Large regular fractional factorial 2-level designs in 8192 or more runs are provided: Resolution V designs in 8096 to 32768 runs with up to 120 factors according to the suggestion by Sanchez and Sanchez 2005 are automatically created (these are not necessarily optimal). Furthermore, manual generation of large regular fractional factorial designs via specification of generators is possible.
FrF2Large(nruns, nfactors = NULL, factor.names = if (!is.null(nfactors)){
if (nfactors Function nrunsV invisibly returns the number of runs requested and
prints a message with the number of runs and the appropriate function.
Function FrF2Large returns a data frame of S3 class
design
and has attached attributes that can be accessed
by functions desnum,
run.order and
design.info.
The data frame itself contains the design with levels coded as requested.
If no center points have been requested, the design columns are factors with
contrasts -1 and +1 (cf. also contr.FrF2); in case
of center points, the design columns are numeric.
The following attributes are attached to it:
Design matrix in -1/1 coding
three column data frame, first column contains the run number in standard order, second column the run number as randomized, third column the run number with replication number as postfix; useful for switching back and forth between actual and standard run number
list with the entries
character string “FrF2.large”
number of runs (replications are not counted)
number of factors
list named with (treatment) factor names and containing as entries vectors of length two each with coded factor levels
for designs of type FrF2.generators only;
character vector of generators in the form D=ABC etc.
alias structure of main effects, 2fis and possibly 3fis,
depending on the choice of alias.info;
For non-blocked and non-split-plot designs, aliased is
itself a list of the two or three components main, fi2, and optionally fi3, given
in terms of factor letters from Letters (up to 50~factors)
or F1, F2, and so forth (more than 50~factors).
For blocked and split-plot designs, aliased is a single list
with an entry for each column of the Yates matrix that accomodates
aliased low-order effects, and entries are in terms of factor names.)
option setting in call to FrF2
option setting in call to FrF2
option setting in call to FrF2
option setting in call to FrF2
call to function FrF2Large; (in future, may also contain stored menu settings from R commander plugin RcmdrPlugin.DoE, once the function has been implemented in that package)
version number of package FrF2,
supporting correct usage of FrF2-specific functionality in
functions summary and generators
methods for class design
number of cube points per block, in case center points have been requested
number of center points per block, in case center points have been requested
Number of runs, must be a power of 2 (8192 to 32768).
The number of runs must match the number of factors. Function nrunsV
can be used for determining the number of runs needed for a resolution V design,
and for advice on the function to be used.
For more detail on specification of the number of runs, see the Details section.
is the number of 2-level factors to be investigated.
It can be omitted, if it is obvious from options factor.names or
generators.
The number of factors must match the length of generators.
a character vector of nfactors factor names
or a list with nfactors elements;
if the list is named, list names represent factor names, otherwise default factor names are used;
the elements of the list are
EITHER vectors of length 2 with factor levels for the respective factor
OR empty strings.
For each factor with an empty string in factor.names, the levels given in
default.levels are used;
Default factor names are the first elements of the character vector Letters,
or the factors position numbers preceded by capital F in case of more than 50 factors.
default levels (vector of length 2) for all factors for which no specific levels are given
number of center points per block; ncenter > 0
is permitted, if all factors are quantitative and the design is not a split-plot design
the number of positions over which the center points
are to be distributed for each block; if NULL (default), center points are
distributed over end, beginning, and middle (in that order, if there are fewer than three center points)
for randomized designs, and appended to the end for non-randomized designs.
for more detail, see function add.center, which does the work.
There are log2(nruns) base factors the full factorial
of which spans the design (e.g. 10 for 1024 runs).
The generators specify how the remaining factors
are to be allocated to interactions of these.
WARNING: Of course, with manual
specification of generators, the structure of the design is in the users
responsibility; the function only prevents confounding of two main effects with each
other.
generators can be
a list of vectors with position numbers of base factors (e.g. c(1,3,4) stands for the interaction between first, third and fourth base factor)
a vector of character representations of these interactions, e.g. “ACD” stands for the same interaction as above
a vector of columns numbers in Yates order (e.g. 13 stands for ACD).
Note that the columns 1, 2, 4, 8, etc., i.e. all powers of 2, are reserved
for the base factors and cannot be used for assigning additional factors,
because the design would become a resolution II design. For looking up
which column number stands for which interaction, type e.g.
names(Yates)[1:15] for a 16 run design.
