Six Sigma Quality Improvement with Minitab Six Sigma Quality Improvement with Minitab Second Edition G. Robin Henderson Halcro Consultancy, Midlothian, UK A John Wiley & Sons, Ltd., Publication Thiseditionfirstpublished2011 (cid:1)2011JohnWiley&Sons,Ltd Registeredoffice JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyforpermission toreusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com. Therightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththe Copyright,DesignsandPatentsAct1988. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inany formorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbytheUK Copyright,DesignsandPatentsAct1988,withoutthepriorpermissionofthepublisher. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbe availableinelectronicbooks. Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrandnames andproductnamesusedinthisbookaretradenames,servicemarks,trademarksorregisteredtrademarksoftheir respectiveowners.Thepublisherisnotassociatedwithanyproductorvendormentionedinthisbook.This publicationisdesignedtoprovideaccurateandauthoritativeinformationinregardtothesubjectmattercovered. Itissoldontheunderstandingthatthepublisherisnotengagedinrenderingprofessionalservices.Ifprofessional adviceorotherexpertassistanceisrequired,theservicesofacompetentprofessionalshouldbesought. LibraryofCongressCataloging-in-PublicationData Henderson,G.Robin. SixSigmaqualityimprovementwithMinitab/G.RobinHenderson.–2nded. p.cm. Includesbibliographicalreferencesandindex. ISBN978-0-470-74175-7(cloth)–ISBN978-0-470-74174-0(pbk.) 1. Processcontrol.2. Sixsigma(Qualitycontrolstandard)3. Minitab. I.Title. TS156.8.H452011 658.5’62–dc23 2011012320 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ThecoverimagewascreatedusingaMinitabmacrothatsimulatestheDemingfunnelexperimentsthathighlightthedangers oftamperingwithstableprocesses.Theexperimentsandmacroarereferredtointhetext. HBISBN:978-0-470-74175-7 PBISBN:978-0-470-74174-0 ePDFISBN:978-1-119-97533-5 oBookISBN:978-1-119-97532-8 ePubISBN:978-1-119-97618-9 MobiISBN:978-1-119-97619-6 Setin10/12pt,TimesRomanbyThomsonDigital,Noida,India To Fiona and Iain Contents Foreword xi Preface xiii Acknowledgements xvii About the Author xix 1 Introduction 1 1.1 Quality and Quality Improvement 2 1.2 Six Sigma Quality Improvement 3 1.3 The SixSigmaRoadmap andDMAIC 6 1.4 The Role ofStatistical Methodsin SixSigma 8 1.5 Minitaband its Role inthe Implementation ofStatistical Methods 10 1.6 Exercises andFollow-Up Activities 11 2 Data Display, Summaryand Manipulation 13 2.1 The Run Chart – a First MinitabSession 13 2.1.1 Input of Data Via Keyboardand Creationof aRun Chart inMinitab 13 2.1.2 MinitabProjects andTheir Components 20 2.2 Displayand Summary ofUnivariate Data 27 2.2.1 Histogram andDistribution 27 2.2.2 Shape ofa Distribution 30 2.2.3 Location 30 2.2.4 Variability 38 2.3 Data Input, Output, Manipulation andManagement 43 2.3.1 Data Input andOutput 43 2.3.2 Stacking and Unstacking ofData; ChangingData Typeand Coding 44 2.3.3 Case Study Demonstrating Ranking, Sorting andExtraction of Informationfrom Date/TimeData 54 2.4 Exercises andFollow-Up Activities 61 3 ExploratoryData Analysis, Display and Summaryof Multivariate Data 63 3.1 Exploratory Data Analysis 63 3.1.1 Stem-and-LeafDisplays 63 3.1.2 Outliersand Outlier Detection 67 3.1.3 Boxplots 68 3.1.4 Brushing 70 3.2 Display and Summary of Bivariate and Multivariate Data 72 3.2.1 Bivariate Data – Scatterplots and MarginalPlots 72 3.2.2 Covariance andCorrelation 74 viii CONTENTS 3.2.3 MultivariateData – Matrix Plots 79 3.2.4 Multi-VariCharts 82 3.3 Other Displays 84 3.3.1 ParetoCharts 84 3.3.2 Cause-and-Effect Diagrams 87 3.4 Exercises andFollow-Up Activities 90 4 Statistical Models 93 4.1 Fundamentals of Probability 93 4.1.1 Concept andNotation 93 4.1.2 Rules for Probabilities 95 4.2 Probability Distributions for Counts and Measurements 99 4.2.1 BinomialDistribution 99 4.2.2 PoissonDistribution 