Homework 13
Kathryn Vernon
11/23/2021
library(FrF2)8.2
Suppose that in Problem 6.15, only a one-half fraction of the 24 design could be run. Construct the design and perform the analysis, using the data from replicate I.
6.15.
A nickel–titanium alloy is used to make components for jet turbine aircraft engines. Cracking is a potentially serious problem in the final part because it can lead to nonrecoverable failure. A test is run at the parts producer to determine the effect of four factors on cracks. The four factors are pouring temperature (A), titanium content (B), heat treatment method (C), and amount of grain refiner used (D). Two replicates of a 24 design are run, and the length of crack (in mm 102) induced in a sample coupon subjected to a standard test is measured. The data are shown in Table P6.2
results <- c(7.037, 16.867, 13.876, 17.273, 11.846, 4.368, 9.36, 15.653)
design<-FrF2(nfactors=4,resolution=3,randomize=FALSE)
design<-add.response(design,results)
DanielPlot(design,half=TRUE)
By the halfnormal Plot above, no factors are significant.
MEPlot(design,show.alias=TRUE)
We can see here that factor D seems to have the most affect on our response.
8.24
Construct a 2^5-1 design. Show how the design may be run in two blocks of eight observations each. Are any main effects or two-factor interactions confounded with blocks?
design<-FrF2(nfactors=6,resolution=5,randomize=FALSE,blocks=2,nruns=16)## Warning in FrF2(nfactors = 6, resolution = 5, randomize = FALSE, blocks = 2, :
## resolution is ignored, if nruns is given.summary(design)## Call:
## FrF2(nfactors = 6, resolution = 5, randomize = FALSE, blocks = 2,
## nruns = 16)
##
## Experimental design of type FrF2.blocked
## 16 runs
## blocked design with 2 blocks of size 8
##
## Factor settings (scale ends):
## A B C D E F
## 1 -1 -1 -1 -1 -1 -1
## 2 1 1 1 1 1 1
##
## Design generating information:
## $legend
## [1] A=A B=B C=C D=D E=E F=F
##
## $`generators for design itself`
## [1] E=ABC F=ABD
##
## $`block generators`
## [1] ACD
##
##
## Alias structure:
## $fi2
## [1] AB=CE=DF AC=BE AD=BF AE=BC AF=BD CD=EF CF=DE
##
## Aliased with block main effects:
## [1] none
##
## The design itself:
## run.no run.no.std.rp Blocks A B C D E F
## 1 1 1.1.1 1 -1 -1 -1 -1 -1 -1
## 2 2 4.1.2 1 -1 -1 1 1 1 1
## 3 3 5.1.3 1 -1 1 -1 -1 1 1
## 4 4 8.1.4 1 -1 1 1 1 -1 -1
## 5 5 10.1.5 1 1 -1 -1 1 1 -1
## 6 6 11.1.6 1 1 -1 1 -1 -1 1
## 7 7 14.1.7 1 1 1 -1 1 -1 1
## 8 8 15.1.8 1 1 1 1 -1 1 -1
## run.no run.no.std.rp Blocks A B C D E F
## 9 9 2.2.1 2 -1 -1 -1 1 -1 1
## 10 10 3.2.2 2 -1 -1 1 -1 1 -1
## 11 11 6.2.3 2 -1 1 -1 1 1 -1
## 12 12 7.2.4 2 -1 1 1 -1 -1 1
## 13 13 9.2.5 2 1 -1 -1 -1 1 1
## 14 14 12.2.6 2 1 -1 1 1 -1 -1
## 15 15 13.2.7 2 1 1 -1 -1 -1 -1
## 16 16 16.2.8 2 1 1 1 1 1 1
## class=design, type= FrF2.blocked
## NOTE: columns run.no and run.no.std.rp are annotation,
## not part of the data frameAs shown above, it would seem that the two factor effect AB would be aliaised/confounded with the blocks, as its low and high levels correspond directly with the blocks. (aka all of block one is -1, all of block 2 is 1)
8.25
Construct a 2^7-2 design. Show how the design may be run in four blocks of eight observations each. Are any main effects or two-factor interactions confounded with blocks?
