## check a small design
oa12 <- oa.design(nlevels=c(2,2,6))
length3(oa12)
## length4 is of course 0, because there are only 3 factors
P3.3(oa12)
## the results need not be an integer
oa12 <- oa.design(L12.2.11,columns=1:6)
length3(oa12)
length4(oa12)
P3.3(oa12) ## all projections have the same pattern
## which is known to be true for the complete L12.2.11 as well
P3.3(L18) ## this is the pattern of the Taguchi L18
## also published by Schoen 2009
P3.3(L18[,-2]) ## without the 2nd column (= the 1st 3-level column)
P3.3(L18[,-2], rela=TRUE) ## relative pattern, divided by theoretical upper
## bound for each 3-factor projection
## choosing among different assignment possibilities
## for two 2-level factors and one 3- and 4-level factor each
show.oas(nlevels=c(2,2,3,4))
## default allocation: first two columns for the 2-level factors
oa24.bad <- oa.design(L24.2.13.3.1.4.1, columns=c(1,2,14,15))
length3(oa24.bad)
## much better: columns 3 and 10
oa24.good <- oa.design(L24.2.13.3.1.4.1, columns=c(3,10,14,15))
length3(oa24.good)
length4(oa24.good) ## there are several variants,
## which produce the same pattern for lengths 3 and 4
## the difference matters
plot(oa24.bad, select=c(2,3,4))
plot(oa24.good, select=c(2,3,4))
## generalized resolution differs as well (resolution is III in both cases)
GR(oa24.bad)
GR(oa24.good)
## and analogously also GRind and ARFT and SCFT
GRind(oa24.bad)
GRind(oa24.good)
## GR and GRind can be different
GRind(L18[, c(1:4,6:8)], arft=FALSE, scft=FALSE)
## choices for columns can be explored with functions oa.min3, oa.min34 or oa.max3
oa.min3(L24.2.13.3.1.4.1, nlevels=c(2,2,3,4))
oa.min34(L24.2.13.3.1.4.1, nlevels=c(2,2,3,4))
## columns for designs with maximum generalized resolution
## (can take very long, if all designs have worst-case aliasing)
## then optimize these for overall relative number of words of length 3
## and in addition absolute number of words of length 4
mGR <- oa.maxGR(L18, c(2,3,3,3,3,3,3))
oa.minRelProjAberr(L18, c(2,3,3,3,3,3,3), maxGR=mGR)
oa.max3(L24.2.13.3.1.4.1, nlevels=c(2,2,3,4)) ## this is not for finding
## a good design!!!
## play with selection of optimum design
## somewhat experimental at present
oa.min3(L32.2.10.4.7, nlevels=c(2,2,2,4,4,4,4,4))
best3 <- oa.min3(L32.2.10.4.7, nlevels=c(2,2,2,4,4,4,4,4), rela=TRUE)
oa.min34(L32.2.10.4.7, nlevels=c(2,2,2,4,4,4,4,4))
oa.min34(L32.2.10.4.7, nlevels=c(2,2,2,4,4,4,4,4), min3=best3)
## generalized resolution according to Groemping 2011, manually
best3GR <- oa.min3(L36.2.11.3.12, c(rep(2,3),rep(3,3)), rela=TRUE, crit="worst")
## optimum GR is 3.59
## subsequent optimization w.r.t. rA3
best3reltot.GR <- oa.min3(L36.2.11.3.12, c(rep(2,3),rep(3,3)), rela=TRUE,
variants=best3GR$column.variants)
## optimum rA3 is 0.5069
## (note: different from first optimizing rA3 (0.3611) and then GR (3.5))
## remaining nine designs: optimize RPFTs
L36 <- oa.design(L36.2.11.3.12, randomize=FALSE)
lapply(1:9, function(obj) P3.3(L36[,best3reltot.GR$column.variants[obj,]]))
## all identical
oa.min34(L36, nlevels=c(rep(2,3),rep(3,3)), min3=best3reltot.GR)
## still all identical
## select among column variants with projection frequencies
## here, all variants have identical projection frequencies
## for larger problems, this may sometimes be relevant
variants <- oa.min34(L24.2.13.3.1.4.1, nlevels=c(2,2,3,4))
for (i in 1:nrow(variants$column.variants)){
cat("variant ", i, "")
print(P3.3(oa.design(L24.2.13.3.1.4.1, columns=variants$column.variants[i,])))
}
## automatic optimization is possible, but can be time-consuming
## (cf. help for oa.design)
plan <- oa.design(L24.2.13.3.1.4.1, nlevels=c(2,2,3,4), columns="min3")
length3(plan)
length4(plan)
plan <- oa.design(L24.2.13.3.1.4.1, nlevels=c(2,2,3,4), columns="min34")
length3(plan)
length4(plan)
## blocked design from FrF2
## the design is of resolution IV
## there is one (generalized) 4-letter word that does not involve the block factor
## there are four more 4-letter words involving the block factor
## all this and more can also be learnt from design.info(plan)
require(FrF2)
plan <- FrF2(32,6,blocks=4)
length3(plan)
length3(plan, with.blocks=TRUE)
length4(plan)
length4(plan, with.blocks=TRUE)
design.info(plan)Run the code above in your browser using DataLab