Function for generating Box-Behnken designs, making use of package rsm
bbd.design(nfactors, ncenter=4, factor.names = NULL, default.levels=c(-1,1),
block.name=NULL, randomize=TRUE, seed=NULL, ...)The function returns a data frame of S3 class design
with attributes attached. The data frame itself is in the original data scale.
The matrix desnum attached as attribute desnum contains the coded data,
the attribute run.order contains the standard order and the actual run order
of the design (contrary to package rsm, the row names of the design refer to
the actual rather than the standard run order).
The attribute design.info is a list of design properties.
The element type of that list is the character string bbd.
Besides the elements present in all class design objects,
there are the elements quantitative (vector with nfactor TRUE entries),
and a codings element usable in the coding functions available in the rsm
package, e.g. coded.data.
number of factors
integer number of center points for each block
list of scale end values for each factor
(the middle value is calculated);
names are used as variable names;
the names must not be x1, x2, ..., as these are used for the variables
in coded units;
if the list is not named, the variable names are A, B and so forth;
in the coded units used in attribute desnum, -1 corresponds to the smaller, +1 to the larger value.
default levels (vector of length 2) for all factors for which no specific levels are given; must consist of two numeric values for the scale ends, the default middle level is calculated
name of block factor that distinguishes between the blocks;
blocks are usable for nfactors=4 and nfactors=5 only, block.name is ignored otherwise.
logical that indicates whether or not randomization should occur
optional seed for random number generation in randomization
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 bbd.design.
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.
reserved for future usage
Since R version 3.6.0, the behavior of function sample has changed
(correction of a biased previous behavior that should not be relevant for the randomization of 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
Function bbd.design creates a Box-Behnken design, which is a design for quantitative
factors with all factors on three levels. Box-Behnken designs should not be used if the combinations
of the extreme levels of the factors are of interest (cf. also Myers, Montgomery and Anderson-Cook 2009).
There are designs for 3 to 7 factors, and the unreplicated versions of these have
14 (3 factors), 24 (4 factors), 40 (5 factors), 48 (6 factors), and 56 (7 factors) runs
plus the specified number of center points ncenter.
Function bbd.design is an interface to function bbd from package rsm
that makes this design accessible using similar syntax as used in packages DoE.base and FrF2
and creates an output object that is also treatable by the convenience functions available in package
DoE.base.
Currently, creation of replications and repeated measurements - as would be usual for other design functions - is not implemented. This is planned for the future, but does not have high priority.
Box, G.E.P. and Behnken, D.W. (1960). Some new three-level designs for the study of quantitative variables. Technometrics 2, 455-475.
Box, G.E.P., Hunter, J.S. and Hunter, W.G. (2005, 2nd ed.). Statistics for Experimenters. Wiley, New York.
Box, G.E.P. and Wilson, K.B. (1951). On the Experimental Attainment of Optimum Conditions. J. Royal Statistical Society, B13, 1-45.
NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/pri/section3/pri3361.htm, accessed August 20th, 2009.
Myers, R.H., Montgomery, D.C. and Anderson-Cook, C.M. (2009). Response Surface Methodology. Process and Product Optimization Using Designed Experiments. Wiley, New York.
See also FrF2, ccd.design, lhs-package, rsm
plan1 <- bbd.design(5) ## default for 5 factors is unblocked design, contrary to package rsm
plan1
## blocked design for 4 factors, using default levels
plan2 <- bbd.design(4,block.name="block",default.levels=c(10,30))
plan2
desnum(plan2)
## design with factor.names and modified ncenter
bbd.design(3,ncenter=6,
factor.names=list("one"=c(25,35),"two"=c(-5,20), "three"=c(20,60)))
## design with character factor.names and default levels
bbd.design(3,factor.names=c("one","two", "three"), default.levels=c(10,20))
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