Homework week 13
Dowthyaksai Lagadapati
2022-11-30
8.2)
we have to run a half of the \(2^{5}\) design.
where k = 5 and p = 1
library(FrF2)## Warning: package 'FrF2' was built under R version 4.2.2## Loading required package: DoE.base## Warning: package 'DoE.base' was built under R version 4.2.2## Loading required package: grid## Loading required package: conf.design## Registered S3 method overwritten by 'DoE.base':
## method from
## factorize.factor conf.design##
## Attaching package: 'DoE.base'## The following objects are masked from 'package:stats':
##
## aov, lm## The following object is masked from 'package:graphics':
##
## plot.design## The following object is masked from 'package:base':
##
## lengthsdesign8.2 <- FrF2(nfactors = 4, resolution = 4, randomize = TRUE)
design8.2## A B C D
## 1 1 -1 1 -1
## 2 1 -1 -1 1
## 3 -1 -1 -1 -1
## 4 1 1 1 1
## 5 1 1 -1 -1
## 6 -1 1 -1 1
## 7 -1 1 1 -1
## 8 -1 -1 1 1
## class=design, type= FrF2aliasprint(design8.2)## $legend
## [1] A=A B=B C=C D=D
##
## $main
## character(0)
##
## $fi2
## [1] AB=CD AC=BD AD=BCwe can observe that no main effect is aliased with any other main effect or with any two-factor interaction, but two factor interactions are aliased with each other.
Collection of dada :
response<-c(7.037, 16.867, 13.876, 17.273, 11.846, 4.368, 9.36, 15.653)
design.res <- add.response(design8.2 ,response)
summary(design.res)## Call:
## FrF2(nfactors = 4, resolution = 4, randomize = TRUE)
##
## Experimental design of type FrF2
## 8 runs
##
## Factor settings (scale ends):
## A B C D
## 1 -1 -1 -1 -1
## 2 1 1 1 1
##
## Responses:
## [1] response
##
## Design generating information:
## $legend
## [1] A=A B=B C=C D=D
##
## $generators
## [1] D=ABC
##
##
## Alias structure:
## $fi2
## [1] AB=CD AC=BD AD=BC
##
##
## The design itself:
## A B C D response
## 1 1 -1 1 -1 7.037
## 2 1 -1 -1 1 16.867
## 3 -1 -1 -1 -1 13.876
## 4 1 1 1 1 17.273
## 5 1 1 -1 -1 11.846
## 6 -1 1 -1 1 4.368
## 7 -1 1 1 -1 9.360
## 8 -1 -1 1 1 15.653
## class=design, type= FrF2Half Normal Plot :
DanielPlot(design.res,half=TRUE)
Main effect plot :
MEPlot(design.res,show.alias=TRUE)
From the Daniel plot we can notice that no factor is significant.
8.24)
Half fraction of \(2^{5}\) can be run with k = 5 and p = 1 and of 16 runs
des.resp <- FrF2(nfactors = 5, resolution = 5 ,randomize = FALSE)
des.resp## A B C D E
## 1 -1 -1 -1 -1 1
## 2 1 -1 -1 -1 -1
## 3 -1 1 -1 -1 -1
## 4 1 1 -1 -1 1
## 5 -1 -1 1 -1 -1
## 6 1 -1 1 -1 1
## 7 -1 1 1 -1 1
## 8 1 1 1 -1 -1
## 9 -1 -1 -1 1 -1
## 10 1 -1 -1 1 1
## 11 -1 1 -1 1 1
## 12 1 1 -1 1 -1
## 13 -1 -1 1 1 1
## 14 1 -1 1 1 -1
## 15 -1 1 1 1 -1
## 16 1 1 1 1 1
## class=design, type= FrF2Aliased relationships :
aliasprint(des.resp)## $legend
## [1] A=A B=B C=C D=D E=E
##
## [[2]]
## [1] no aliasing among main effects and 2fisBy looking at the above design we can notice that no main effect or two factor interaction is aliased with any other main effect or two-factor interaction.