105 4.2.3 Normal(Gaussian) Distribution 108 4.3 DistributionofMeans andProportions 118 4.3.1 Two Preliminary Results 118 4.3.2 Distributionofthe Sample Mean 120 4.3.3 Distributionofthe Sample Proportion 125 4.4 MultivariateNormalDistribution 127 4.5 Statistical Models Applied toAcceptance Sampling 129 4.5.1 Acceptance Sampling by Attributes 129 4.5.2 Acceptance Sampling by Variables 132 4.6 Exercises andFollow-Up Activities 134 5 ControlCharts 141 5.1 Shewhart Charts for Measurement Data 141 5.1.1 I andMR Chartsfor IndividualMeasurements 141 5.1.2 Testsfor Evidence ofSpecial Cause Variation on Shewhart Charts 148 5.1.3 Xbarand R Charts for Samples (Subgroups) ofMeasurements 151 5.2 Shewhart Charts for AttributeData 160 5.2.1 P Chart for Proportion Nonconforming 160 5.2.2 NP Chart for Number Nonconforming 167 5.2.3 C Chart for Count of Nonconformities 168 5.2.4 UChart for NonconformitiesPer Unit 169 5.2.5 Funnel Plots 170 5.3 Time-Weighted ControlCharts 171 5.3.1 MovingAveragesand their Applications 171 5.3.2 Exponentially Weighted MovingAverageControlCharts 179 5.3.3 CumulativeSumControlCharts 181 5.4 ProcessAdjustment 186 5.4.1 ProcessTampering 186 5.4.2 Autocorrelated Data andProcessFeedback Adjustment 189 5.5 MultivariateControlCharts 193 5.6 Exercises andFollow-Up Activities 194 CONTENTS ix 6 ProcessCapability Analysis 203 6.1 ProcessCapability 203 6.1.1 ProcessCapability Analysis with Measurement Data 203 6.1.2 ProcessCapability Indices and Sigma Quality Levels 212 6.1.3 ProcessCapability Analysis with Nonnormal Data 214 6.1.4 Tolerance Intervals 217 6.1.5 ProcessCapability Analysis with AttributeData 220 6.2 Exercises andFollow-Up Activities 222 7 ProcessExperimentation with aSingle Factor 225 7.1 Fundamentals of Hypothesis Testing 226 7.2 Testsand ConfidenceIntervals for the Comparison of Means and Proportions with aStandard 234 7.2.1 TestsBased on the Standard NormalDistribution– z-Tests 234 7.2.2 TestsBased on the Studentt-Distribution– t-Tests 243 7.2.3 Testsfor Proportions 247 7.2.4 Nonparametric Sign andWilcoxon Tests 249 7.3 Testsand ConfidenceIntervals for the Comparison of Two Meansor Two Proportions 252 7.3.1 Two-Sample t-Tests 252 7.3.2 Testsfor Two Proportions 256 7.3.3 Nonparametric Mann–WhitneyTest 259 7.4 The Analysis ofPairedData – t-Testsand SignTests 261 7.5 Experiments with a Single FactorHavingMore Than Two Levels 264 7.5.1 Design andAnalysis of aSingle-FactorExperiment 264 7.5.2 The FixedEffects Model 274 7.5.3 The Random Effects Model 276 7.5.4 The Nonparametric Kruskal–WallisTest 281 7.6 Blockingin Single-Factor Experiments 283 7.7 Experiments with a Single Factor,withMore Than Two Levels, where the Response is aProportion 291 7.8 Testsfor Equality ofVariances 294 7.9 Exercises andFollow-Up Activities 296 8 ProcessExperimentation with Two or More Factors 303 8.1 General FactorialExperiments 304 8.1.1 Creationofa GeneralFactorial Experimental Design 304 8.1.2 Displayand Analysis ofData from aGeneral Factorial Experiment 306 8.1.3 The FixedEffects Model,Comparisons 313 8.1.4 The Random Effects Model,Components ofVariance 321 k 8.2 Full FactorialExperiments inthe 2 Series 326 8.2.1 22 Factorial Experimental Designs, Display and Analysis of Data 326 8.2.2 Modelsand AssociatedDisplays 334 8.2.3 Examples of23 and 24Experiments,the Use of Pareto and NormalProbability Plots ofEffects 343 x CONTENTS k(cid:1)p 8.3 Fractional Factorial Experiments inthe 2 Series 357 8.3.1 Introduction toFractional Factorial Experiments, Confounding and Resolution 357 8.3.2 Case Study Examples 362 8.4 Taguchi Experimental Designs 366 8.5 Exercises andFollow-Up Activities 379 9 Evaluation ofMeasurement Processes 391 9.1 Measurement ProcessConcepts 391 9.1.1 Bias, Linearity, Repeatability andReproducibility 391 9.1.2 Inadequate Measurement Units 396 9.2 GaugeRepeatability and ReproducibilityStudies 399 9.3 Comparison ofMeasurement Systems 406 9.4 AttributeScenarios 408 