```
# NOT RUN {
## smallest available array for 6 factors with 3 levels each
oa.design(nfactors=6, nlevels=3)
## level combination for which only a full factorial is (currently) found
oa.design(nlevels=c(4,3,3,2))
## array requested via factor.names
oa.design(factor.names=list(one=c("a","b","c"), two=c(125,275),
three=c("old","new"), four=c(-1,1), five=c("min","medium","max")))
## array requested via character factor.names and nlevels
## (with a little German lesson for one two three four five)
oa.design(factor.names=c("eins","zwei","drei","vier","fuenf"), nlevels=c(2,2,2,3,7))
## array requested via explicit name, Taguchi L18
oa.design(ID=L18)
## array requested via explicit name, with column selection
oa.design(ID=L18.3.6.6.1,columns=c(2,3,7))
## array requested with nruns, not very reasonable
oa.design(nruns=12, nfactors=3, nlevels=2)
## array requested with min.residual.df
oa.design(nfactors=3, nlevels=2, min.residual.df=12)
## examples showing alias structures and their improvment with option columns
plan <- oa.design(nfactors=6,nlevels=3)
plan
## generalized word length pattern
length3(plan)
## length3 (first element of GWP) can be slightly improved by columns="min3"
plan <- oa.design(nfactors=6,nlevels=3,columns="min3")
summary(plan) ## the first 3-level column of the array is not used
length3(plan)
plan <- oa.design(nlevels=c(2,2,2,6))
length3(plan)
plan.opt <- oa.design(nlevels=c(2,2,2,6),columns="min3") ## substantial improvement
length3(plan.opt)
length4(plan.opt)
## visualize practical relevance of improvement:
## for optimal plan, all 3-dimensional projections are full factorials
plot(plan, select=1:3)
plot(plan, select=c(1,2,4))
plot(plan, select=c(1,3,4))
plot(plan, select=2:4)
plot(plan.opt, select=1:3)
plot(plan.opt, select=c(1,2,4))
plot(plan.opt, select=c(1,3,4))
plot(plan.opt, select=2:4)
## The last example:
## generate an orthogonal array equivalent to Taguchi's L18
## by combining L18.3.6.6.1 with a full factorial in 2 and 3 levels
show.oas(nruns=18, parents.only=FALSE)
## lineage entry leads the way:
## start from L18.3.6.6.1
## insert L6.2.1.3.1 for the 6 level factor
## prepare the parent
parent.des <- L18.3.6.6.1
colnames(parent.des) <- c(Letters[3:9])
## new columns will become A and B
## 6-level design can be created by fac.design or expand.grid or cbind
nest.des <- as.matrix(expand.grid(1:3,1:2))[c(1:3,5,6,4),c(2,1)]
## want first column to change most slowly
## want resulting design to be easily transformable into Taguchi L18
## see mathematical comments in section Details
colnames(nest.des) <- c("A","B")
## do the expansion (see mathematical comments in section Details)
## using function expansive.replace
L18.2.1.3.7.manual <- expansive.replace(parent.des, nest.des)[,c(7:8,1:6)]
L18.2.1.3.7.manual <- L18.2.1.3.7.manual[ord(L18.2.1.3.7.manual),] ## sort array
rownames(L18.2.1.3.7.manual) <- 1:18
## (ordering is not necessary, just **tidy**)
## prepare for using it with function oa.design
## note: function expansive.replace creates a matrix of class "oa"
## rearranging the columns removed that class and makes it necessary
## to add the class again for using the array in DoE.base
attr(L18.2.1.3.7.manual, "origin") <-
c(show.oas(name="L18.2.1.3.7", parents.only=FALSE,show=0)$lineage,
"unconventional order")
class(L18.2.1.3.7.manual) <- c("oa", "matrix")
comment(L18.2.1.3.7.manual) <- "Interaction of first two factors estimable"
## indicates that first two factors are full factorial from 6-level factor
origin(L18.2.1.3.7.manual)
comment(L18.2.1.3.7.manual)
L18 ## Taguchi array
L18.2.1.3.7.manual ## manually expanded array
oa.design(L18.2.1.3.7, randomize=FALSE)
## automatically expanded array
P3.3(L18.2.1.3.7.manual) ## length 3 pattern of 3 factor projections
## this also identifies the array as isomorphic to L18
## according to Schoen 2009
## the array can now be used in oa.design, like the built-in arrays
oa.design(ID=L18.2.1.3.7.manual,nfactors=7,nlevels=3)
# }
```

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