DOE - HW - Week 13
Tajammul Mohammed
11/28/2021
Answer 8.2
The required design is a 24-1 with I=ABCD.
design.res6.7 <- FrF2(nfactors=4, resolution=4, randomize=FALSE)
Response <- c(7.037, 16.867, 13.876, 17.273, 11.846, 4.368, 9.360, 15.653)
design.reponse6.7 <- add.response(design.res6.7, Response)
design.reponse6.7## 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= FrF2aliasprint(design.reponse6.7)## $legend
## [1] A=A B=B C=C D=D
##
## $main
## character(0)
##
## $fi2
## [1] AB=CD AC=BD AD=BCHence, we see that this is a resolution 4 design and so the main effects are not aliased with other two interactions.
summary(design.reponse6.7)## Call:
## FrF2(nfactors = 4, resolution = 4, randomize = FALSE)
##
## 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= FrF2DanielPlot(design.reponse6.7)
Therefore, we see that none of the factors are significant.
Answer 8.24
design.reponse8.24 <- FrF2(nfactors = 5, resolution = 5 ,randomize = FALSE)
design.reponse8.24## 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= FrF2aliasprint(design.reponse8.24)## $legend
## [1] A=A B=B C=C D=D E=E
##
## [[2]]
## [1] no aliasing among main effects and 2fissummary(design.reponse8.24)## 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= FrF2The above is the design summary. We see that AB & CDE factors are confounded within blocks.
AB <- c("+","-","-","+","+","-","-","+","+","-","-","+","+","-","-","+")
Blocks <- c(1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1)
Dat<-data.frame(design.reponse8.24, AB, Blocks)
Dat## A B C D E AB Blocks
## 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 + 1Hence, we see that no main effects are confounded within the blocks.
Answer 8.25
design.reponse8.25 <- FrF2(nfactors=7, blocks=4, nruns=32, resolution = 4, randomize=FALSE)## Warning in FrF2(nfactors = 7, blocks = 4, nruns = 32, resolution = 4, randomize
## = FALSE): resolution is ignored, if nruns is given.summary(design.reponse8.25)## Call:
## FrF2(nfactors = 7, blocks = 4, nruns = 32, resolution = 4, randomize = FALSE)
##
## 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 framealiasprint(design.reponse8.25)## $legend
## [1] A=A B=B C=C D=D E=E F=F G=G
##
## $main
## character(0)
##
## $fi2
## [1] AB=CF=DG AC=BF AD=BG AF=BC AG=BD CD=FG CG=DFsummary(design.reponse8.25)## Call:
## FrF2(nfactors = 7, blocks = 4, nruns = 32, resolution = 4, randomize = FALSE)
##
## 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 frameThe above is the design summary. We see that ACE, BFG & ABCEFG factors are confounded within blocks. Also, no main effects or two factor interactions are confounded within the blocks.
Answer 8.28
design.reponse8.28 <- FrF2(nfactors = 6, resolution = 4, randomize = FALSE)
