6σ Quality Using R     Emilio LopezSix SigmaMethodologyIntroduction                                  Six Sigma Quality Usi...
6σ Quality Using R        Outline     Emilio LopezSix Sigma                          1    Six Sigma MethodologyMethodology...
6σ Quality Using R        Outline     Emilio LopezSix Sigma                          1    Six Sigma MethodologyMethodology...
6σ Quality Using R        Outline     Emilio LopezSix Sigma                          1    Six Sigma MethodologyMethodology...
6σ Quality Using R        Outline     Emilio LopezSix Sigma                          1    Six Sigma MethodologyMethodology...
6σ Quality Using R        The Basics     Emilio Lopez         QualitySix SigmaMethodologyIntroductionRolesToolsSix Sigma w...
6σ Quality Using R        The Basics     Emilio Lopez         QualitySix SigmaMethodologyIntroductionRolesTools           ...
6σ Quality Using R        The Basics     Emilio Lopez         QualitySix SigmaMethodologyIntroductionRolesTools           ...
6σ Quality Using R        The Basics     Emilio Lopez         QualitySix SigmaMethodologyIntroductionRolesTools           ...
6σ Quality Using R        The Basics     Emilio Lopez         QualitySix SigmaMethodologyIntroductionRolesTools           ...
6σ Quality Using R        The Basics     Emilio Lopez         QualitySix SigmaMethodologyIntroductionRolesTools           ...
6σ Quality Using R        The Basics     Emilio Lopez         ExampleSix SigmaMethodologyIntroductionRolesToolsSix Sigma w...
6σ Quality Using R        The Basics     Emilio Lopez         DMAIC StrategySix SigmaMethodologyIntroductionRolesToolsSix ...
6σ Quality Using R        The Basics     Emilio Lopez         DMAIC StrategySix SigmaMethodologyIntroductionRolesToolsSix ...
6σ Quality Using R        The Basics     Emilio Lopez         DMAIC StrategySix SigmaMethodologyIntroduction              ...
6σ Quality Using R        The Basics     Emilio Lopez         DMAIC StrategySix SigmaMethodologyIntroduction              ...
6σ Quality Using R        The Basics     Emilio Lopez         DMAIC StrategySix SigmaMethodologyIntroduction              ...
6σ Quality Using R        The Basics     Emilio Lopez         DMAIC StrategySix SigmaMethodologyIntroduction              ...
6σ Quality Using R        The Basics     Emilio Lopez         DMAIC StrategySix SigmaMethodologyIntroduction              ...
6σ Quality Using R        Roles in Six Sigma     Emilio Lopez         DescriptionSix SigmaMethodologyIntroductionRolesTool...
6σ Quality Using R        Roles in Six Sigma     Emilio Lopez         DescriptionSix SigmaMethodologyIntroductionRolesTool...
6σ Quality Using R        Roles for Six Sigma     Emilio Lopez         DiagramSix SigmaMethodologyIntroductionRolesToolsSi...
6σ Quality Using R        Tools     Emilio Lopez         For Every DMAIC PhaseSix SigmaMethodologyIntroduction            ...
6σ Quality Using R        Tools     Emilio Lopez         For Every DMAIC PhaseSix SigmaMethodologyIntroduction            ...
6σ Quality Using R        Outline     Emilio LopezSix Sigma                          1    Six Sigma MethodologyMethodology...
6σ Quality Using R        Commercial Software     Emilio Lopez         State-of-the-artSix SigmaMethodologyIntroductionRol...
6σ Quality Using R        Commercial Software     Emilio Lopez         State-of-the-artSix SigmaMethodologyIntroductionRol...
6σ Quality Using R        Commercial Software     Emilio Lopez         TrendsSix SigmaMethodologyIntroductionRolesToolsSix...
6σ Quality Using R        Commercial Software     Emilio Lopez         TrendsSix SigmaMethodologyIntroductionRolesTools   ...
6σ Quality Using R        Commercial Software     Emilio Lopez         TrendsSix SigmaMethodologyIntroductionRolesTools   ...
6σ Quality Using R        R Advantages     Emilio Lopez         Customization + Innovation = CompetitivenessSix SigmaMetho...
6σ Quality Using R        R Advantages     Emilio Lopez         Customization + Innovation = CompetitivenessSix SigmaMetho...
6σ Quality Using R        R Advantages     Emilio Lopez         Customization + Innovation = CompetitivenessSix SigmaMetho...
6σ Quality Using R        Other Authors     Emilio Lopez         PackagesSix SigmaMethodologyIntroduction                 ...
6σ Quality Using R        Other Authors     Emilio Lopez         PackagesSix SigmaMethodologyIntroduction                 ...
6σ Quality Using R        Other Authors     Emilio Lopez         PackagesSix SigmaMethodologyIntroduction                 ...
6σ Quality Using R        SixSigma package     Emilio Lopez         Focused in SixSigma PractitionersSix SigmaMethodologyI...
6σ Quality Using R        Helicopter     Emilio Lopez         Training StuffSix SigmaMethodologyIntroductionRolesTools     ...
Six Sigma with R | Paper Helicopter template                                                                              ...
6σ Quality Using R        Diagrams     Emilio Lopez         SixSigma PackageSix SigmaMethodology                Cause-and-...
6σ Quality Using R        Cause-and-Effect Diagram     Emilio Lopez         SixSigma PackageSix SigmaMethodologyIntroductio...
6σ Quality Using R        Diagrams     Emilio Lopez         SixSigma PackageSix SigmaMethodology                          ...
6σ Quality Using R        Process Map Diagram     Emilio Lopez         SixSigma PackageSix SigmaMethodologyIntroduction   ...