summary(des.resp)## Call:
## FrF2(nfactors = 5, resolution = 5, randomize = FALSE)
##
## Experimental design of type FrF2
## 16 runs
##
## Factor settings (scale ends):
## A B C D E
## 1 -1 -1 -1 -1 -1
## 2 1 1 1 1 1
##
## Design generating information:
## $legend
## [1] A=A B=B C=C D=D E=E
##
## $generators
## [1] E=ABCD
##
##
## Alias structure:
## [[1]]
## [1] no aliasing among main effects and 2fis
##
##
## The design itself:
## A B C D E
## 1 -1 -1 -1 -1 1
## 2 1 -1 -1 -1 -1
## 3 -1 1 -1 -1 -1
## 4 1 1 -1 -1 1
## 5 -1 -1 1 -1 -1
## 6 1 -1 1 -1 1
## 7 -1 1 1 -1 1
## 8 1 1 1 -1 -1
## 9 -1 -1 -1 1 -1
## 10 1 -1 -1 1 1
## 11 -1 1 -1 1 1
## 12 1 1 -1 1 -1
## 13 -1 -1 1 1 1
## 14 1 -1 1 1 -1
## 15 -1 1 1 1 -1
## 16 1 1 1 1 1
## class=design, type= FrF2If we block as per factor combination AB then, we’ll divide our factor combinations into 2 blocks.
AB <- c("+","-","-","+","+","-","-","+","+","-","-","+","+","-","-","+")
block <- c(1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1)
data <- data.frame(des.resp,AB,block)
data## A B C D E AB block
## 1 -1 -1 -1 -1 1 + 1
## 2 1 -1 -1 -1 -1 - 2
## 3 -1 1 -1 -1 -1 - 2
## 4 1 1 -1 -1 1 + 1
## 5 -1 -1 1 -1 -1 + 1
## 6 1 -1 1 -1 1 - 2
## 7 -1 1 1 -1 1 - 2
## 8 1 1 1 -1 -1 + 1
## 9 -1 -1 -1 1 -1 + 1
## 10 1 -1 -1 1 1 - 2
## 11 -1 1 -1 1 1 - 2
## 12 1 1 -1 1 -1 + 1
## 13 -1 -1 1 1 1 + 1
## 14 1 -1 1 1 -1 - 2
## 15 -1 1 1 1 -1 - 2
## 16 1 1 1 1 1 + 1By blocking AB and CDE combinations of factors are confounded.
8.25)
Half fraction of \(2^{7}\) can be run with k = 7 and p = 2 and of 32 runs.
design8.25 <- FrF2(nruns = 32, nfactors=7, blocks = 4, randomize=TRUE)
summary(design8.25)## Call:
## FrF2(nruns = 32, nfactors = 7, blocks = 4, randomize = TRUE)
##
## 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 29.1.8 1 1 1 1 -1 -1 1 -1
## 3 3 20.1.5 1 1 -1 -1 1 1 1 -1
## 4 4 10.1.3 1 -1 1 -1 -1 1 1 1
## 5 5 7.1.2 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 16.1.4 1 -1 1 1 1 1 -1 -1
## run.no run.no.std.rp Blocks A B C D E F G
## 9 9 19.2.5 2 1 -1 -1 1 -1 1 -1
## 10 10 15.2.4 2 -1 1 1 1 -1 -1 -1
## 11 11 2.2.1 2 -1 -1 -1 -1 1 -1 -1
## 12 12 8.2.2 2 -1 -1 1 1 1 1 1
## 13 13 9.2.3 2 -1 1 -1 -1 -1 1 1
## 14 14 30.2.8 2 1 1 1 -1 1 1 -1
## 15 15 28.2.7 2 1 1 -1 1 1 -1 1
## 16 16 21.2.6 2 1 -1 1 -1 -1 -1 1
## run.no run.no.std.rp Blocks A B C D E F G
## 17 17 24.3.6 3 1 -1 1 1 1 -1 -1
## 18 18 31.3.8 3 1 1 1 1 -1 1 1
## 19 19 3.3.1 3 -1 -1 -1 1 -1 -1 1
## 20 20 5.3.2 3 -1 -1 1 -1 -1 1 -1
## 21 21 12.3.3 3 -1 1 -1 1 1 1 -1
## 22 22 18.3.5 3 1 -1 -1 -1 1 1 1
## 23 23 14.3.4 3 -1 1 1 -1 1 -1 1
## 24 24 25.3.7 3 1 1 -1 -1 -1 -1 -1
## run.no run.no.std.rp Blocks A B C D E F G
## 25 25 26.4.7 4 1 1 -1 -1 1 -1 -1
## 26 26 23.4.6 4 1 -1 1 1 -1 -1 -1
## 27 27 32.4.8 4 1 1 1 1 1 1 1
## 28 28 11.4.3 4 -1 1 -1 1 -1 1 -1
## 29 29 13.4.4 4 -1 1 1 -1 -1 -1 1
## 30 30 4.4.1 4 -1 -1 -1 1 1 -1 1
## 31 31 6.4.2 4 -1 -1 1 -1 1 1 -1
## 32 32 17.4.5 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 frameWith blocks no main effects or two factor interactions are confounded.