design.reponse8.28## A B C D E F
## 1 -1 -1 -1 -1 -1 -1
## 2 1 -1 -1 -1 1 1
## 3 -1 1 -1 -1 1 1
## 4 1 1 -1 -1 -1 -1
## 5 -1 -1 1 -1 1 -1
## 6 1 -1 1 -1 -1 1
## 7 -1 1 1 -1 -1 1
## 8 1 1 1 -1 1 -1
## 9 -1 -1 -1 1 -1 1
## 10 1 -1 -1 1 1 -1
## 11 -1 1 -1 1 1 -1
## 12 1 1 -1 1 -1 1
## 13 -1 -1 1 1 1 1
## 14 1 -1 1 1 -1 -1
## 15 -1 1 1 1 -1 -1
## 16 1 1 1 1 1 1
## class=design, type= FrF2summary(design.reponse8.28)## Call:
## FrF2(nfactors = 6, resolution = 4, randomize = FALSE)
##
## Experimental design of type FrF2
## 16 runs
##
## 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
## [1] E=ABC F=ABD
##
##
## Alias structure:
## $fi2
## [1] AB=CE=DF AC=BE AD=BF AE=BC AF=BD CD=EF CF=DE
##
##
## The design itself:
## A B C D E F
## 1 -1 -1 -1 -1 -1 -1
## 2 1 -1 -1 -1 1 1
## 3 -1 1 -1 -1 1 1
## 4 1 1 -1 -1 -1 -1
## 5 -1 -1 1 -1 1 -1
## 6 1 -1 1 -1 -1 1
## 7 -1 1 1 -1 -1 1
## 8 1 1 1 -1 1 -1
## 9 -1 -1 -1 1 -1 1
## 10 1 -1 -1 1 1 -1
## 11 -1 1 -1 1 1 -1
## 12 1 1 -1 1 -1 1
## 13 -1 -1 1 1 1 1
## 14 1 -1 1 1 -1 -1
## 15 -1 1 1 1 -1 -1
## 16 1 1 1 1 1 1
## class=design, type= FrF2(a). This is a 16 run design with 2^(6-2).
aliasprint(design.reponse8.28)## $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=DE(b). The defining relation is I=ABCE=ACDF=BDEF.
LaminationTemp <- c(rep(c("-1","1"),8))
LaminationTime <- c(rep(c("-1","-1","1","1"),4))
LaminationPressure <- c(rep(c("-1","-1","-1","-1","1","1","1","1"),2))
FiringTemp <- c(rep(c("-1","-1","-1","-1","-1","-1","-1","-1","1","1","1","1","1","1","1","1"),1))
FiringCycleTime <- c(rep(c("-1","1","1","-1","1","-1","-1","1"),2))
FiringDewPoint <- c(rep(c("-1","1","-1","1","1","-1","1","-1"),2))
Response2 <- 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)
Total <- c(629,192,176,223,223,920,389,900,201,341,126,640,455,371,603,460)
Mean <- c(157.25,48,44,55.75,55.75,230,97.25,225,50.25,85.25,31.5,160,113.75,92.75,150.75,115)
Standard <- 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
)
Dat8.28Q <- cbind(LaminationTemp,LaminationTime,LaminationPressure,FiringTemp,FiringCycleTime,FiringDewPoint,Response2,Total,Mean,Standard)
Dat8.28Q <- as.data.frame(Dat8.28Q)
Dat8.28Q## LaminationTemp LaminationTime LaminationPressure FiringTemp FiringCycleTime
## 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
## 17 -1 -1 -1 -1 -1
## 18 1 -1 -1 -1 1
## 19 -1 1 -1 -1 1
## 20 1 1 -1 -1 -1
## 21 -1 -1 1 -1 1
## 22 1 -1 1 -1 -1
## 23 -1 1 1 -1 -1
## 24 1 1 1 -1 1
## 25 -1 -1 -1 1 -1
## 26 1 -1 -1 1 1
## 27 -1 1 -1 1 1
## 28 1 1 -1 1 -1
## 29 -1 -1 1 1 1
## 30 1 -1 1 1 -1
## 31 -1 1 1 1 -1
## 32 1 1 1 1 1
## 33 -1 -1 -1 -1 -1
## 34 1 -1 -1 -1 1
## 35 -1 1 -1 -1 1
## 36 1 1 -1 -1 -1
## 37 -1 -1 1 -1 1
## 38 1 -1 1 -1 -1
## 39 -1 1 1 -1 -1
## 40 1 1 1 -1 1
## 41 -1 -1 -1 1 -1
## 42 1 -1 -1 1 1
## 43 -1 1 -1 1 1
## 44 1 1 -1 1 -1
## 45 -1 -1 1 1 1
## 46 1 -1 1 1 -1
## 47 -1 1 1 1 -1
## 48 1 1 1 1 1
## 49 -1 -1 -1 -1 -1
## 50 1 -1 -1 -1 1
## 51 -1 1 -1 -1 1
## 52 1 1 -1 -1 -1
## 53 -1 -1 