6σ Quality Using R        Gage R&R Study     Emilio Lopez         Measurement System AnalysisSix SigmaMethodologyIntroduct...
Six Sigma Gage R&R Study                                                  Components of Variation                         ...
6σ Quality Using R        Capability Analysis     Emilio LopezSix SigmaMethodologyIntroductionRolesToolsSix Sigma with R  ...
Six Sigma Capability Analysis Study              Histogram & Density                                Density Lines Legend  ...
6σ Quality Using R        Further Development     Emilio Lopez         On the WaySix SigmaMethodologyIntroductionRolesTool...
6σ Quality Using R        Further Development     Emilio Lopez         On the WaySix SigmaMethodologyIntroductionRolesTool...
6σ Quality Using R        Further Development     Emilio Lopez         On the WaySix SigmaMethodologyIntroductionRolesTool...
6σ Quality Using R        Further Development     Emilio Lopez         On the WaySix SigmaMethodologyIntroductionRolesTool...
6σ Quality Using R        Further Development     Emilio Lopez         On the WaySix SigmaMethodologyIntroductionRolesTool...
6σ Quality Using R        Further Development     Emilio Lopez         On the WaySix SigmaMethodologyIntroductionRolesTool...
6σ Quality Using R        Outline     Emilio LopezSix Sigma                          1    Six Sigma MethodologyMethodology...
6σ Quality Using R        VRTUOSI project     Emilio Lopez         European Lifelong Learning ProgrammeSix SigmaMethodolog...
6σ Quality Using R        VRTUOSI project     Emilio Lopez         European Lifelong Learning ProgrammeSix SigmaMethodolog...
6σ Quality Using R        VRTUOSI project     Emilio Lopez         European Lifelong Learning ProgrammeSix SigmaMethodolog...
6σ Quality Using R        VRTUOSI project     Emilio Lopez         European Lifelong Learning ProgrammeSix SigmaMethodolog...
6σ Quality Using R        Master On Line     Emilio Lopez         Master in Decision Systems EngineeringSix SigmaMethodolo...
6σ Quality Using R        Master On Line     Emilio Lopez         Master in Decision Systems EngineeringSix SigmaMethodolo...
6σ Quality Using R        Master On Line     Emilio Lopez         Master in Decision Systems EngineeringSix SigmaMethodolo...
6σ Quality Using R        Master On Line     Emilio Lopez         Master in Decision Systems EngineeringSix SigmaMethodolo...
6σ Quality Using R        Master On Line     Emilio Lopez         Master in Decision Systems EngineeringSix SigmaMethodolo...
6σ Quality Using R        Book     Emilio Lopez         Springer Use R! SeriesSix SigmaMethodologyIntroductionRolesToolsSi...
6σ Quality Using R        Book     Emilio Lopez         Springer Use R! SeriesSix SigmaMethodologyIntroductionRoles       ...
6σ Quality Using R        Further Projects     Emilio Lopez         PlatformSix SigmaMethodologyIntroductionRolesToolsSix ...
6σ Quality Using R        Further Projects     Emilio Lopez         PlatformSix SigmaMethodologyIntroduction              ...
6σ Quality Using R        Further Projects     Emilio Lopez         PlatformSix SigmaMethodologyIntroduction              ...
6σ Quality Using R        Summary     Emilio LopezSix Sigma                         Six Sigma is a breakthrough strategy f...
6σ Quality Using R        Summary     Emilio LopezSix Sigma                         Six Sigma is a breakthrough strategy f...
6σ Quality Using R        Summary     Emilio LopezSix Sigma                         Six Sigma is a breakthrough strategy f...
6σ Quality Using R        Summary     Emilio LopezSix Sigma                         Six Sigma is a breakthrough strategy f...
6σ Quality Using R        Summary     Emilio LopezSix Sigma                         Six Sigma is a breakthrough strategy f...
6σ Quality Using R        Summary     Emilio LopezSix Sigma                         Six Sigma is a breakthrough strategy f...
6σ Quality Using R        Summary     Emilio LopezSix Sigma                         Six Sigma is a breakthrough strategy f...
6σ Quality Using R        References     Emilio Lopez                          George Box. Teaching engineers experimental...
6σ Quality Using R        Acknowledgements     Emilio LopezSix SigmaMethodologyIntroduction                          Dept....
6σ Quality Using R        Discussion     Emilio LopezSix SigmaMethodologyIntroductionRolesTools                           ...
