, but number of clear 2fis can be requested alternatively. The best 10 designs are displayed per default; this number can be changed by the show option. Options gen.letters and show.alias influence the style and amount of printed output.

The catalogue catlg, which is included with package FrF2, is of class catlg and is a living object, since it has to be updated with recent research results for larger designs. In particular, new MA designs may be found, or it may be proven that previous “good” designs are in fact of minimum aberration.

Currently, the catalogue contains

• the Chen, Sun and Wu (1993) 2-level designs (complete list of 2-level fractional factorials from 4 to 32~runs, complete list of resolution IV 2-level fractional factorials with 64~runs). Note that the Chen Sun Wu paper only shows a selection of the 64~run designs, the complete catalogue has been obtained from Don Sun and is numbered according to minimum aberration (lower number = better design); numbering in the paper is not everywhere in line with this numbering.

• minimum aberration (MA) resolution III designs for 33 to 63 factors in 64 runs. The first few of these have been obtained from Appendix G of Mee 2009, the designs for 38 and more factors have been constructed by combining a duplicated minimum aberration design in 32 runs and the required number of factors with columns 32 to 63 of the Yates matrix for 64 run designs. Using complementary design theory (cf. e.g. Chapter 6.2.2 in Mee 2009), it can be shown that the resulting designs are minimum aberration (because they are complementary to basically the same designs as the designs in 32 runs on which they are based). The author is grateful to Robert Mee for pointing this out.

• the MA designs in 128 runs:

  • for up to 24 factors obtained from Xu (2009),

  • for 25 to 64 factors taken from Block and Mee (2005, with corrigendum 2006),

  • for 65 to 127 factors (resolution III): up to 69 factors coming from Appendix G in Mee, whereas the designs for 70 or more factors have been constructed according to the same principle mentioned for the 64 run designs.

• various further “good” resolution IV designs in 128 runs obtained by evaluating designs from the complete catalogue by Xu (2009, catalogue on his website) w.r.t. aberration and number of clear 2fis (including also all designs that yield minimum aberration clear compromise designs according to Groemping 2010); all designs with resolution at least IV for up to 11 factors have been added with version 2.2.

• the MA even designs in 128 runs, in support of blocking according to the Godolphin approach have been added with version 2.2.

  Note that additional non-isomorphic resolution IV designs in 128 runs are available in package (FrF2.catlg128); since the catalogues are quite large, they are not forced upon users of this package who do not need them. Since version 1.1 of that package, the catalogues are not complete but contain high resolution fractions and even/odd fractions only (status: version 1.2-x); re-inclusion of at least selected even fractions is intended, because these may yield improved support of blocking in connection with estimable 2fis.

• the best (MA) resolution IV or higher designs in
  256 runs for up to 36 factors (resolution V up to 17 factors),
  512 runs for up to 29 factors (resolution V for up to 23 factors).
  These have been taken from Xu (2009) with additions by Ryan and Bulutoglu (2010).

• Further “good” resolution IV designs with up to 80 factors in 256 runs and up to 160 factors in 512 runs have also been implemented from Xu (2009).

• the best (MA) resolution V or higher design for each number of factors or a “good” such design (if it is not known which one is best) in
  1024 runs (up to 33 factors, MA up to 28 factors, resolution VI up to 24 factors),
  2048 runs (up to 47 factors, MA up to 32 factors, resolution VI up to 34 factors),
  and 4096 runs (up to 65 factors, MA up to 26 factors, resolution VI up to 48 factors).
  

  Most of the large designs in catlg have been taken from Xu (2009), where complete catalogues of some scenarios are provided (cf. also his website) as well as “good” (not necessarily MA) designs for a larger set of situations. Some of the good designs by Xu (2009) have later been shown to be MA by Ryan and Bulutoglu (2010), who also found some additional larger MA designs, which are also included in catlg. Non-MA designs that were already available before Bulutoglu (2010) are still in the catalogue with their old name. (Note that designs that are not MA and cannot be placed in the ranking do not have a running number in the design name; for example, the MA 2048 runs design in 28 factors is named 28-17.1, the older previous design that was not MA is named 28-17 (without “.1” or another placement, because the designs position in the ranking of all designs is not known.))