1 -1 1
## 54 1 -1 1 -1 -1
## 55 -1 1 1 -1 -1
## 56 1 1 1 -1 1
## 57 -1 -1 -1 1 -1
## 58 1 -1 -1 1 1
## 59 -1 1 -1 1 1
## 60 1 1 -1 1 -1
## 61 -1 -1 1 1 1
## 62 1 -1 1 1 -1
## 63 -1 1 1 1 -1
## 64 1 1 1 1 1
## FiringDewPoint Response2 Total Mean Standard
## 1 -1 0.0167 629 157.25 24.418
## 2 1 0.0062 192 48 20.976
## 3 -1 0.0041 176 44 4.083
## 4 1 0.0073 223 55.75 25.025
## 5 1 0.0047 223 55.75 22.41
## 6 -1 0.0219 920 230 63.639
## 7 1 0.0121 389 97.25 16.029
## 8 -1 0.0255 900 225 39.42
## 9 -1 0.0032 201 50.25 26.725
## 10 1 0.0078 341 85.25 50.341
## 11 -1 0.0043 126 31.5 7.681
## 12 1 0.0186 640 160 20.083
## 13 1 0.011 455 113.75 31.12
## 14 -1 0.0065 371 92.75 29.51
## 15 1 0.0155 603 150.75 6.75
## 16 -1 0.0093 460 115 17.45
## 17 -1 0.0128 629 157.25 24.418
## 18 1 0.0066 192 48 20.976
## 19 -1 0.0043 176 44 4.083
## 20 1 0.0081 223 55.75 25.025
## 21 1 0.0047 223 55.75 22.41
## 22 -1 0.0258 920 230 63.639
## 23 1 0.009 389 97.25 16.029
## 24 -1 0.025 900 225 39.42
## 25 -1 0.0023 201 50.25 26.725
## 26 1 0.0158 341 85.25 50.341
## 27 -1 0.0027 126 31.5 7.681
## 28 1 0.0137 640 160 20.083
## 29 1 0.0086 455 113.75 31.12
## 30 -1 0.0109 371 92.75 29.51
## 31 1 0.0158 603 150.75 6.75
## 32 -1 0.0124 460 115 17.45
## 33 -1 0.0149 629 157.25 24.418
## 34 1 0.0044 192 48 20.976
## 35 -1 0.0042 176 44 4.083
## 36 1 0.0039 223 55.75 25.025
## 37 1 0.004 223 55.75 22.41
## 38 -1 0.0147 920 230 63.639
## 39 1 0.0092 389 97.25 16.029
## 40 -1 0.0226 900 225 39.42
## 41 -1 0.0077 201 50.25 26.725
## 42 1 0.006 341 85.25 50.341
## 43 -1 0.0028 126 31.5 7.681
## 44 1 0.0158 640 160 20.083
## 45 1 0.0101 455 113.75 31.12
## 46 -1 0.0126 371 92.75 29.51
## 47 1 0.0145 603 150.75 6.75
## 48 -1 0.011 460 115 17.45
## 49 -1 0.0185 629 157.25 24.418
## 50 1 0.002 192 48 20.976
## 51 -1 0.005 176 44 4.083
## 52 1 0.003 223 55.75 25.025
## 53 1 0.0089 223 55.75 22.41
## 54 -1 0.0296 920 230 63.639
## 55 1 0.0086 389 97.25 16.029
## 56 -1 0.0169 900 225 39.42
## 57 -1 0.0069 201 50.25 26.725
## 58 1 0.0045 341 85.25 50.341
## 59 -1 0.0028 126 31.5 7.681
## 60 1 0.0159 640 160 20.083
## 61 1 0.0158 455 113.75 31.12
## 62 -1 0.0071 371 92.75 29.51
## 63 1 0.0145 603 150.75 6.75
## 64 -1 0.0133 460 115 17.45Dat8.28Q$LaminationTemp <- as.fixed(Dat8.28Q$LaminationTemp)
Dat8.28Q$LaminationTime <- as.fixed(Dat8.28Q$LaminationTime)
Dat8.28Q$LaminationPressure <- as.fixed(Dat8.28Q$LaminationPressure)
Dat8.28Q$FiringTemp <- as.fixed(Dat8.28Q$FiringTemp)
Dat8.28Q$FiringDewPoint <- as.fixed(Dat8.28Q$FiringDewPoint)
Dat8.28Q$FiringCycleTime <- as.fixed(Dat8.28Q$FiringCycleTime)
Model8.28Q <- aov(Response2~LaminationTemp*LaminationTime*LaminationPressure*FiringTemp*FiringCycleTime*FiringDewPoint,data = Dat8.28Q)
summary(Model8.28Q)## Df Sum Sq Mean Sq F value