Six Sigma Quality Using R: Tools and Training
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Six Sigma Quality Using R: Tools and Training

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Presentation at the Use R! 2011 Conference (University of Warwick, Coventry, UK)

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Six Sigma Quality Using R: Tools and Training

  1. 1. 6σ Quality Using R Emilio LopezSix SigmaMethodologyIntroduction Six Sigma Quality Using RRolesTools Tools and TrainingSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & R Emilio Lopez, Andres Redchuk andCoursesPublications Javier M. MoguerzaFurtherReferences Department of Statistics and Operations Research Rey Juan Carlos University (Madrid) The University of Warwick, August 2011 The R User Conference 2011 1/37
  2. 2. 6σ Quality Using R Outline Emilio LopezSix Sigma 1 Six Sigma MethodologyMethodologyIntroduction IntroductionRolesTools RolesSix Sigma with RSix Sigma Software ToolsR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 2/37
  3. 3. 6σ Quality Using R Outline Emilio LopezSix Sigma 1 Six Sigma MethodologyMethodologyIntroduction IntroductionRolesTools RolesSix Sigma with RSix Sigma Software ToolsR AdvantagesR Packages for SixSigma 2 Six Sigma with RSpreading 6σ & RCourses Six Sigma SoftwarePublicationsFurther R AdvantagesReferences R Packages for SixSigma The R User Conference 2011 2/37
  4. 4. 6σ Quality Using R Outline Emilio LopezSix Sigma 1 Six Sigma MethodologyMethodologyIntroduction IntroductionRolesTools RolesSix Sigma with RSix Sigma Software ToolsR AdvantagesR Packages for SixSigma 2 Six Sigma with RSpreading 6σ & RCourses Six Sigma SoftwarePublicationsFurther R AdvantagesReferences R Packages for SixSigma 3 Spreading 6σ & R thinking Courses Publications Further The R User Conference 2011 2/37
  5. 5. 6σ Quality Using R Outline Emilio LopezSix Sigma 1 Six Sigma MethodologyMethodologyIntroduction IntroductionRolesTools RolesSix Sigma with RSix Sigma Software ToolsR AdvantagesR Packages for SixSigma 2 Six Sigma with RSpreading 6σ & RCourses Six Sigma SoftwarePublicationsFurther R AdvantagesReferences R Packages for SixSigma 3 Spreading 6σ & R thinking Courses Publications Further The R User Conference 2011 3/37
  6. 6. 6σ Quality Using R The Basics Emilio Lopez QualitySix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 4/37
  7. 7. 6σ Quality Using R The Basics Emilio Lopez QualitySix SigmaMethodologyIntroductionRolesTools Classical approachSix Sigma with R The Key Characteristic of aSix Sigma SoftwareR Advantages product/service/processR Packages for SixSigma must be inside theSpreading 6σ & RCourses specification limitsPublicationsFurtherReferences The R User Conference 2011 4/37
  8. 8. 6σ Quality Using R The Basics Emilio Lopez QualitySix SigmaMethodologyIntroductionRolesTools Classical approachSix Sigma with R The Key Characteristic of aSix Sigma SoftwareR Advantages product/service/processR Packages for SixSigma must be inside theSpreading 6σ & RCourses specification limitsPublicationsFurtherReferences Six Sigma approach The Key Characteristic approximate the target, with as less variation as possible. The R User Conference 2011 4/37
  9. 9. 6σ Quality Using R The Basics Emilio Lopez QualitySix SigmaMethodologyIntroductionRolesTools Classical approachSix Sigma with R The Key Characteristic of aSix Sigma SoftwareR Advantages product/service/processR Packages for SixSigma must be inside theSpreading 6σ & R specification limits Cost of Poor QualityCoursesPublications LSL T USLFurtherReferences Six Sigma approach The Key Characteristic approximate the target, with as less variation as Observed value of the characteristic possible. The R User Conference 2011 4/37
  10. 10. 6σ Quality Using R The Basics Emilio Lopez QualitySix SigmaMethodologyIntroductionRolesTools Classical approachSix Sigma with R The Key Characteristic of aSix Sigma SoftwareR Advantages product/service/processR Packages for SixSigma must be inside theSpreading 6σ & R specification limits Cost of Poor QualityCoursesPublications LSL T USLFurtherReferences Six Sigma approach The Key Characteristic approximate the target, with as less variation as Observed value of the characteristic possible. The R User Conference 2011 4/37
  11. 11. 6σ Quality Using R The Basics Emilio Lopez QualitySix SigmaMethodologyIntroductionRolesTools Classical approachSix Sigma with R The Key Characteristic of aSix Sigma SoftwareR Advantages product/service/processR Packages for SixSigma must be inside theSpreading 6σ & R specification limits Cost of Poor QualityCoursesPublications LSL T USLFurtherReferences Six Sigma approach The Key Characteristic approximate the target, with as less variation as Observed value of the characteristic possible. The R User Conference 2011 4/37
  12. 12. 6σ Quality Using R The Basics Emilio Lopez ExampleSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences Figure: Paper Helicopter Design Box [1992] The R User Conference 2011 5/37
  13. 13. 6σ Quality Using R The Basics Emilio Lopez DMAIC StrategySix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 6/37
  14. 14. 6σ Quality Using R The Basics Emilio Lopez DMAIC StrategySix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 7/37
  15. 15. 6σ Quality Using R The Basics Emilio Lopez DMAIC StrategySix SigmaMethodologyIntroduction DefineRolesTools State problem, objectives, prioritize, and launch projectSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 7/37