8.28)
PART A :
A 16 run experiment was done to study effects of 6 factors.
K=6 and P=2
\(2^{6-2}\) with resolution 4
PART B :
des.res <- FrF2(nfactors = 6,resolution = 4 , randomize = TRUE)
aliasprint(des.res)## $legend
## [1] A=A B=B C=C D=D E=E F=F
##
## $main
## character(0)
##
## $fi2
## [1] AB=CE=DF AC=BE AD=BF AE=BC AF=BD CD=EF CF=DEPART C :
A <- c(-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)
C <- c(-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)
E <- c(-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)
A <- as.factor(A)
B <- as.factor(B)
C <- as.factor(C)
D <- as.factor(D)
E <- as.factor(E)
F <- as.factor(F)
response <- c(0.0167,0.0062,0.0041,0.0073,0.0047,0.0219,0.0121,0.0255,0.0032,0.0078,0.0043,0.0186,0.0110,0.0065,0.0155,0.0093,0.0128,0.0066,0.0043,0.0081,0.0047,0.0258,0.0090,0.0250,0.0023,0.0158,0.0027,0.0137,0.0086,0.0109,0.0158,0.0124,0.0149,0.0044,0.0042,0.0039,0.0040,0.0147,0.0092,0.0226,0.0077,0.0060,0.0028,0.0158,0.0101,0.0126,0.0145,0.0110,0.0185,0.0020,0.0050,0.0030,0.0089,0.0296,0.0086,0.0169,0.0069,0.0045,0.0028,0.0159,0.0158,0.0071,0.0145,0.0133)
dat <- data.frame(A,B,C,D,E,F,response)Performing AOV :
Model <- aov(response~A*B*C*D*E*F,data = dat)
summary(Model)## 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 ' ' 1Seeing the above ANOVA analysis we can say that the factors A, C, E, F would significantly affect average chamber.
PART D :
x <- 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)
var <- x^2
dat2 <- data.frame(A,B,C,D,E,F,var)Half Normal Plot :
Model2 <- lm(x ~ A*B*C*D*E*F,data = dat2)
DanielPlot(Model2)
By observing the above plot we can say that Laminating temperature and Laminating time significantly affect standard deviation.
Model3 <- aov(x ~ A + B,data = dat2)
summary(Model3)## Df Sum Sq Mean Sq F value Pr(>F)
## A 1 1012 1012 8.505 0.01202 *
## B 1 1099 1099 9.241 0.00948 **
## Residuals 13 1546 119
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1From the model above we can say that factors A and B are significant.
PART E :
Model2 <- lm(response ~ A*B*C*D*E*F,data = dat)
coef(Model2)## (Intercept) A1 B1 C1
## 0.015725000 0.001009375 -0.007137500 0.001784375
## D1 E1 F1 A1:B1
## -0.002953125 -0.004187500 -0.007746875 0.003725000
## A1:C1 B1:C1 A1:D1 B1:D1
## 0.004481250 0.007100000 -0.002550000 0.007968750
## C1:D1 A1:E1 B1:E1 C1:E1
## -0.000475000 NA NA NA
## D1:E1 A1:F1 B1:F1 C1:F1
## 0.001481250 NA NA NA
## D1:F1 E1:F1 A1:B1:C1 A1:B1:D1
## NA NA NA 0.000212500
## A1:C1:D1 B1:C1:D1 A1:B1:E1 A1:C1:E1
## NA -0.006937500 NA NA
## B1:C1:E1 A1:D1:E1 B1:D1:E1 C1:D1:E1
## NA NA NA NA
## A1:B1:F1 A1:C1:F1 B1:C1:F1 A1:D1:F1
## NA NA NA NA
## B1:D1:F1 C1:D1:F1 A1:E1:F1 B1:E1:F1
## NA NA NA NA
## C1:E1:F1 D1:E1:F1 A1:B1:C1:D1 A1:B1:C1:E1
## NA NA NA NA
## A1:B1:D1:E1 A1:C1:D1:E1 B1:C1:D1:E1 A1:B1:C1:F1
## NA NA NA NA
## A1:B1:D1:F1 A1:C1:D1:F1 B1:C1:D1:F1 A1:B1:E1:F1
## NA NA NA NA
## A1:C1:E1:F1 B1:C1:E1:F1 A1:D1:E1:F1 B1:D1:E1:F1
## NA NA NA NA
## C1:D1:E1:F1 A1:B1:C1:D1:E1 A1:B1:C1:D1:F1 A1:B1:C1:E1:F1
## NA NA NA NA
## A1:B1:D1:E1:F1 A1:C1:D1:E1:F1 B1:C1:D1:E1:F1 A1:B1:C1:D1:E1:F1
## NA NA NA NAsummary(Model2)##
## Call:
## lm.default(formula = response ~ A * B * C * D * E * F, data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.008300 -0.001350 -0.000350 0.001744 0.007275