9.5 Exercises andFollow-Up Activities 412 10 Regression and Model Building 413 10.1 Regression with aSingle PredictorVariable 413 10.2 Multiple Regression 426 10.3 Response Surface Methods 431 10.4 Categorical Data andLogistic Regression 436 10.4.1 Testsof AssociationUsing the Chi-Square Distribution 436 10.4.2 BinaryLogistic Regression 441 10.5 Exercises andFollow-Up Activities 450 11 LearningMore and Further Minitab 459 11.1 LearningMore about Minitab andObtaining Help 459 11.1.1 Meet Minitab 459 11.1.2 Help 460 11.1.3 StatGuide 462 11.1.4 Tutorials 466 11.1.5 Assistant 468 11.1.6 Glossary,Methodsand Formulas 472 11.1.7 Minitab on the Web andKnowledgebase/FAQ 473 11.2 Macros 476 11.2.1 MinitabSessionCommands 476 11.2.2 Global and Local MinitabMacros 478 11.3 Further Features ofMinitab 479 11.4 Quality Companion 480 11.5 Postscript 481 Appendix 1 483 Appendix 2 485 Appendix 3 487 Appendix 4 491 References 493 Index 499 Foreword If it were possible to add up, on a global basis, all of the benefits that organisations have experienced as a result of deploying Six Sigma techniques, the result would be truly staggering. The place of Six Sigma as an effectivemethodology for improving quality and performance is verywell established. SixSigmaisoftenintroducedtoorganisationsthroughtraining.SixSigmapractitioners gainpersonaldevelopmentbyattendingaspectrumofcoursesfromintroductorysessionsto expertlevelthatisnormallyreferredtoasSixSigmaBlackBelt.Ipersonallyhaveledmany hundredsofpractitionersthroughthisprocess,andwhilstIhopemyinterventionshavebeen successful,Iamonlytooawarethatthereisalimittowhatparticipants canbeexpectedto absorb in aclassroom. This is where Robin Henderson’s book becomes truly invaluable. As well as providing students new to Six Sigma with a very readable and easy to understand introduction, this publication serves as comprehensive consolidation for those already trained. Furthermore this book extends the knowledgegained by recognisedexperienced practitioners. Thoselookingforrelevantandmoderncasestudiesfrombothserviceandmanufacturing environmentswillbemostsatisfiedtofindtheminabundancethroughoutthefollowingpages. Robin Henderson demonstrates thewide applicability and power of these methods with an impressive collection of analyses and improvements drawn from his broad experience of working as a consultant as well as an academic. The combination of many chapter-end exercises,followupactivities,andtheaccompanyingwebsite,formawealth ofextremely useful resources. ThesuccessofSixSigmawouldnothavebeenrealisedhaditnotbeenforthedevelopment ofstatisticalsoftwaresuchasMinitab.Minitabbringstechniquestoallofusthatpreviously were only the domain of statisticians. Robin Henderson’s book complements other well- known texts by taking the theory and explaining how to implement these methods in real situationsthroughtheuseofMinitabsoftware.StartingfromagentleintroductiontoMinitab, Robinbuildsourknowledgethroughdetailedyetfriendlyexplanations,andaswepractice, graduallyleadsus on totackle moresophisticated techniques with confidence. I have spent much of my career working in the field of quality and performance improvement,utilisingthesetoolsandtechniques,andteachingthesubjecttoothers.Since itspublication,IhaveregularlyturnedtoRobinHenderson’sfirsteditionofSixSigmaQuality ImprovementwithMinitabtocheckmyunderstanding,tolearnabitmore,andtofindawayof explainingto myteams,a challenging conceptina straightforward way. Now we have the benefit of this second edition that keeps us up to date on the latest developments within the Minitab tool and its brand new features. For example, Robin HendersonintroducesthenewMinitabAssistantthatguidesusersthroughananalysisprocess. ThereisnodoubtthatRobinHendersonhashelpedallofusinourendeavourstoimprove qualityasauthorofvariouspapersonthesubjectandthroughhisinvolvementwiththeSix Sigma Study Group andthe Quality ImprovementSection ofthe Royal Statistical Society.