  16. 16. 6σ Quality Using R The Basics Emilio Lopez DMAIC StrategySix SigmaMethodologyIntroduction DefineRolesTools State problem, objectives, prioritize, and launch projectSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigma MeasureSpreading 6σ & R Understand theCoursesPublications Process, validateFurther data accuracy,References determine process capability The R User Conference 2011 7/37
  17. 17. 6σ Quality Using R The Basics Emilio Lopez DMAIC StrategySix SigmaMethodologyIntroduction DefineRolesTools State problem, objectives, prioritize, and launch projectSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigma Measure AnalyzeSpreading 6σ & R Understand the Determine theCoursesPublications Process, validate relationshipFurther data accuracy, between the Y’sReferences determine process and the X’s and capability look for causes. The R User Conference 2011 7/37
  18. 18. 6σ Quality Using R The Basics Emilio Lopez DMAIC StrategySix SigmaMethodologyIntroduction DefineRolesTools State problem, objectives, prioritize, and launch projectSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigma Measure Analyze ImproveSpreading 6σ & R Understand the Determine the DetermineCoursesPublications Process, validate relationship solutions toFurther data accuracy, between the Y’s achieve theReferences determine process and the X’s and objective, and capability look for causes. implement. The R User Conference 2011 7/37
  19. 19. 6σ Quality Using R The Basics Emilio Lopez DMAIC StrategySix SigmaMethodologyIntroduction DefineRolesTools State problem, objectives, prioritize, and launch projectSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigma Measure Analyze ImproveSpreading 6σ & R Understand the Determine the DetermineCoursesPublications Process, validate relationship solutions toFurther data accuracy, between the Y’s achieve theReferences determine process and the X’s and objective, and capability look for causes. implement. Control Process control, monitoring and auto-controlling methods The R User Conference 2011 7/37
  20. 20. 6σ Quality Using R Roles in Six Sigma Emilio Lopez DescriptionSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma Software In Six Sigma, everyone in the organization hasR AdvantagesR Packages for SixSigma a role in the project. Six Sigma methodologySpreading 6σ & R uses an intuitive categorization of these roles.CoursesPublicationsFurtherReferences The R User Conference 2011 8/37
  21. 21. 6σ Quality Using R Roles in Six Sigma Emilio Lopez DescriptionSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma Software In Six Sigma, everyone in the organization hasR AdvantagesR Packages for SixSigma a role in the project. Six Sigma methodologySpreading 6σ & R uses an intuitive categorization of these roles.CoursesPublicationsFurtherReferences The R User Conference 2011 8/37
  22. 22. 6σ Quality Using R Roles for Six Sigma Emilio Lopez DiagramSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 9/37
  23. 23. 6σ Quality Using R Tools Emilio Lopez For Every DMAIC PhaseSix SigmaMethodologyIntroduction Any Statistical, planning or management toolRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 10/37
  24. 24. 6σ Quality Using R Tools Emilio Lopez For Every DMAIC PhaseSix SigmaMethodologyIntroduction Any Statistical, planning or management toolRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 10/37
  25. 25. 6σ Quality Using R Outline Emilio LopezSix Sigma 1 Six Sigma MethodologyMethodologyIntroduction IntroductionRolesTools RolesSix Sigma with RSix Sigma Software ToolsR AdvantagesR Packages for SixSigma 2 Six Sigma with RSpreading 6σ & RCourses Six Sigma SoftwarePublicationsFurther R AdvantagesReferences R Packages for SixSigma 3 Spreading 6σ & R thinking Courses Publications Further The R User Conference 2011 11/37
  26. 26. 6σ Quality Using R Commercial Software Emilio Lopez State-of-the-artSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 12/37
  27. 27. 6σ Quality Using R Commercial Software Emilio Lopez State-of-the-artSix SigmaMethodologyIntroductionRolesTools ProgramsSix Sigma with RSix Sigma SoftwareR Advantages MinitabR Packages for SixSigmaSpreading 6σ & R SPSSCoursesPublications StatGraphicsFurtherReferences JMP & SAS Any statistical software, or even spreadsheets The R User Conference 2011 12/37
  28. 28. 6σ Quality Using R Commercial Software Emilio Lopez TrendsSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 13/37
  29. 29. 6σ Quality Using R Commercial Software Emilio Lopez TrendsSix SigmaMethodologyIntroductionRolesTools InternetSix Sigma with RSix Sigma Software Software as aR AdvantagesR Packages for SixSigma ServiceSpreading 6σ & RCourses WebPublicationsFurther ApplicationsReferences Everywhere Every display The R User Conference 2011 13/37
  30. 30. 6σ Quality Using R Commercial Software Emilio Lopez TrendsSix SigmaMethodologyIntroductionRolesTools Internet OpenSix Sigma with RSix Sigma Software Software as a TechnologiesR AdvantagesR Packages for SixSigma Service LinuxSpreading 6σ & RCourses Web OpenOfficePublicationsFurther ApplicationsReferences R Everywhere ... Every display The R User Conference 2011 13/37
  31. 31. 6σ Quality Using R R Advantages Emilio Lopez Customization + Innovation = CompetitivenessSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 14/37
  32. 32. 6σ Quality Using R R Advantages Emilio Lopez Customization + Innovation = CompetitivenessSix SigmaMethodologyIntroduction CustomizationRolesTools A company can develop a package that fits itsSix Sigma with R inner procedures and methods.Six Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 14/37
