Optimal design of experiments : a case study approach

305 Pages·2011·1.131 MB·English

by  Peter Goos, Bradley Jones

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JWST075-FM JWST075-Goos June6,2011 8:54 PrinterName:YettoCome
Optimal Design of Experiments
A Case Study Approach
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P1:OTA/XYZ P2:ABC
JWST075-FM JWST075-Goos June6,2011 8:54 PrinterName:YettoCome
Optimal Design of Experiments
A Case Study Approach
Peter Goos
UniversityofAntwerpandErasmusUniversityRotterdam
Bradley Jones
JMPDivisionofSAS
A John Wiley & Sons, Ltd., Publication
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JWST075-FM JWST075-Goos June6,2011 8:54 PrinterName:YettoCome
Thiseditionfirstpublished2011
©2011JohnWiley&Sons,Ltd
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LibraryofCongressCataloging-in-PublicationData
Goos,Peter.
Optimaldesignofexperiments:acasestudyapproach/PeterGoosandBradleyJones.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-74461-1(hardback)
1.Industrialengineering–Experiments–Computer-aideddesign. 2.Experimentaldesign–Data
processing. 3.Industrialengineering–Casestudies. I.Jones,Bradley. II.Title.
T57.5.G662011
670.285–dc22
2011008381
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
PrintISBN:978-0-470-74461-1
ePDFISBN:978-1-119-97400-0
oBookISBN:978-1-119-97401-7
ePubISBN:978-1-119-97616-5
MobiISBN:978-1-119-97617-2
Setin10/12ptTimesbyAptaraInc.,NewDelhi,India.
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Contents
Preface xiii
Acknowledgments xv
1 Asimplecomparativeexperiment 1
1.1 Keyconcepts 1
1.2 Thesetupofacomparativeexperiment 2
1.3 Summary 8
2 Anoptimalscreeningexperiment 9
2.1 Keyconcepts 9
2.2 Case:anextractionexperiment 10
2.2.1 Problemanddesign 10
2.2.2 Dataanalysis 14
2.3 Peekintotheblackbox 21
2.3.1 Main-effectsmodels 21
2.3.2 Modelswithtwo-factorinteractioneffects 22
2.3.3 Factorscaling 24
2.3.4 Ordinaryleastsquaresestimation 24
2.3.5 Significancetestsandstatisticalpowercalculations 27
2.3.6 Varianceinflation 28
2.3.7 Aliasing 29
2.3.8 Optimaldesign 33
2.3.9 Generatingoptimalexperimentaldesigns 35
2.3.10 Theextractionexperimentrevisited 40
2.3.11 Principlesofsuccessfulscreening:sparsity,hierarchy,
andheredity 41
2.4 Backgroundreading 44
2.4.1 Screening 44
2.4.2 Algorithmsforfindingoptimaldesigns 44
2.5 Summary 45
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viii CONTENTS
3 Addingrunstoascreeningexperiment 47
3.1 Keyconcepts 47
3.2 Case:anaugmentedextractionexperiment 48
3.2.1 Problemanddesign 48
3.2.2 Dataanalysis 55
3.3 Peekintotheblackbox 59
3.3.1 Optimalselectionofafollow-updesign 60
3.3.2 Designconstructionalgorithm 65
3.3.3 Foldoverdesigns 66
3.4 Backgroundreading 67
3.5 Summary 67
4 Aresponsesurfacedesignwithacategoricalfactor 69
4.1 Keyconcepts 69
4.2 Case:arobustandoptimalprocessexperiment 70
4.2.1 Problemanddesign 70
4.2.2 Dataanalysis 79
4.3 Peekintotheblackbox 82
4.3.1 Quadraticeffects 82
4.3.2 Dummyvariablesformultilevelcategoricalfactors 83
4.3.3 ComputingD-efficiencies 86
4.3.4 ConstructingFractionofDesignSpaceplots 87
4.3.5 Calculatingtheaveragerelativevarianceofprediction 88
4.3.6 ComputingI-efficiencies 90
4.3.7 Ensuringthevalidityofinferencebasedonordinary
leastsquares 90
4.3.8 Designregions 91
4.4 Backgroundreading 92
4.5 Summary 93
5 Aresponsesurfacedesigninanirregularlyshapeddesignregion 95
5.1 Keyconcepts 95
5.2 Case:theyieldmaximizationexperiment 95
5.2.1 Problemanddesign 95
5.2.2 Dataanalysis 103
5.3 Peekintotheblackbox 108
5.3.1 Cubicfactoreffects 108
5.3.2 Lack-of-fittest 109
5.3.3 Incorporatingfactorconstraintsinthedesign
constructionalgorithm 111
5.4 Backgroundreading 112
5.5 Summary 112
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CONTENTS ix
6 A“mixture”experimentwithprocessvariables 113
6.1 Keyconcepts 113
6.2 Case:therollingmillexperiment 114
6.2.1 Problemanddesign 114
6.2.2 Dataanalysis 121
6.3 Peekintotheblackbox 123
6.3.1 Themixtureconstraint 123
6.3.2 Theeffectofthemixtureconstraintonthemodel 123
6.3.3 Commonlyusedmodelsfordatafrommixture
experiments 125
6.3.4 Optimaldesignsformixtureexperiments 127
6.3.5 Designconstructionalgorithmsformixtureexperiments 130
6.4 Backgroundreading 132
6.5 Summary 133
7 Aresponsesurfacedesigninblocks 135
7.1 Keyconcepts 135
7.2 Case:thepastrydoughexperiment 136
7.2.1 Problemanddesign 136
7.2.2 Dataanalysis 144
7.3 Peekintotheblackbox 151
7.3.1 Model 151
7.3.2 Generalizedleastsquaresestimation 153
7.3.3 Estimationofvariancecomponents 156
7.3.4 Significancetests 157
7.3.5 Optimaldesignofblockedexperiments 157
7.3.6 Orthogonalblocking 158
7.3.7 Optimalversusorthogonalblocking 160
7.4 Backgroundreading 160
7.5 Summary 161
8 Ascreeningexperimentinblocks 163
8.1 Keyconcepts 163
8.2 Case:thestabilityimprovementexperiment 164
8.2.1 Problemanddesign 164
8.2.2 Afterthoughtsaboutthedesignproblem 169
8.2.3 Dataanalysis 175
8.3 Peekintotheblackbox 179
8.3.1 Modelsinvolvingblockeffects 179
8.3.2 Fixedblockeffects 182
8.4 Backgroundreading 184
8.5 Summary 185