design<-FrF2(nfactors=7,resolution=3,randomize=FALSE,blocks=4,nruns=32)
summary(design)## Call:
## FrF2(nfactors = 7, resolution = 3, randomize = FALSE, blocks = 4,
## nruns = 32)
##
## Experimental design of type FrF2.blocked
## 32 runs
## blocked design with 4 blocks of size 8
##
## Factor settings (scale ends):
## A B C D E F G
## 1 -1 -1 -1 -1 -1 -1 -1
## 2 1 1 1 1 1 1 1
##
## Design generating information:
## $legend
## [1] A=A B=B C=C D=D E=E F=F G=G
##
## $`generators for design itself`
## [1] F=ABC G=ABD
##
## $`block generators`
## [1] ACD ABE
##
##
## Alias structure:
## $fi2
## [1] AB=CF=DG AC=BF AD=BG AF=BC AG=BD CD=FG CG=DF
##
## Aliased with block main effects:
## [1] none
##
## The design itself:
## run.no run.no.std.rp Blocks A B C D E F G
## 1 1 1.1.1 1 -1 -1 -1 -1 -1 -1 -1
## 2 2 7.1.2 1 -1 -1 1 1 -1 1 1
## 3 3 10.1.3 1 -1 1 -1 -1 1 1 1
## 4 4 16.1.4 1 -1 1 1 1 1 -1 -1
## 5 5 20.1.5 1 1 -1 -1 1 1 1 -1
## 6 6 22.1.6 1 1 -1 1 -1 1 -1 1
## 7 7 27.1.7 1 1 1 -1 1 -1 -1 1
## 8 8 29.1.8 1 1 1 1 -1 -1 1 -1
## run.no run.no.std.rp Blocks A B C D E F G
## 9 9 2.2.1 2 -1 -1 -1 -1 1 -1 -1
## 10 10 8.2.2 2 -1 -1 1 1 1 1 1
## 11 11 9.2.3 2 -1 1 -1 -1 -1 1 1
## 12 12 15.2.4 2 -1 1 1 1 -1 -1 -1
## 13 13 19.2.5 2 1 -1 -1 1 -1 1 -1
## 14 14 21.2.6 2 1 -1 1 -1 -1 -1 1
## 15 15 28.2.7 2 1 1 -1 1 1 -1 1
## 16 16 30.2.8 2 1 1 1 -1 1 1 -1
## run.no run.no.std.rp Blocks A B C D E F G
## 17 17 3.3.1 3 -1 -1 -1 1 -1 -1 1
## 18 18 5.3.2 3 -1 -1 1 -1 -1 1 -1
## 19 19 12.3.3 3 -1 1 -1 1 1 1 -1
## 20 20 14.3.4 3 -1 1 1 -1 1 -1 1
## 21 21 18.3.5 3 1 -1 -1 -1 1 1 1
## 22 22 24.3.6 3 1 -1 1 1 1 -1 -1
## 23 23 25.3.7 3 1 1 -1 -1 -1 -1 -1
## 24 24 31.3.8 3 1 1 1 1 -1 1 1
## run.no run.no.std.rp Blocks A B C D E F G
## 25 25 4.4.1 4 -1 -1 -1 1 1 -1 1
## 26 26 6.4.2 4 -1 -1 1 -1 1 1 -1
## 27 27 11.4.3 4 -1 1 -1 1 -1 1 -1
## 28 28 13.4.4 4 -1 1 1 -1 -1 -1 1
## 29 29 17.4.5 4 1 -1 -1 -1 -1 1 1
## 30 30 23.4.6 4 1 -1 1 1 -1 -1 -1
## 31 31 26.4.7 4 1 1 -1 -1 1 -1 -1
## 32 32 32.4.8 4 1 1 1 1 1 1 1
## class=design, type= FrF2.blocked
## NOTE: columns run.no and run.no.std.rp are annotation,
## not part of the data frameAfter looking this over by eyeball calculations, it does not appear to contain any confounding/aliasing with any two factor interactions or main effects.