  33. 33. 6σ Quality Using R R Advantages Emilio Lopez Customization + Innovation = CompetitivenessSix SigmaMethodologyIntroduction CustomizationRolesTools A company can develop a package that fits itsSix Sigma with R inner procedures and methods.Six Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & R InnovationCoursesPublications A company can develop and deploy anFurtherReferences innovative method from its R&D department, or from the result of other published researches. The R User Conference 2011 14/37
  34. 34. 6σ Quality Using R Other Authors Emilio Lopez PackagesSix SigmaMethodologyIntroduction qcc 2.01 (Scrucca [2004])RolesTools Shewhart quality control charts for continuous,Six Sigma with RSix Sigma Software attribute and count data [. . . ]R AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 15/37
  35. 35. 6σ Quality Using R Other Authors Emilio Lopez PackagesSix SigmaMethodologyIntroduction qcc 2.01 (Scrucca [2004])RolesTools Shewhart quality control charts for continuous,Six Sigma with RSix Sigma Software attribute and count data [. . . ]R AdvantagesR Packages for SixSigmaSpreading 6σ & RCourses IQCC 0.5 (Recchia et al. [2010])PublicationsFurther Builds statistical control charts with exact limits forReferences univariate and multivariate cases. The R User Conference 2011 15/37
  36. 36. 6σ Quality Using R Other Authors Emilio Lopez PackagesSix SigmaMethodologyIntroduction qcc 2.01 (Scrucca [2004])RolesTools Shewhart quality control charts for continuous,Six Sigma with RSix Sigma Software attribute and count data [. . . ]R AdvantagesR Packages for SixSigmaSpreading 6σ & RCourses IQCC 0.5 (Recchia et al. [2010])PublicationsFurther Builds statistical control charts with exact limits forReferences univariate and multivariate cases. qualityTools 1.47 (Roth [2011]) This is a package for teaching statistical methods in the field of Quality Science [. . . ] The focus is on teaching [. . . ] The R User Conference 2011 15/37
  37. 37. 6σ Quality Using R SixSigma package Emilio Lopez Focused in SixSigma PractitionersSix SigmaMethodologyIntroductionRolesToolsSix Sigma with R Version History FunctionsSix Sigma Software ss.pMapR Advantages 1 0.2.0 March 2011R Packages for SixSigma ss.ceDiagSpreading 6σ & R 2 0.2.1 April 2011 ss.rrCoursesPublications ss.ciFurther 3 0.3.0 July 2011 ss.study.caReferences (current) ss.ca.yield ss.ca.z Data ss.ca.cp ss.data.rr ss.ca.cpk ss.data.ca ss.heli The R User Conference 2011 16/37
  38. 38. 6σ Quality Using R Helicopter Emilio Lopez Training StuffSix SigmaMethodologyIntroductionRolesTools Template in pdf format to build paperSix Sigma with RSix Sigma Software helicopter prototypes (Box [1992])R AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences > ss.heli() null device 1 > #vignette("HelicopterInstructions") for instructions The R User Conference 2011 17/37
  39. 39. Six Sigma with R | Paper Helicopter template max (9.5cm) std (8cm) min (6.5cm) ← wings length → cut ? pe fold ↑ fold ↓ tacut cut cut ← body length → tape? tape? min (6.5cm) std fold ↓ ↓ fold ↑ ↑ (8cm) clip? max max min ← body width → min max (9.5cm) (6cm) (4cm) (4cm) (6cm)
  40. 40. 6σ Quality Using R Diagrams Emilio Lopez SixSigma PackageSix SigmaMethodology Cause-and-effect DiagramIntroductionRolesToolsSix Sigma with RSix Sigma Software > example(ss.ceDiag)R AdvantagesR Packages for SixSigma ss.cDg> #DataSpreading 6σ & R ss.cDg> effect<-"Flight Time"Courses ss.cDg> causes.gr<-c("Operator", "Environment", "Tools", "Design",Publications ss.cDg+ "Raw.Material","Measure.Tool")Further ss.cDg> causes<-vector(mode="list", length=length(causes.gr))References ss.cDg> causes[1]<-list(c("operator #1", "operator #2", "operator #3 ss.cDg> causes[2]<-list(c("height", "cleaning")) ss.cDg> causes[3]<-list(c("scissors", "tape")) ss.cDg> causes[4]<-list(c("rotor.length", "rotor.width2", "paperclip ss.cDg> causes[5]<-list(c("thickness", "marks")) ss.cDg> causes[6]<-list(c("calibrate", "model")) ss.cDg> ss.ceDiag(effect, causes.gr, causes, sub="Paper Helicopter P The R User Conference 2011 19/37
  41. 41. 6σ Quality Using R Cause-and-Effect Diagram Emilio Lopez SixSigma PackageSix SigmaMethodologyIntroduction Six Sigma Cause−and−effect DiagramRolesToolsSix Sigma with RSix Sigma Software Operator Environment ToolsR Advantages operator #1 height scissors operator #2 cleaning tapeR Packages for SixSigma operator #3Spreading 6σ & RCoursesPublicationsFurther Flight TimeReferences paperclip model marks rotor.width2 calibrate thickness rotor.length Measure.Tool Raw.Material Design Paper Helicopter Project The R User Conference 2011 20/37
  42. 42. 6σ Quality Using R Diagrams Emilio Lopez SixSigma PackageSix SigmaMethodology Process MapIntroductionRolesTools > example(ss.pMap)Six Sigma with R ss.pMp> inputs.overall<-c("operators", "tools", "raw material", "facSix Sigma SoftwareR Advantages ss.pMp> outputs.overall<-c("helicopter")R Packages for SixSigma ss.pMp> procs<-c("INSPECTION", "ASSEMBLY", "TEST", "LABELING")Spreading 6σ & R ss.pMp> input.output<-vector(mode="list",length=length(procs))Courses ss.pMp> input.output[1]<-list(c("sheets", "..."))Publications . . .Further ss.pMp> x.parameters<-vector(mode="list",length=length(procs))References ss.pMp> x.parameters[1]<-list(c(list(c("width", "NC")),list(c("opera ss.pMp+ list(c("Measure pattern", "P")), list(c("discard", "P")))) . . . ss.pMp> y.features<-vector(mode="list",length=length(procs)) ss.pMp> y.features[1]<-list(c(list(c("ok", "Cr")))) . . . ss.pMp> ss.pMap(procs, inputs.overall, outputs.overall, ss.pMp+ input.output, x.parameters, y.features, ss.pMp+ sub="Paper Helicopter Project") The R User Conference 2011 21/37