There are also some non-regular 2-level fractional factorial designs of resolution V which may be interesting, as it is possible to increase the number of factors for which resolution V is possible (cf. Mee 2009, Chapter 8). These are part of package DoE.base, which is automatically loaded with this package. With versions higher than 0.9-14 of that package, the following arrays are available:
L128.2.15.8.1, which allows 4 additional factors and blocking into up to 8 blocks
L256.2.19, which allows just 2 additonal factors
L2048.2.63, which allows 16 additional factors. These non-regular arrays should be fine for most purposes; the difference to the arrays generated by function FrF2 lies in the fact that there is partial aliasing, e.g. between 3-factor interactions and 2-factor interactions. This means that an affected 3-factor interaction is partially aliased with several different 2-factor interactions rather than being aliased either fully or not at all.

Value

[ selects a subset of designs based on i, which is again a list of class catlg, even if a single element is selected. res, nruns, nfac, nclear.2fis and dominating return a named vector, the print method does not return anything (i.e. it returns NULL), and the remaining functions return a list.

Author(s)

Ulrike Groemping

References

Block, R. and Mee, R. (2005) Resolution IV Designs with 128 Runs Journal of Quality Technology 37, 282-293.

Block, R. and Mee, R. (2006) Corrigenda Journal of Quality Technology 38, 196.

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

Groemping, U. (2012). Creating clear designs: a graph-based algorithm and a catalog of clear compromise plans. IIE Transactions 44, 988-1001. doi: 10.1080/0740817X.2012.654848. Early preprint at http://www1.bht-berlin.de/FB_II/reports/Report-2010-005.pdf.

Mee, R. (2009). A Comprehensive Guide to Factorial Two-Level Experimentation. New York: Springer.

Ryan, K.J. and Bulutoglu, D.A. (2010). Minimum Aberration Fractional Factorial Designs With Large N. Technometrics 52, 250-255.

Sun, D.X., Wu, C.F.J. and Chen, Y.Y. (1997). Optimal blocking schemes for 2^p and 2^{n-p} designs. Technometrics 39, 298-307.

Wu, H., Mee, R. and Tang, B. (2012). Fractional Factorial Designs With Admissible Sets of Clear Two-Factor Interactions. Technometrics 54, 191-197.

Xu, H. (2009) Algorithmic Construction of Efficient Fractional Factorial Designs With Large Run Sizes. Technometrics 51, 262-277.

See Also

See also FrF2, oa.design

Examples

c8 <- catlg[nruns(catlg)==8]
nclear.2fis(c8)
clear.2fis(c8)
all.2fis.clear.catlg(c8)

## inspecting a specific catalogue element
clear.2fis("9-4.2")

## usage of print function for inspecting catalogued designs
## the first 10 resolution V+ designs in catalogue catlg
print(catlg, res.min=5)
## the 10 resolution V+ designs in catalogue catlg with the most factors
## (for more than one possible value of nfactors, MaxC2 does usually not make sense)
print(catlg, res.min=5, MaxC2=TRUE)

## designs with 12 factors in 64 runs (minimum resolution IV because 
## no resolution III designs of this size are in the catalogue)
## best 10 aberration designs
print(catlg, nfactors=12, nruns=64)
## best 10 clear 2fi designs
print(catlg, nfactors=12, nruns=64, MaxC2=TRUE)
## show alias structure
print(catlg, nfactors=12, nruns=64, MaxC2=TRUE, show.alias=TRUE)
## show best 20 designs
print(catlg, nfactors=12, nruns=64, MaxC2=TRUE, show=20)

## use vector-valued nruns 
print(catlg, nfactors=7, nruns=c(16,32))
## all designs (as show=100 is larger than available number of designs)
##    with 7 or 8 factors in 16 runs
print(catlg, nfactors=c(7,8), nruns=16, show=100)

## the irregular resolution V arrays from package DoE.base (from version 0.9-17)
## designs can be created from them using function oa.design
## Not run: 
## not run in case older version of DoE.base does not have these
length3(L128.2.15.8.1)
length4(L128.2.15.8.1)  ## aliasing of 2fis with block factor
length4(L128.2.15.8.1[,-16])

length3(L256.2.19)
length4(L256.2.19)

##length3(L2048.2.63) 
##length4(L2048.2.63) do not work resource wise
## but the array is also resolution V (but irregular)

## End(Not run)