8.28.
A 16-run experiment was performed in a semiconductor manufacturing plant to study the effects of six factors on the curvature or camber of the substrate devices produced. Each run was replicated four times, and a camber measurement was taken on the substrate.
A <-c(-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1)
B <-c(-1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1,-1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1,-1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1,-1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1)
C <-c(-1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1,-1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1,-1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1,-1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1)
D <-c(-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1,-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1,-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1,-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1)
E <-c(-1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1,-1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1,-1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1,-1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1)
F <-c(-1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1,-1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1,-1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1,-1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1)
results <- c(0.0167, 0.0062, 0.0041, 0.0073, 0.0047, 0.0219, 0.0121, 0.0255, 0.0032, 0.0078, 0.0043, 0.0186, 0.011, 0.0065, 0.0155, 0.0093, 0.0128, 0.0066, 0.0043, 0.0081, 0.0047, 0.0258, 0.009, 0.025, 0.0023, 0.0158, 0.0027, 0.0137, 0.0086, 0.0109, 0.0158, 0.0124, 0.0149, 0.0044, 0.0042, 0.0039, 0.004, 0.0147, 0.0092, 0.0226, 0.0077, 0.006, 0.0028, 0.0158, 0.0101, 0.0126, 0.0145, 0.011, 0.0185, 0.002, 0.005, 0.003, 0.0089, 0.0296, 0.0086, 0.0169, 0.0069, 0.0045, 0.0028, 0.0159, 0.0158, 0.0071, 0.0145, 0.0133
)
dafr <- data.frame(A,B,C,D,E,F,results)(a)
What type of design did the experimenters use?
This seems to be a \(2^{6-2}_{IV}\) experiment. \(2^6\) because there are six factors. \(2^{6-2}\) because there are only 16 runs in the experiment, which is \(1/4\) of a full experiment load of 64 (if we had tested every combination). Because we are doing 16 combinations, our defining word will be 4 letters. leaving us with \(2^{6-2}_{IV}\)
(b)
What are the alias relationships in this design?
design<-FrF2(nfactors=6,resolution=4,randomize=FALSE)
aliases(aov(results~A*B*C*D*E*F,dafr))##
## A = B:C:E = C:D:F = A:B:D:E:F
## B = A:C:E = D:E:F = A:B:C:D:F
## C = A:B:E = A:D:F = B:C:D:E:F
## D = A:C:F = B:E:F = A:B:C:D:E
## E = A:B:C = B:D:F = A:C:D:E:F
## F = A:C:D = B:D:E = A:B:C:E:F
## A:B = C:E = B:C:D:F = A:D:E:F
## A:C = B:E = D:F = A:B:C:D:E:F
## B:C = A:E = A:B:D:F = C:D:E:F
## A:D = C:F = B:C:D:E = A:B:E:F
## B:D = E:F = A:C:D:E = A:B:C:F
## C:D = A:F = A:B:D:E = B:C:E:F
## D:E = B:F = A:B:C:D = A:C:E:F
## A:B:D = C:D:E = B:C:F = A:E:F
## B:C:D = A:D:E = A:B:F = C:E:FOur aliases are shown above.
(c)
Do any of the process variables affect average camber?