  43. 43. 6σ Quality Using R Process Map Diagram Emilio Lopez SixSigma PackageSix SigmaMethodologyIntroduction Six Sigma Process MapRolesTools operators INPUTS toolsSix Sigma with R X raw materialSix Sigma Software facilitiesR AdvantagesR Packages for SixSigma INSPECTION ASSEMBLY TEST LABELING sheets sheets helicopter helicopterSpreading 6σ & R ... INPUTS INPUTS INPUTS INPUTSCoursesPublicationsFurther Param.(x): width NC Param.(x): operator C Param.(x): operator C Param.(x): operator CReferences operator C cut P throw P label P Measure pattern P fix P discard P Featur.(y): label discard P rotor.width C environment N Featur.(y): ok rotor.length C Featur.(y): time paperclip C tape C Featur.(y): weight LEGEND helicopter (C)ontrollable OUTPUTS (Cr)itical (N)oise Y (P)rocedure Paper Helicopter Project The R User Conference 2011 22/37
  44. 44. 6σ Quality Using R Gage R&R Study Emilio Lopez Measurement System AnalysisSix SigmaMethodologyIntroduction > #... Some theme instructionsRoles > ss.rr(time1, prototype, operator,Tools + data=ss.data.rr, sub="Helicopter Project")Six Sigma with RSix Sigma Software Analysis of Variance TableR AdvantagesR Packages for SixSigma Response: varSpreading 6σ & R Df Sum Sq Mean Sq F value Pr(>F)Courses part 2 1.20072 0.60036 28.0396 2.952e-06Publications appr 2 0.05294 0.02647 1.2363 0.3140Further part:appr 4 0.08339 0.02085 0.9737 0.4462References Repeatability 18 0.38540 0.02141 VarComp %Contrib Total Gage R&R 0.0220358 25.50 Repeatability 0.0214111 24.77 Reproducibility 0.0006247 0.72 appr 0.0006247 0.72 part:appr 0.0000000 0.00 Part-To-Part 0.0643901 74.50 Total Variation 0.0864259 100.00 . . . The R User Conference 2011 23/37
  45. 45. Six Sigma Gage R&R Study Components of Variation Var by Part 1.8 q 80 q q q q 1.6 60 q qPercent 1.4 var 40 q q q q q q 1.2 20 q q q q q 1.0 q 0 q G.R&R Repeat Reprod Part2Part prot #1 prot #2 prot #3 %Contribution %Study Var R Chart by appraiser Var by appraiser prot #1 prot #2 prot #3 1.8 q q op #1 op #2 op #3 q 0.5 q q q q q 1.6 0.4 q q q q 1.4 var 0.3 qvar q q q q q q q q 0.2 1.2 q q q q q q q q 0.1 q q 1.0 q q prot #1 prot #2 prot #3 prot #1 prot #2 prot #3 op #1 op #2 op #3 part x Chart by appraiser Part*appraiser Interaction prot #1 prot #2 prot #3 1.7 q op #1 op #2 op #3 1.7 q 1.6 q 1.6 q q 1.5 var 1.5 1.4var 1.4 q 1.3 q q 1.3 q 1.2 1.2 q q q 1.1 q q 1.1 q q prot #1 prot #2 prot #3 prot #1 prot #2 prot #3 prot #1 prot #2 prot #3 op #1 op #3 part op #2 Helicopter Project
  46. 46. 6σ Quality Using R Capability Analysis Emilio LopezSix SigmaMethodologyIntroductionRolesToolsSix Sigma with R > ss.ca.yield(c(3, 5, 12), c(1, 2, 4), 1915)Six Sigma SoftwareR Advantages Yield FTY RTY DPU DPMOR Packages for SixSigma 1 0.9895561 0.9859008 0.9859563 20 10443.86Spreading 6σ & RCourses > ss.ca.cpk(ss.data.ca$Volume, 740, 760)PublicationsFurther [1] 1.546513References > ss.study.ca(ss.data.ca$Volume, rnorm(40, 753, 3), LSL = 740, + USL = 760, T = 750, alpha = 0.5, f.sub = "Winery Project") The R User Conference 2011 25/37
  47. 47. Six Sigma Capability Analysis Study Histogram & Density Density Lines Legend Target Density ST Theoretical Dens. ST Density LT Theoretical Density LT LSL USL Specifications LSL: 740 Target: 750 USL: 760 Short Term Process Long Term740 745 750 755 760 Mean: 749.7625 Mean: 752.8443 Check Normality SD: 2.1042 SD: 2.9577 n: 20 n: 40 Shapiro−Wilk Test Zs: 3.14 Zs: 2.42 q p−value: 0.07506 DPMO: q Short Term Indices Long Term qq q qq Lilliefors (K−S) Test Cp: 1.5841 Pp: 1.1270 qq qq qq q p−value: 0.2291 CI: [1.1,2.1] CI: [0.9,1.4] qq qq qq Cpk: 1.5465 Ppk: 0.8065 CI: [1.1,2.1] CI: [0.9,1.4] Normality accepted when p−value > 0.05 Winery Project
  48. 48. 6σ Quality Using R Further Development Emilio Lopez On the WaySix SigmaMethodologyIntroductionRolesTools Functions for a wide range of tools alongSix Sigma with RSix Sigma Software all the DMAIC phases.R AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 27/37
  49. 49. 6σ Quality Using R Further Development Emilio Lopez On the WaySix SigmaMethodologyIntroductionRolesTools Functions for a wide range of tools alongSix Sigma with RSix Sigma Software all the DMAIC phases.R AdvantagesR Packages for SixSigma Improved graphicsSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 27/37
  50. 50. 6σ Quality Using R Further Development Emilio Lopez On the WaySix SigmaMethodologyIntroductionRolesTools Functions for a wide range of tools alongSix Sigma with RSix Sigma Software all the DMAIC phases.R AdvantagesR Packages for SixSigma Improved graphicsSpreading 6σ & RCoursesPublications Tackle Further methodologies (DFSS,Further Lean, . . . )References The R User Conference 2011 27/37
  51. 51. 6σ Quality Using R Further Development Emilio Lopez On the WaySix SigmaMethodologyIntroductionRolesTools Functions for a wide range of tools alongSix Sigma with RSix Sigma Software all the DMAIC phases.R AdvantagesR Packages for SixSigma Improved graphicsSpreading 6σ & RCoursesPublications Tackle Further methodologies (DFSS,Further Lean, . . . )References Non-normal / Non-linear methods The R User Conference 2011 27/37
  52. 52. 6σ Quality Using R Further Development Emilio Lopez On the WaySix SigmaMethodologyIntroductionRolesTools Functions for a wide range of tools alongSix Sigma with RSix Sigma Software all the DMAIC phases.R AdvantagesR Packages for SixSigma Improved graphicsSpreading 6σ & RCoursesPublications Tackle Further methodologies (DFSS,Further Lean, . . . )References Non-normal / Non-linear methods Bayesian perspective The R User Conference 2011 27/37
