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STATISTICAL
ROBUST
Arnér
DESIGN
S
An Industrial Perspective T
A
Magnus Arnér, Tetra Pak Packaging Solutions, Sweden T
I
S
A UNIQUELY PRACTICAL APPROACH TO ROBUST DESIGN
T
FROM A STATISTICAL AND ENGINEERING PERSPECTIVE
I
Variation in environment, usage conditions, and the manufacturing process has C
long presented a challenge in product engineering, and reducing variation is
A
universally recognized as a key to improving reliability and productivity. One key
and cost-effective way to achieve this is by robust design – making the product as L
insensitive as possible to variation.
With Design for Six Sigma training programs primarily in mind, the author of this R Magnus Arnér
book offers practical examples that will help to guide product engineers through O
every stage of experimental design: formulating problems, planning experiments,
and analysing data. He discusses both physical and virtual techniques, and B
includes numerous exercises and solutions that make the book an ideal resource
for teaching or self-study. U STATISTICAL
• Presents a practical approach to robust design through design of experiments. S
• Offers a balance between statistical and industrial aspects of robust design. T
• Includes practical exercises, making the book useful for teaching. ROBUST
D
• Covers both physical and virtual approaches to robust design.
• Supported by an accompanying website (www.wiley/com/go/robust) E
featuring MATLAB® scripts and solutions to exercises. S
• Written by an experienced industrial design practitioner. I DESIGN
G
This book’s state of the art perspective will be of benefi t to practitioners of robust
N
design in industry, consultants providing training in Design for Six Sigma, and
quality engineers. It will also be a valuable resource for specialized university
courses in statistics or quality engineering.
An Industrial Perspective
www.wiley/com/go/robust
Statistical Robust Design
Statistical Robust Design
An Industrial Perspective
Magnus Arne´r
TetraPakPackagingSolutions, Sweden
Thiseditionfirstpublished2014
©2014JohnWiley&Sons,Ltd
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LibraryofCongressCataloging-in-PublicationData
Arner,Magnus,author.
Statisticalrobustdesign:anindustrialperspective/MagnusArner.
pagescm
Includesbibliographicalreferencesandindex.
ISBN978-1-118-62503-3(cloth)
1.Industrialdesign–Statisticalmethods. 2.Robuststatistics. I.Title.
TS171.9.A762014
745.2–dc23
2013046030
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN:978-1-118-62503-3
Setin10/12ptTimesbyAptaraInc.,NewDelhi,India
1 2014
Contents
Preface ix
1 Whatisrobustdesign? 1
1.1 Theimportanceofsmallvariation 1
1.2 Variancereduction 2
1.3 Variationpropagation 4
1.4 Discussion 5
1.4.1 Limitations 6
1.4.2 Theoutlineofthisbook 7
Exercises 8
2 DOEforrobustdesign,part1 11
2.1 Introduction 11
2.1.1 Noisefactors 11
2.1.2 Controlfactors 12
2.1.3 Control-by-noiseinteractions 12
2.2 Combinedarrays:Anexamplefromthepackagingindustry 13
2.2.1 Theexperimentalarray 15
2.2.2 Factoreffectplots 15
2.2.3 Analyticalanalysisandstatisticalsignificance 17
2.2.4 Someadditionalcommentsontheplotting 20
2.3 Dispersioneffects 21
Exercises 23
Reference 25
3 Noiseandcontrolfactors 27
3.1 Introductiontonoisefactors 27
3.1.1 Categoriesofnoise 28
3.2 Findingtheimportantnoisefactors 33