summary(aov(results~A*B*C*D*E*F,dafr))## Df Sum Sq Mean Sq F value Pr(>F)
## A 1 0.0002422 0.0002422 27.793 3.17e-06 ***
## B 1 0.0000053 0.0000053 0.614 0.43725
## C 1 0.0005023 0.0005023 57.644 9.14e-10 ***
## D 1 0.0000323 0.0000323 3.712 0.05995 .
## E 1 0.0001901 0.0001901 21.815 2.45e-05 ***
## F 1 0.0009602 0.0009602 110.192 5.05e-14 ***
## A:B 1 0.0000587 0.0000587 6.738 0.01249 *
## A:C 1 0.0000803 0.0000803 9.218 0.00387 **
## B:C 1 0.0000527 0.0000527 6.053 0.01754 *
## A:D 1 0.0000239 0.0000239 2.741 0.10431
## B:D 1 0.0000849 0.0000849 9.739 0.00305 **
## C:D 1 0.0000622 0.0000622 7.139 0.01027 *
## D:E 1 0.0000088 0.0000088 1.007 0.32062
## A:B:D 1 0.0000000 0.0000000 0.005 0.94291
## B:C:D 1 0.0000481 0.0000481 5.523 0.02293 *
## Residuals 48 0.0004183 0.0000087
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Looking at just the main Effects, we can see that A(Temp),C(Pressure),E(Time), and F(Dew Point). There are also some two factor interactions.
par(mfcol=c(2,2))
plot(aov(results~A*B*C*D*E*F,dafr))## hat values (leverages) are all = 0.25
## and there are no factor predictors; no plot no. 5
On a quick check, our data does not seem to violate any assumptions either.
(d)
Do any of the process variables affect the variability in camber measurements?
variability <- c(24.418, 20.976, 4.083, 25.025, 22.41, 63.639, 16.029, 39.42, 26.725, 50.341, 7.681, 20.083, 31.12, 29.51, 6.75, 17.45)
A1 <-as.factor(c(-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1))
B1 <-as.factor(c(-1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1))
C1 <-as.factor(c(-1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1))
D1 <-as.factor(c(-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1))
E1 <-as.factor(c(-1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1))
F1 <-as.factor(c(-1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1))
halfnormal(aov(variability~A1*B1*C1*D1*E1*F1),ME.partial=TRUE)
It looks like A and B may be important to the variability of our results.
(e)
If it is important to reduce camber as much as possible, what recommendations would you make?
MEPlot(aov(results~A*B*C*D*E*F,dafr),show.alias=TRUE)
I would recommend setting:
A to low
B to low
C to low
D to high
E to high
F to high
The most important factors to set however would be A,C,E, and F, since those were shown to be significant.
Additionally, A (and B) seemed to perhaps have an effect on the variability of the results, which should be kept in mind.
8.40
Answer the following questions about this experiment:
(a)
How many factors did this experiment investigate?
Four.
(b)
What is the resolution of this design? Also four.
(c)
Calculate the estimates of the main effects.
This is done for each factor via adding all the results where the factor is present, subtracting all the effects where the factor is not present, and then in this case divding by four.
A=\(1/4(-8+10-12+7-13+6-5+11)=1\)
B=\(1/4(-8-10+12+7-13-6+5+11)=-.5\)
C=\(1/4(-8-10-12-7+13+6+5+11)=-.5\)
D=\(1/4(-8+10+12-7+13-6-5+11)=5\)
(d)
What is the complete defining relation for this design?
The same as what defines our resolution, it is I=ABCD.
8.48
(a)
What is the generator for column D?
-ABC would have the same sign as D, it is the generator.
(b)
What is the generator for column E?
BC has the same sign as E each time, it is the generator.
(c)
If this design were folded over, what is the resolution of the combined design?
Three(IV)
8.60
Consider a partial fold over for the \(2^{7-4}_{III}\)design. Suppose that the partial fold over of this design is constructed using column A ( + signs only). Determine the alias relationships in the combined design.
