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Six Sigma With R
  (Springer, 2012)

      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e
                                             Six Sigma with R
Frontmatter
                                   Statistical Engineering for Process
Mainmatter                                     Improvement
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
                                 Emilio L. Cano, Javier M. Moguerza
VII Further and Beyond

Backmatter
                                         and Andr´s Redchuk
                                                  e

                                                 November 20, 2012

                                        Facultad de Estudios Estad´
                                                                  ısticos
                                       Universidad Complutense de Madrid


                         Book Presentation UCM                              1/59
Six Sigma With R
  (Springer, 2012)       Contenido
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e                 1   Frontmatter
Frontmatter

Mainmatter
                         2   Mainmatter
I Basics
II Define                      I Basics
III Measure
IV Analyze
V Improve
                              II Define
VI Control
VII Further and Beyond
                              III Measure
Backmatter                    IV Analyze
                              V Improve
                              VI Control
                              VII Further and Beyond
                         3   Backmatter

                         Book Presentation UCM         2/59
Six Sigma With R
  (Springer, 2012)       Contents
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e                 1   Frontmatter
Frontmatter

Mainmatter
                         2   Mainmatter
I Basics
II Define                      I Basics
III Measure
IV Analyze
V Improve
                              II Define
VI Control
VII Further and Beyond
                              III Measure
Backmatter                    IV Analyze
                              V Improve
                              VI Control
                              VII Further and Beyond
                         3   Backmatter

                         Book Presentation UCM         3/59
Six Sigma With R
  (Springer, 2012)       Publisher
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                            http://www.springer.com/statistics/book/978-1-4614-3651-5




                         Book Presentation UCM                                          4/59
Six Sigma With R
  (Springer, 2012)       Book website
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                                 http://www.sixsigmawithr.com/

                         Book Presentation UCM                   5/59
Six Sigma With R
  (Springer, 2012)       R Package
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                            http://cran.r-project.org/web/packages/SixSigma/index.html



                         Book Presentation UCM                                           6/59
Six Sigma With R
  (Springer, 2012)       Frontmatter
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e
                                 Foreword
Frontmatter
                                 Preface
Mainmatter
                                          Why Six Sigma with R
I Basics
II Define
                                          Who is this book for
III Measure                               Conventions
IV Analyze
V Improve                                 Production
VI Control
VII Further and Beyond                    Resources
Backmatter                                About the Authors
                                 Acknowledgements
                                 Contents
                                 List of Tables and Figures
                                 Acronyms
                         http://link.springer.com/book/10.1007/978-1-4614-3652-2//page/1
                         Book Presentation UCM                                       7/59
Six Sigma With R
  (Springer, 2012)       Contents
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e                 1   Frontmatter
Frontmatter

Mainmatter
                         2   Mainmatter
I Basics
II Define                      I Basics
III Measure
IV Analyze
V Improve
                              II Define
VI Control
VII Further and Beyond
                              III Measure
Backmatter                    IV Analyze
                              V Improve
                              VI Control
                              VII Further and Beyond
                         3   Backmatter

                         Book Presentation UCM         8/59
Six Sigma With R
  (Springer, 2012)       1. Six Sigma in a Nutshell
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter              Herbert Spencer
Mainmatter
I Basics                            “Science is organised knowledge”
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                         9/59
Six Sigma With R
  (Springer, 2012)       The DMAIC Cycle
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM   10/59
Six Sigma With R
  (Springer, 2012)       Six Sigma Roles
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter              In Six Sigma, everyone in the organization has
Mainmatter
I Basics                  a role in the project. Six Sigma methodology
II Define
III Measure
IV Analyze
                          uses an intuitive categorization of these roles.
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                         11/59
Six Sigma With R
  (Springer, 2012)       Six Sigma Roles
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter              In Six Sigma, everyone in the organization has
Mainmatter
I Basics                  a role in the project. Six Sigma methodology
II Define
III Measure
IV Analyze
                          uses an intuitive categorization of these roles.
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                         11/59
Six Sigma With R
  (Springer, 2012)       2. R from the Beginning
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter              Linus Torvalds
Mainmatter
I Basics
                         “Software is like sex; it’s better when it’s free”
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                         12/59
Six Sigma With R
  (Springer, 2012)       The R Project
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                                       http://www.r-project.org


                         Book Presentation UCM                    13/59
Six Sigma With R
  (Springer, 2012)       The R Environment
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM   14/59
Six Sigma With R
  (Springer, 2012)       3. Process Mapping with R
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter
                         Charles Franklin Kettering
Mainmatter
I Basics
                             “A problem well stated is a problem half
II Define
III Measure
                                             solved”
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                          15/59
Six Sigma With R
  (Springer, 2012)       A Process Map
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e                                             Six Sigma Process Map
Frontmatter                                               operators
                                     INPUTS
                                                          tools
Mainmatter                              X                 raw material
I Basics                                                  facilities
II Define
                            INSPECTION                        ASSEMBLY                           TEST                      LABELING
III Measure
                               sheets                           sheets                         helicopter                  helicopter
IV Analyze
                                 ...
                            INPUTS




                                                          INPUTS




                                                                                      INPUTS




                                                                                                                  INPUTS
V Improve
VI Control
VII Further and Beyond
                          Param.(x): width NC          Param.(x): operator C        Param.(x): operator C       Param.(x): operator C
Backmatter                            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