WARNING: Contrary to function FrF2, it is not possible to
precede generator entries with a minus sign for reversing column levels;
instead, the levels must be swapped.
positive integer number. Default 1 (i.e. each row just once).
If larger, each design run is executed replication times.
If repeat.only, repeated measurements
are carried out directly in sequence, i.e. no true replication takes place,
and all the repeat runs are conducted together. It is likely that the error
variation generated by such a procedure will be too small, so that average values
should be analyzed for an unreplicated design.
Otherwise (default), the full experiment is first carried out once, then for the second replication and so forth. In case of randomization, each such blocks is randomized separately. In this case, replication variance is more likely suitable for usage as error variance (unless e.g. the same parts are used for replication runs although build variation is important).
logical, relevant only if replications > 1. If TRUE,
replications of each run are grouped together
(repeated measurement rather than true replication). The default is
repeat.only=FALSE, i.e. the complete experiment
is conducted in replications blocks, and each run occurs in each block.
logical. If TRUE, the design is randomized. This is the default.
In case of replications, the nature of randomization depends on the setting of
option repeat.only.
optional seed for the randomization process
In R version 3.6.0 and later, the default behavior of function sample
has changed. If you work in a new (i.e., >= 3.6.-0) R version and want to reproduce
a randomized design from an earlier R version (before 3.6.0),
you have to change the RNGkind setting by
RNGkind(sample.kind="Rounding")
before running function FrF2Large.
It is recommended to change the setting back to the new recommended way afterwards:
RNGkind(sample.kind="default")
For an example, see the documentation of the example data set VSGFS.
can be 2 or 3, gives the order of interaction effects for which
alias information is to be included in the aliased component of the
design.info element of the output object.
currently not used
Since R version 3.6.0, the behavior of function sample has changed
(correction of a biased previous behavior that might be relevant for the randomization
of very large designs).
For reproducing a randomized design that was produced with an earlier R version,
please follow the steps described with the argument seed.
Ulrike Groemping
If generators are not explicitly specified, function FrF2Large creates a
resolution V design according to the
rules by Sanchez and Sanchez (2005) for the specified number of factors in
the specified number of runs. The Sanchez and Sanchez article offers designs with
at least 1024 runs for 25 to 29 factors (1024 up to 33 factors with FrF2),
at least 2048 runs for 30 to 38 factors (2048 up to 47 factors with FrF2),
at least 4096 runs for 39 to 52 factors (4096 up to 65 factors with FrF2),
at least 8192 runs for 53 to 69 factors (up to 65 factors in half the run size with FrF2),
at least 16384 runs for 70 to 92 factors, (
at least 32768 runs for 93 to 120 factors.
For designs with up to 4096 runs, function FrF2
creates better automatic designs.
Therefore, function FrF2Large is restricted to usage for larger designs.
Users can explicitly specify a design through specifying
generators via the generators option. For up to 4096 runs, this is also possible
with function FrF2, even with more flexibility. Therefore, manual design generation
with function FrF2Large is also restricted to designs of at least 8192 runs.
Manual generation of large designs with the option generators is limited by
computer memory only. nruns must be at least large enough to accomodate the
rightmost generator column; for example, if generators contains an element ABEP,
P is the 15th base factor (15th letter in Letters),
i.e. nruns must be at least 2^15=32768;
if the largest generator column number in Yates column notation is 4201,
nruns must be at least 2^ceiling(log2(4201))=8192.
Mee, R. (2009). A Comprehensive Guide to Factorial Two-Level Experimentation. New York: Springer.
Sanchez, S.M. and Sanchez, P.J. (2005). Very Large Fractional Factorial and Central Composite Designs. ACM Transactions on Modeling and Computer Simulation 15, 362-377.
See also FrF2 for smaller regular fractional factorials and
oacat for two non-regular resolution V fractional factorials (reported e.g. by
Mee 2009) for up to 19 factors in 256 runs or up to 63 factors in 2048 runs
## numbers of runs needed for resolution V designs in different numbers of factors
nrunsV(8)
nrunsV(18)
needed <- nrunsV(27)
needed
nrunsV(65)
nrunsV(71)
if (FALSE) {
plan <- FrF2Large(nrunsV(75),75)
summary(plan)
}
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