pb {FrF2} | R Documentation |
The function generates Plackett-Burman designs and in some cases other screening designs in run numbers that are a multiple of 4. These designs are particularly suitable for screening a large number of factors, since interactions are not fully aliased with one main effect each but partially aliased. (The designs in 8 and 64 runs are exceptions from this rule.)
pb(nruns, nfactors = nruns - 1, factor.names = if (nfactors <= 50) Letters[1:nfactors] else paste("F", 1:nfactors, sep = ""), default.levels = c(-1, 1), boxtyssedal = TRUE, n12.taguchi = FALSE, replications = 1, repeat.only = FALSE, randomize = TRUE, seed = NULL, ...) pb.list
nruns |
number of runs, must be a multiple of 4 |
nfactors |
number of factors, default is nruns - 1, and it is recommended to retain this default.
It is possible to specify factor names for fewer factors, and the remaining columns will be named e1 , e2 , ...
They are useful for representing error in effects plots. |
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 |
boxtyssedal |
logical, relevant only for nruns=16. If FALSE, the geometric (=standard) 16 run plan is used. If TRUE, the proposal by Box and Tyssedal is used instead, which has the advantage (for screening) of aliasing each interaction with several main effects, like the other Plackett-Burman designs. |
n12.taguchi |
logical, relevant only for nruns=12. If TRUE, the 12 run design is given in Taguchi order. |
replications |
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). |
repeat.only |
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. |
randomize |
logical. If TRUE, the design is randomized. This is the default. |
seed |
optional seed for the randomization process |
... |
currently not used |
For most run numbers, designs from Plackett and Burman (1946) are used, and columns are filled from left to right. The generating rows for these designs can be found in pb.list
(a 0 entry indicates that the design is constructed by a different method, e.g. doubling).
For 12 runs, the isomorphic design by Taguchi can be requested. For 16 runs, the default is to use the designs suggested by Box and Tyssedal (2001), which up to 14 factors do not suffer from perfect aliasing. For 32 runs, a cyclic design with generating row given in Samset and Tyssedal (1999) is used. For 64 runs, the 32 run design is doubled. For 92 runs, a design is constructed according to the Williamson construction with matrices A, B, C and D from Hedayat and Stufken (1999), p. 160.
So far, designs up to 96~runs are covered. More and different ones may follow, since the package is currently under intensive development.
Usage of the 8~run design for more than 4~factors is discouraged, as it completely aliases main effects with individual two-factor interactions. It is recommended to use the 12~run design instead for screening more than 4~factors.
Value is a data frame of S3 class design
with attributes attached.
The data frame itself contains the design with levels coded as requested.
The following attributes are attached to it:
desnum |
Design matrix in -1/1 coding |
run.order |
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 |
design.info |
list with entries
|
Ulrike Groemping
Box, G.E.P. and Tyssedal, J. (2001) Sixteen Run Designs of High Projectivity for Factor Screening. Communications in Statistics - Simulation and Computation 30, 217-228.
Hedayat, A.S., Sloane, N.J.A. and Stufken, J. (1999) Orthogonal Arrays: Theory and Applications, Springer, New York.
Plackett, R.L.; Burman, J.P. (1946) The design of optimum multifactorial experiments. Biometrika 33, 305-325.
Samset, O.; Tyssedal, J. (1999) Two-level designs with good projection properties. Technical Report 12, Department of Mathematical Sciences, The Norwegian University of Science and Technology, Norway.
Williamson, J. (1946) Determinants whose elements are 0 and 1. American Mathematical Monthly 53, 427-434.
See Also FrF2
for regular fractional factorial designs
pb(12,randomize=FALSE) pb(12,randomize=FALSE,n12.taguchi=TRUE) pb(20,seed=29869) pb(16,factor.names=list(A="",B="",C="",D=c("min","max"), E="",F="",G="",H="",J=c("new","old"))) pb(8,default.levels=c("current","new")) test <- pb(40) ## design created by doubling the 20 run design