Functions to select elements or extract information from design catalogues of class catlg
res(catlg)
# S3 method for catlg
res(catlg)
# S3 method for character
res(catlg)
nruns(catlg)
# S3 method for catlg
nruns(catlg)
# S3 method for character
nruns(catlg)
nfac(catlg)
# S3 method for catlg
nfac(catlg)
# S3 method for character
nfac(catlg)
WLP(catlg)
# S3 method for catlg
WLP(catlg)
# S3 method for character
WLP(catlg)
nclear.2fis(catlg)
# S3 method for catlg
nclear.2fis(catlg)
# S3 method for character
nclear.2fis(catlg)
clear.2fis(catlg)
# S3 method for catlg
clear.2fis(catlg)
# S3 method for character
clear.2fis(catlg)
all.2fis.clear.catlg(catlg)
dominating(catlg)
# S3 method for catlg
dominating(catlg)
# S3 method for character
dominating(catlg)
catlg
# S3 method for catlg
[(catlg,i)
# S3 method for catlg
print(x, name="all", nruns="all", nfactors="all",
res.min=3, MaxC2=FALSE, show=10,
gen.letters=FALSE, show.alias=FALSE, ...)
block.catlg[ 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.
Catalogue of designs of class catlg (cf. details section), or character vector with name(s) of catlg element(s) in case of accessor functions
vector of index positions or logical vector that can be used for indexing a catlg object
an object of class catlg
character vector of entry names from x; default “all” means: no selection made
numeric integer (vector), giving the run size(s) for entries of x to be shown;
default “all” means: no selection made
numeric integer (vector), giving the factor number(s) for entries of x to be shown;
default “all” means: no selection made
numeric integer giving the minimum resolution for entries of x to be shown
logical indicating whether designs are ordered by minimum aberration (default, MaxC2=FALSE)
or by maximum number of clear 2fis (MaxC2=TRUE)
integer number indicating maximum number of designs to be shown; default is 10
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)
logical indicating whether the alias structure (up to 2fis) is to be printed
further arguments to function print
data frame with block generators for full factorial designs up to 256~runs, taken from Sun, Wu and Chen (1997)
Ulrike Groemping
The class catlg is a named list of design entries.
Each design entry is again a list with the following items:
resolution, numeric, i.e. 3 denotes resolution III and so forth
number of factors
number of runs
column numbers of additional factors in Yates order
word length pattern (starting with words of length 1,
i.e. the first two entries are 0 for all designs in catlg)
number of clear 2-factor interactions (i.e. free of aliasing with main effects or other 2-factor interactions)
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
vector of factors with all 2-factor interactions clear in the above sense
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.
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. tools:::Rd_expr_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 FrF2, oa.design
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
if (FALSE) {
## 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)
}
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