##
## Coefficients: (48 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0157250 0.0014760 10.654 3.06e-14 ***
## A1 0.0010094 0.0016502 0.612 0.543644
## B1 -0.0071375 0.0018077 -3.948 0.000257 ***
## C1 0.0017844 0.0016502 1.081 0.284963
## D1 -0.0029531 0.0019525 -1.512 0.136976
## E1 -0.0041875 0.0010437 -4.012 0.000210 ***
## F1 -0.0077469 0.0007380 -10.497 5.05e-14 ***
## A1:B1 0.0037250 0.0020874 1.785 0.080655 .
## A1:C1 0.0044812 0.0014760 3.036 0.003866 **
## B1:C1 0.0071000 0.0020874 3.401 0.001359 **
## A1:D1 -0.0025500 0.0020874 -1.222 0.227809
## B1:D1 0.0079688 0.0025565 3.117 0.003083 **
## C1:D1 -0.0004750 0.0020874 -0.228 0.820954
## A1:E1 NA NA NA NA
## B1:E1 NA NA NA NA
## C1:E1 NA NA NA NA
## D1:E1 0.0014813 0.0014760 1.004 0.320619
## A1:F1 NA NA NA NA
## B1:F1 NA NA NA NA
## C1:F1 NA NA NA NA
## D1:F1 NA NA NA NA
## E1:F1 NA NA NA NA
## A1:B1:C1 NA NA NA NA
## A1:B1:D1 0.0002125 0.0029520 0.072 0.942912
## A1:C1:D1 NA NA NA NA
## B1:C1:D1 -0.0069375 0.0029520 -2.350 0.022926 *
## A1:B1:E1 NA NA NA NA
## A1:C1:E1 NA NA NA NA
## B1:C1:E1 NA NA NA NA
## A1:D1:E1 NA NA NA NA
## B1:D1:E1 NA NA NA NA
## C1:D1:E1 NA NA NA NA
## A1:B1:F1 NA NA NA NA
## A1:C1:F1 NA NA NA NA
## B1:C1:F1 NA NA NA NA
## A1:D1:F1 NA NA NA NA
## B1:D1:F1 NA NA NA NA
## C1:D1:F1 NA NA NA NA
## A1:E1:F1 NA NA NA NA
## B1:E1:F1 NA NA NA NA
## C1:E1:F1 NA NA NA NA
## D1:E1:F1 NA NA NA NA
## A1:B1:C1:D1 NA NA NA NA
## A1:B1:C1:E1 NA NA NA NA
## A1:B1:D1:E1 NA NA NA NA
## A1:C1:D1:E1 NA NA NA NA
## B1:C1:D1:E1 NA NA NA NA
## A1:B1:C1:F1 NA NA NA NA
## A1:B1:D1:F1 NA NA NA NA
## A1:C1:D1:F1 NA NA NA NA
## B1:C1:D1:F1 NA NA NA NA
## A1:B1:E1:F1 NA NA NA NA
## A1:C1:E1:F1 NA NA NA NA
## B1:C1:E1:F1 NA NA NA NA
## A1:D1:E1:F1 NA NA NA NA
## B1:D1:E1:F1 NA NA NA NA
## C1:D1:E1:F1 NA NA NA NA
## A1:B1:C1:D1:E1 NA NA NA NA
## A1:B1:C1:D1:F1 NA NA NA NA
## A1:B1:C1:E1:F1 NA NA NA NA
## A1:B1:D1:E1:F1 NA NA NA NA
## A1:C1:D1:E1:F1 NA NA NA NA
## B1:C1:D1:E1:F1 NA NA NA NA
## A1:B1:C1:D1:E1:F1 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.002952 on 48 degrees of freedom
## Multiple R-squared: 0.849, Adjusted R-squared: 0.8018
## F-statistic: 18 on 15 and 48 DF, p-value: 9.012e-15\(Y_{ijkl}\) = 0.0157250 + 0.0010094(A) + 0.0017844(C) - 0.0041875(E) - 0.0077469(F)
Hence it is sensible to keep E and F at high level and A and C at low level to reduce camber.