designe<-FrF2(nfactors=7,resolution=3,randomize=FALSE)
fold.design(designe, columns = 1)## A B C fold D E F G
## 1 -1 -1 -1 original 1 1 1 -1
## 2 1 -1 -1 original -1 -1 1 1
## 3 -1 1 -1 original -1 1 -1 1
## 4 1 1 -1 original 1 -1 -1 -1
## 5 -1 -1 1 original 1 -1 -1 1
## 6 1 -1 1 original -1 1 -1 -1
## 7 -1 1 1 original -1 -1 1 -1
## 8 1 1 1 original 1 1 1 1
## 9 1 -1 -1 mirror 1 1 1 -1
## 10 -1 -1 -1 mirror -1 -1 1 1
## 11 1 1 -1 mirror -1 1 -1 1
## 12 -1 1 -1 mirror 1 -1 -1 -1
## 13 1 -1 1 mirror 1 -1 -1 1
## 14 -1 -1 1 mirror -1 1 -1 -1
## 15 1 1 1 mirror -1 -1 1 -1
## 16 -1 1 1 mirror 1 1 1 1
## class=design, type= FrF2.foldedHere is the folded design over A
design.info(designe)$aliased$main## [1] "A=BD=CE=FG" "B=AD=CF=EG" "C=AE=BF=DG" "D=AB=CG=EF" "E=AC=BG=DF"
## [6] "F=AG=BC=DE" "G=AF=BE=CD"Our aliasing relationships shown above.
All Code Used:
results <- c(7.037, 16.867, 13.876, 17.273, 11.846, 4.368, 9.36, 15.653)
design<-FrF2(nfactors=4,resolution=3,randomize=FALSE)
design<-add.response(design,results)
DanielPlot(design,half=TRUE)
MEPlot(design,show.alias=TRUE)
design<-FrF2(nfactors=6,resolution=5,randomize=FALSE,blocks=2,nruns=16)
summary(design)
design<-FrF2(nfactors=7,resolution=3,randomize=FALSE,blocks=4,nruns=32)
summary(design)
A <-c(-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1)
B <-c(-1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1,-1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1,-1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1,-1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1)
C <-c(-1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1,-1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1,-1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1,-1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1)
D <-c(-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1,-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1,-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1,-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1)
E <-c(-1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1,-1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1,-1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1,-1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1)
F <-c(-1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1,-1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1,-1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1,-1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1)
results <- c(0.0167, 0.0062, 0.0041, 0.0073, 0.0047, 0.0219, 0.0121, 0.0255, 0.0032, 0.0078, 0.0043, 0.0186, 0.011, 0.0065, 0.0155, 0.0093, 0.0128, 0.0066, 0.0043, 0.0081, 0.0047, 0.0258, 0.009, 0.025, 0.0023, 0.0158, 0.0027, 0.0137, 0.0086, 0.0109, 0.0158, 0.0124, 0.0149, 0.0044, 0.0042, 0.0039, 0.004, 0.0147, 0.0092, 0.0226, 0.0077, 0.006, 0.0028, 0.0158, 0.0101, 0.0126, 0.0145, 0.011, 0.0185, 0.002, 0.005, 0.003, 0.0089, 0.0296, 0.0086, 0.0169, 0.0069, 0.0045, 0.0028, 0.0159, 0.0158, 0.0071, 0.0145, 0.0133
)
dafr <- data.frame(A,B,C,D,E,F,results)
design<-FrF2(nfactors=6,resolution=4,randomize=FALSE)
aliases(aov(results~A*B*C*D*E*F,dafr))
summary(aov(results~A*B*C*D*E*F,dafr))
variability <- c(24.418, 20.976, 4.083, 25.025, 22.41, 63.639, 16.029, 39.42, 26.725, 50.341, 7.681, 20.083, 31.12, 29.51, 6.75, 17.45)
A1 <-as.factor(c(-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1))
B1 <-as.factor(c(-1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1))
C1 <-as.factor(c(-1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1))
D1 <-as.factor(c(-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1))
E1 <-as.factor(c(-1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1))
F1 <-as.factor(c(-1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1))
halfnormal(aov(variability~A1*B1*C1*D1*E1*F1),ME.partial=TRUE)
MEPlot(aov(results~A*B*C*D*E*F,dafr),show.alias=TRUE)
designe<-FrF2(nfactors=7,resolution=3,randomize=FALSE)
fold.design(designe, columns = 1)
design.info(designe)$aliased$main