## LaminationTemp 1 0.0002422 0.0002422 27.793
## LaminationTime 1 0.0000053 0.0000053 0.614
## LaminationPressure 1 0.0005023 0.0005023 57.644
## FiringTemp 1 0.0000323 0.0000323 3.712
## FiringCycleTime 1 0.0001901 0.0001901 21.815
## FiringDewPoint 1 0.0000803 0.0000803 9.218
## LaminationTemp:LaminationTime 1 0.0000587 0.0000587 6.738
## LaminationTime:LaminationPressure 1 0.0000527 0.0000527 6.053
## LaminationTemp:FiringTemp 1 0.0000239 0.0000239 2.741
## LaminationTime:FiringTemp 1 0.0000849 0.0000849 9.739
## LaminationPressure:FiringTemp 1 0.0000622 0.0000622 7.139
## FiringTemp:FiringCycleTime 1 0.0000088 0.0000088 1.007
## FiringTemp:FiringDewPoint 1 0.0009602 0.0009602 110.192
## LaminationTemp:LaminationTime:FiringTemp 1 0.0000000 0.0000000 0.005
## LaminationTime:LaminationPressure:FiringTemp 1 0.0000481 0.0000481 5.523
## Residuals 48 0.0004183 0.0000087
## Pr(>F)
## LaminationTemp 3.17e-06 ***
## LaminationTime 0.43725
## LaminationPressure 9.14e-10 ***
## FiringTemp 0.05995 .
## FiringCycleTime 2.45e-05 ***
## FiringDewPoint 0.00387 **
## LaminationTemp:LaminationTime 0.01249 *
## LaminationTime:LaminationPressure 0.01754 *
## LaminationTemp:FiringTemp 0.10431
## LaminationTime:FiringTemp 0.00305 **
## LaminationPressure:FiringTemp 0.01027 *
## FiringTemp:FiringCycleTime 0.32062
## FiringTemp:FiringDewPoint 5.05e-14 ***
## LaminationTemp:LaminationTime:FiringTemp 0.94291
## LaminationTime:LaminationPressure:FiringTemp 0.02293 *
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(c) variables A, C, E, and F affect average camber.
(d) A, B, F, and AF interaction affect the variability in camber measurements.
camber <- 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)
A <- c(rep(c("-1","1"),8))
B <- c(rep(c("-1","-1","1","1"),4))
C <- c(rep(c("-1","-1","-1","-1","1","1","1","1"),2))
D <- c(rep(c("-1","-1","-1","-1","-1","-1","-1","-1","1","1","1","1","1","1","1","1"),1))
E <- c(rep(c("-1","1","1","-1","1","-1","-1","1"),2))
F<- c(rep(c("-1","1","-1","1","1","-1","1","-1"),2))
Dat8.28C <- data.frame(A,B,C,D,E,F,camber)
Model8.28C <- lm(camber~A*B*C*D*E*F,data = Dat8.28C)
DanielPlot(Model8.28C)
A & B affect the camber measurements.
Answer 8.40
(a) 4 factors
(b) resolution is 4
(c) Effects estimate
One <- c(8)
AD <- c(10)
BD <- c(12)
AB <- c(7)
CD <- c(13)
AC <- c(6)
BC <- c(5)
ABCD <- c(11)
EffectA <- (2*(AD+AB+AC+ABCD-One-BD-CD-BC))/(16)
EffectA## [1] -0.5(d) The complete defining relation is I = ABCD.
Answer 8.48
(a) D = –ABC
(b) E = BC
(c) Resolution of the combined design is 4.
Answer 8.60
design.reponse6.7 <- FrF2(nfactors=7,resolution=3,randomize=FALSE)
design.reponse6.7## 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= FrF2design.reponse6.7b <- fold.design(design.reponse6.7,column=1)
design.reponse6.7b## 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.foldeddesign.reponse6.7c <- design.reponse6.7b[-c(1,3,5,7,10,12,14,16),]
design.reponse6.7c## A B C fold D E F G
## 2 1 -1 -1 original -1 -1 1 1
## 4 1 1 -1 original 1 -1 -1 -1
## 6 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
## 11 1 1 -1 mirror -1 1 -1 1
## 13 1 -1 1 mirror 1 -1 -1 1
## 15 1 1 1 mirror -1 -1 1 -1