8.40)
Part A :
The experiment investigated ‘4’ factors.
Part B :
Resolution in the experiment is “4”.
Part C :
Effects are
One <- c(8)
AB <- c(7)
AC <- c(6)
AD <- c(10)
BC <- c(5)
BD <- c(12)
CD <- c(13)
ABCD <- c(11)Effect A :
effectA <- (2*(AD + AB + AC + ABCD - One - BD - CD - BC))/(8)
effectA## [1] -1Effect B :
effectB <- (2*(BD + AB + BC + ABCD - One - AD - CD - AC))/(8)
effectB## [1] -0.5Effect C :
effectC <- (2*(CD + AC + BC + ABCD - One - AD - BD - AB))/(8)
effectC## [1] -0.5Effect D :
effectD <- (2*(AD + BD + CD + ABCD - One - AB - AC - BC))/(8)
effectD## [1] 5Part D :
Relation defining this relation is I = ABCD
8.48)
design<- FrF2(nfactors = 5,nruns = 8, generators = c("-ABC","BC"), randomize = FALSE)
summary(design)## Call:
## FrF2(nfactors = 5, nruns = 8, generators = c("-ABC", "BC"), randomize = FALSE)
##
## Experimental design of type FrF2.generators
## 8 runs
##
## Factor settings (scale ends):
## A B C D E
## 1 -1 -1 -1 -1 -1
## 2 1 1 1 1 1
##
## Design generating information:
## $legend
## [1] A=A B=B C=C D=D E=E
##
## $generators
## [1] D=-ABC E=BC
##
##
## Alias structure:
## $main
## [1] A=-DE B=CE C=BE D=-AE E=-AD=BC
##
## $fi2
## [1] AB=-CD AC=-BD
##
##
## The design itself:
## A B C D E
## 1 -1 -1 -1 1 1
## 2 1 -1 -1 -1 1
## 3 -1 1 -1 -1 -1
## 4 1 1 -1 1 -1
## 5 -1 -1 1 -1 -1
## 6 1 -1 1 1 -1
## 7 -1 1 1 1 1
## 8 1 1 1 -1 1
## class=design, type= FrF2.generatorsa)
From column D we can see that the design generator for column D is -ABC.
b)
From column E we can see that the design generator for column E is BC.
c)
The resolution for Folded over design is “4”
8.60)
library(FrF2)
design8.60 <- FrF2(nfactors=7, resolution = 3, randomize = FALSE)
design8.60## A B C D E F G
## 1 -1 -1 -1 1 1 1 -1
## 2 1 -1 -1 -1 -1 1 1
## 3 -1 1 -1 -1 1 -1 1
## 4 1 1 -1 1 -1 -1 -1
## 5 -1 -1 1 1 -1 -1 1
## 6 1 -1 1 -1 1 -1 -1
## 7 -1 1 1 -1 -1 1 -1
## 8 1 1 1 1 1 1 1
## class=design, type= FrF2design8.60.2 <- fold.design(design, column = 1)
design8.60.2## A B C fold D E
## 1 -1 -1 -1 original 1 1
## 2 1 -1 -1 original -1 1
## 3 -1 1 -1 original -1 -1
## 4 1 1 -1 original 1 -1
## 5 -1 -1 1 original -1 -1
## 6 1 -1 1 original 1 -1
## 7 -1 1 1 original 1 1
## 8 1 1 1 original -1 1
## 9 1 -1 -1 mirror 1 1
## 10 -1 -1 -1 mirror -1 1
## 11 1 1 -1 mirror -1 -1
## 12 -1 1 -1 mirror 1 -1
## 13 1 -1 1 mirror -1 -1
## 14 -1 -1 1 mirror 1 -1
## 15 1 1 1 mirror 1 1
## 16 -1 1 1 mirror -1 1
## class=design, type= FrF2.generators.foldeddesign8.60.3 <- design8.60.2[-c(1,3,5,7,10,12,14,16),]
design8.60.3## A B C fold D E
## 2 1 -1 -1 original -1 1
## 4 1 1 -1 original 1 -1
## 6 1 -1 1 original 1 -1
## 8 1 1 1 original -1 1
## 9 1 -1 -1 mirror 1 1
## 11 1 1 -1 mirror -1 -1
## 13 1 -1 1 mirror -1 -1
## 15 1 1 1 mirror 1 1aliasprint(design8.60.2)## $legend
## [1] A=A B=B C=C D=fold E=D F=E
##
## $main
## [1] B=CF C=BF F=BC
##
## $fi2
## [1] AD=EF AE=DF AF=DE