3.2.1 Relatingnoisetofailuremodes 33
3.2.2 Reducingthenumberofnoisefactors 34
3.3 Howtoincludenoiseinadesignedexperiment 40
3.3.1 Compoundingofnoisefactors 40
vi CONTENTS
3.3.2 Howtoincludenoiseinexperimentation 45
3.3.3 Processparameters 48
3.4 Controlfactors 48
Exercises 49
References 51
4 Response,signal,andPdiagrams 53
4.1 Theideaofsignalandresponse 53
4.1.1 Twosituations 54
4.2 IdealfunctionsandPdiagrams 55
4.2.1 Noiseorsignalfactor 56
4.2.2 Controlorsignalfactor 56
4.2.3 Thescope 58
4.3 Thesignal 63
4.3.1 Includingasignalinadesignedexperiment 64
Exercises 65
5 DOEforrobustdesign,part2 69
5.1 Combinedandcrossedarrays 69
5.1.1 ClassicalDOEversusDOEforrobustdesign 69
5.1.2 Thestructureofinnerandouterarrays 70
5.2 Includingasignalinadesignedexperiment 74
5.2.1 Combinedarrayswithasignal 74
5.2.2 Innerandouterarrayswithasignal 81
5.3 Crossedarraysversuscombinedarrays 89
5.3.1 Differencesinfactoraliasing 91
5.4 Crossedarraysandsplit-plotdesigns 94
5.4.1 Limitsofrandomization 94
5.4.2 Split-plotdesigns 95
Exercises 98
References 99
6 Smaller-the-betterandlarger-the-better 101
6.1 Differenttypesofresponses 101
6.2 Failuremodesandsmaller-the-better 102
6.2.1 Failuremodes 102
6.2.2 STBwithinnerandouterarrays 103
6.2.3 STBwithcombinedarrays 106
6.3 Larger-the-better 106
6.4 Operatingwindow 108
6.4.1 Thewindowwidth 110
Exercises 113
References 115
CONTENTS vii
7 Regressionforrobustdesign 117
7.1 Graphicaltechniques 117
( )
7.2 Analyticalminimizationof g′(z) 2 120
7.3 Regressionandcrossedarrays 121
7.3.1 Regressiontermsintheinnerarray 127
Exercises 128
8 Mathematicsofrobustdesign 131
8.1 Notationalsystem 131
8.2 Theobjectivefunction 132
8.2.1 Multidimensionalproblems 136
8.2.2 Optimizationinthepresenceofasignal 138
8.2.3 Matrixformulation 139
8.2.4 Paretooptimality 141
8.3 ANOVAforrobustdesign 144
8.3.1 TraditionalANOVA 144
8.3.2 FunctionalANOVA 146
8.3.3 Sensitivityindices 149
Exercises 152
References 153
9 Designandanalysisofcomputerexperiments 155
9.1 Overviewofcomputerexperiments 156
9.1.1 Robustdesign 157
9.2 Experimentalarraysforcomputerexperiments 161
9.2.1 Screeningdesigns 161
9.2.2 Spacefillingdesigns 163
9.2.3 Latinhypercubes 165
9.2.4 Latinhypercubedesignsandalphabetical
optimalitycriteria 166
9.3 Responsesurfaces 167
9.3.1 Localleastsquares 168
9.3.2 Kriging 169
9.4 Optimization 171
9.4.1 Theobjectivefunction 171
9.4.2 AnalyticaltechniquesorMonteCarlo 173
Exercises 175
References 176
10 MonteCarlomethodsforrobustdesign 177
10.1 Geometryvariation 177
10.1.1 Electroniccircuits 179
10.2 Geometryvariationintwodimensions 179
10.3 Crossedarrays 192
viii CONTENTS
11 Taguchiandhisideasonrobustdesign 195
11.1 Historyandorigin 195
11.2 Theexperimentalarrays 197
11.2.1 Thenatureofinnerarrays 197
11.2.2 Interactionsandenergythinking 199
11.2.3 Crossingthearrays 200
11.3 Signal-to-noiseratios 200
11.4 Someotherideas 203
11.4.1 Randomization 203
11.4.2 Scienceversusengineering 204
11.4.3 Linefittingfordynamicmodels 204
11.4.4 Anaspectonthenoise 206
11.4.5 Dynamicmodels 207
Exercises 208
References 208
AppendixA Lossfunctions 209
A.1 WhyAmericansdonotbuyAmericantelevisionsets 209
A.2 Taguchi’sviewonlossfunction 211
A.3 Theaveragelossanditselements 211
A.4 Lossfunctionsinrobustdesign 214
Exercises 215
References 217
AppendixB Dataforchapter2 219
AppendixC Dataforchapter5 223
AppendixD Dataforchapter6 231
Index 233