  53. 53. 6σ Quality Using R Further Development Emilio Lopez On the WaySix SigmaMethodologyIntroductionRolesTools Functions for a wide range of tools alongSix Sigma with RSix Sigma Software all the DMAIC phases.R AdvantagesR Packages for SixSigma Improved graphicsSpreading 6σ & RCoursesPublications Tackle Further methodologies (DFSS,Further Lean, . . . )References Non-normal / Non-linear methods Bayesian perspective Maybe a GUI The R User Conference 2011 27/37
  54. 54. 6σ Quality Using R Outline Emilio LopezSix Sigma 1 Six Sigma MethodologyMethodologyIntroduction IntroductionRolesTools RolesSix Sigma with RSix Sigma Software ToolsR AdvantagesR Packages for SixSigma 2 Six Sigma with RSpreading 6σ & RCourses Six Sigma SoftwarePublicationsFurther R AdvantagesReferences R Packages for SixSigma 3 Spreading 6σ & R thinking Courses Publications Further The R User Conference 2011 28/37
  55. 55. 6σ Quality Using R VRTUOSI project Emilio Lopez European Lifelong Learning ProgrammeSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences www.vrtuosi.com The R User Conference 2011 29/37
  56. 56. 6σ Quality Using R VRTUOSI project Emilio Lopez European Lifelong Learning ProgrammeSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences www.vrtuosi.com Code Project: LLP 502869-LLP-1-2009-ES-ERASMUS-EVC The R User Conference 2011 29/37
  57. 57. 6σ Quality Using R VRTUOSI project Emilio Lopez European Lifelong Learning ProgrammeSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences www.vrtuosi.com Code Project: LLP 502869-LLP-1-2009-ES-ERASMUS-EVC One of the Courses: Quality Control: Six Sigma The R User Conference 2011 29/37
  58. 58. 6σ Quality Using R VRTUOSI project Emilio Lopez European Lifelong Learning ProgrammeSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences www.vrtuosi.com Code Project: LLP 502869-LLP-1-2009-ES-ERASMUS-EVC One of the Courses: Quality Control: Six Sigma Developed and carried out through the Six Sigma methodology. The R User Conference 2011 29/37
  59. 59. 6σ Quality Using R Master On Line Emilio Lopez Master in Decision Systems EngineeringSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurther Rey Juan Carlos University (www.urjc.es)References The R User Conference 2011 31/37
  60. 60. 6σ Quality Using R Master On Line Emilio Lopez Master in Decision Systems EngineeringSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurther Rey Juan Carlos University (www.urjc.es)References First master in Business Analytics in Spain The R User Conference 2011 31/37
  61. 61. 6σ Quality Using R Master On Line Emilio Lopez Master in Decision Systems EngineeringSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurther Rey Juan Carlos University (www.urjc.es)References First master in Business Analytics in Spain Unique Certificate in e-learning The R User Conference 2011 31/37
  62. 62. 6σ Quality Using R Master On Line Emilio Lopez Master in Decision Systems EngineeringSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurther Rey Juan Carlos University (www.urjc.es)References First master in Business Analytics in Spain Unique Certificate in e-learning Mention of Quality in ANECA The R User Conference 2011 31/37
  63. 63. 6σ Quality Using R Master On Line Emilio Lopez Master in Decision Systems EngineeringSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurther Rey Juan Carlos University (www.urjc.es)References First master in Business Analytics in Spain Unique Certificate in e-learning Mention of Quality in ANECA Six Sigma Quality subject. R used in most of the subjects. The R User Conference 2011 31/37
  64. 64. 6σ Quality Using R Book Emilio Lopez Springer Use R! SeriesSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 32/37
  65. 65. 6σ Quality Using R Book Emilio Lopez Springer Use R! SeriesSix SigmaMethodologyIntroductionRoles FeaturesToolsSix Sigma with R Title:Six Sigma SoftwareR Advantages Six Sigma with RR Packages for SixSigmaSpreading 6σ & R Due 2012CoursesPublicationsFurther 350 pages approx.References Wide background scope Examples, a Case Study and practices The R User Conference 2011 32/37
  66. 66. 6σ Quality Using R Further Projects Emilio Lopez PlatformSix SigmaMethodologyIntroductionRolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 33/37
  67. 67. 6σ Quality Using R Further Projects Emilio Lopez PlatformSix SigmaMethodologyIntroduction Open Platform for QualityRolesTools MethodologiesSix Sigma with RSix Sigma SoftwareR Advantages Improving the European Factory (link)R Packages for SixSigmaSpreading 6σ & R FP7 PPP Funding SchemeCoursesPublications Looking for PartnersFurtherReferences The R User Conference 2011 33/37
  68. 68. 6σ Quality Using R Further Projects Emilio Lopez PlatformSix SigmaMethodologyIntroduction Open Platform for QualityRolesTools MethodologiesSix Sigma with RSix Sigma SoftwareR Advantages Improving the European Factory (link)R Packages for SixSigmaSpreading 6σ & R FP7 PPP Funding SchemeCoursesPublications Looking for PartnersFurtherReferences Other Projects We are available for other projects that need partners in this area The R User Conference 2011 33/37
  69. 69. 6σ Quality Using R Summary Emilio LopezSix Sigma Six Sigma is a breakthrough strategy forMethodologyIntroduction improvement.RolesToolsSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 34/37
  70. 70. 6σ Quality Using R Summary Emilio LopezSix Sigma Six Sigma is a breakthrough strategy forMethodologyIntroduction improvement.RolesTools R is becoming a real alternative toSix Sigma with RSix Sigma SoftwareR Advantages commercial software inside Companies.R Packages for SixSigmaSpreading 6σ & RCoursesPublicationsFurtherReferences The R User Conference 2011 34/37
  71. 71. 6σ Quality Using R Summary Emilio LopezSix Sigma Six Sigma is a breakthrough strategy forMethodologyIntroduction improvement.RolesTools R is becoming a real alternative toSix Sigma with RSix Sigma SoftwareR Advantages commercial software inside Companies.R Packages for SixSigmaSpreading 6σ & R The combination of both strategies canCoursesPublications improve the competitiveness of theFurtherReferences Companies, and open a world of possibilities to R professionals. The R User Conference 2011 34/37
  72. 72. 6σ Quality Using R Summary Emilio LopezSix Sigma Six Sigma is a breakthrough strategy forMethodologyIntroduction improvement.RolesTools R is becoming a real alternative toSix Sigma with RSix Sigma SoftwareR Advantages commercial software inside Companies.R Packages for SixSigmaSpreading 6σ & R The combination of both strategies canCoursesPublications improve the competitiveness of theFurtherReferences Companies, and open a world of possibilities to R professionals. Further steps The R User Conference 2011 34/37
  73. 73. 6σ Quality Using R Summary Emilio LopezSix Sigma Six Sigma is a breakthrough strategy forMethodologyIntroduction improvement.RolesTools R is becoming a real alternative toSix Sigma with RSix Sigma SoftwareR Advantages commercial software inside Companies.R Packages for SixSigmaSpreading 6σ & R The combination of both strategies canCoursesPublications improve the competitiveness of theFurtherReferences Companies, and open a world of possibilities to R professionals. Further steps SixSigma package development The R User Conference 2011 34/37
  74. 74. 6σ Quality Using R Summary Emilio LopezSix Sigma Six Sigma is a breakthrough strategy forMethodologyIntroduction improvement.RolesTools R is becoming a real alternative toSix Sigma with RSix Sigma SoftwareR Advantages commercial software inside Companies.R Packages for SixSigmaSpreading 6σ & R The combination of both strategies canCoursesPublications improve the competitiveness of theFurtherReferences Companies, and open a world of possibilities to R professionals. Further steps SixSigma package development Publications in preparation The R User Conference 2011 34/37
  75. 75. 6σ Quality Using R Summary Emilio LopezSix Sigma Six Sigma is a breakthrough strategy forMethodologyIntroduction improvement.RolesTools R is becoming a real alternative toSix Sigma with RSix Sigma SoftwareR Advantages commercial software inside Companies.R Packages for SixSigmaSpreading 6σ & R The combination of both strategies canCoursesPublications improve the competitiveness of theFurtherReferences Companies, and open a world of possibilities to R professionals. Further steps SixSigma package development Publications in preparation Six Sigma platform? The R User Conference 2011 34/37
  76. 76. 6σ Quality Using R References Emilio Lopez George Box. Teaching engineers experimental design with a paper helicopter.Six Sigma Quality Engineering, 4(3):453–459, 1992.MethodologyIntroduction John M. Chambers. Software for data analysis. Programming with R.Roles Statistics and Computing. Springer, 2008.Tools C. Gygi, N. DeCarlo, and B. Williams. Six sigma for dummies. –ForSix Sigma with R dummies. Wiley Pub., 2005. ISBN 9780764567988.Six Sigma SoftwareR Advantages D.C. Montgomery. Introduction to Statistical Quality Control. Wiley, NewR Packages for SixSigma York, 5th edition, 2005.Spreading 6σ & R Daniela R. Recchia, Emanuel P. Barbosa, and Elias de Jesus Goncalves.Courses IQCC: Improved Quality Control Charts, 2010. URLPublicationsFurther http://CRAN.R-project.org/package=IQCC. R package version 0.5.References Thomas Roth. qualityTools: A Package for Teaching Statistics in Quality Science., 2011. R package version 1.44. Deepayan Sarkar. Lattice: Multivariate Data Visualization with R. Springer, New York, 2008. URL http://lmdvr.r-forge.r-project.org. ISBN 978-0-387-75968-5. Luca Scrucca. qcc: an r package for quality control charting and statistical process control. R News, 4/1:11–17, 2004. URL http://CRAN.R-project.org/doc/Rnews/. H. Wickham. ggplot2: elegant graphics for data analysis. Use R! Springer, 2009. ISBN 9780387981406. The R User Conference 2011 35/37
  77. 77. 6σ Quality Using R Acknowledgements Emilio LopezSix SigmaMethodologyIntroduction Dept. Statistics & OR URJCRolesTools David Rios, Javier M. Moguerza, Andres RedchukSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigma R peopleSpreading 6σ & R Kurt Hornik, Heather Turner, Rob J Hyndman, DianeCoursesPublications Cook, R Core TeamFurtherReferences Springer Marc Strauss. Springer This work has been partially funded by VRTUOSI project, www.vrtuosi.org, within the Virtual Campus methodological framework of the EU Lifelong Learning Programme (LLP, code 502869-LLP-1-2009-ES-ERASMUS-EVC) The R User Conference 2011 36/37
  78. 78. 6σ Quality Using R Discussion Emilio LopezSix SigmaMethodologyIntroductionRolesTools Thanks for yourSix Sigma with RSix Sigma SoftwareR AdvantagesR Packages for SixSigma attention !Spreading 6σ & RCoursesPublicationsFurtherReferences Any question? emilio.lopez@urjc.es The R User Conference 2011 37/37
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