                         Book Presentation UCM                                                                                          16/59
Six Sigma With R
  (Springer, 2012)       4. Loss Funtion Analysis with R
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter              W. Edwards Deming
Mainmatter
I Basics
II Define
                          Defects are not free. Somebody makes them,
III Measure
IV Analyze
                                 and gets paid for making them
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                    17/59
Six Sigma With R
  (Springer, 2012)       A Loss Function Example
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e                 > ss . lfa ( ss . data . bolts , " diameter " , 0.5 , 10 , 0.001 ,
                              lfa . sub = " 10 mm . Bolts Project " ,
Frontmatter
                              lfa . size = 100000 , lfa . output = " both " )
Mainmatter
I Basics
II Define                 $ lfa . k
III Measure              [1] 0.002
IV Analyze
V Improve
VI Control               $ lfa . lf
VII Further and Beyond   expression ( bold ( L == 0.002 %. % ( Y - 10) ^2) )
Backmatter
                         $ lfa . MSD
                         [1] 0.03372065

                         $ lfa . avLoss
                         [1] 6.74413 e -05

                         $ lfa . Loss
                         [1] 6.74413



                         Book Presentation UCM                                            18/59
Six Sigma With R
  (Springer, 2012)       A Loss Function Example (cont.)
      November, 2012


  Emilio L. Cano
Javier M. Moguerza                                                        Loss Function Analysis
  Andr´s Redchuk
       e

Frontmatter                                                5e−04                       T
                                                                                                                      Data
Mainmatter
I Basics                                                   4e−04                                                 CTQ: diameter
II Define                                                                                                             Y0 = 10
III Measure                         Cost of Poor Quality                                                             ∆ = 0.5
IV Analyze                                                                                                         L0 = 0.001
                                                           3e−04
V Improve                                                                                                         Size = 1e+05
VI Control
VII Further and Beyond
                                                           2e−04
Backmatter                                                                                                       Mean = 10.0308
                                                                                                                    k = 0.002
                                                           1e−04                                                  MSD = 0.0337
                                                                   LSL                                    USL    Av.Loss = 1e−04
                                                                                                                  Loss = 6.7441
                                                           0e+00

                                                                    9.6      9.8       10.0       10.2    10.4
                                                                                Observed Value

                                                                          L = 0.002 ⋅ (Y − 10)
                                                                                              2



                                                                                   10 mm. Bolts Project


                         Book Presentation UCM                                                                                     19/59
Six Sigma With R
  (Springer, 2012)       5. Measurement System Analysis
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter
                         Lord Kelvin
Mainmatter                                “If you cannot measure it,
I Basics
II Define                                    you cannot improve it.”
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                         20/59
Six Sigma With R
  (Springer, 2012)       Repeatability & Reproducibility
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
                         Repetible and Reproducible   Repetible but non Reproducible   Reproducible but non Repetible   Non Repetible & Non Reproducible
II Define
                                                                                                                                   q               q
III Measure                                                     qq
                                                                 q
                                                            q    q                           q
                                                                                             q   q                                             q
IV Analyze                                                      q
                                                                                                                                       q

V Improve                            q
                                     qq
                                      q
                                      qq
VI Control
VII Further and Beyond                                                                                                         q
                                                                                                     q
                                                                                                         q
                                                                                                     q                                     q

Backmatter




                           Book Presentation UCM                                                                                                       21/59
Six Sigma With R
  (Springer, 2012)       MSA with R
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e                                                                                                                   Six Sigma Gage R&R Study
                                                                           Components of Variation                                                                                       Var by Part

                                                                                                                                                               1.8

Frontmatter                        80
                                                                                                                                                                                                                  q
                                                                                                                                                                                                                  q
                                                                                                                                                                                                                  q
                                                                                                                                                                                                                  q
                                                                                                                                                                                                                  q
                                                                                                                                                               1.6
                                   60
                                                                                                                                                                                                q
                                                                                                                                                                                                                  q
                         Percent




Mainmatter                                                                                                                                                     1.4




                                                                                                                                                         var
                                   40                                                                                                                                  q
                                                                                                                                                                       q
                                                                                                                                                                       q
                                                                                                                                                                       q                                          q
                                                                                                                                                                                                q
                                                                                                                                                               1.2
I Basics                           20
                                                                                                                                                                       q
                                                                                                                                                                                                q
                                                                                                                                                                                                q
                                                                                                                                                                                                q
                                                                                                                                                                                                q
                                                                                                                                                               1.0                              q
                                   0
II Define                                           G.R&R                    Repeat                      Reprod               Part2Part
                                                                                                                                                                       q

                                                                                                                                                                     prot #1                  prot #2           prot #3
III Measure                                                     %Contribution                       %Study Var


IV Analyze                                                                   R Chart by appraiser                                                                                      Var by appraiser

                                                                                prot #1   prot #2      prot #3
V Improve                                                                                                                                                      1.8
                                                                                                                                                                       q
                                                                                                                                                                       q
                                                                                                                                                                                                q
                                                      op #1                               op #2                             op #3
                                   0.5                                                                                                                                                                            q
                                                                   q                                                                                                                            q
                                                                                                                                                                                                q                 q
VI Control                                                                                                                                                     1.6
                                   0.4                                                                                                                                                                            q
                                           q                                                                                                                                                                      q
VII Further and Beyond                                                                                                       q                                 1.4




                                                                                                                                                         var
                                   0.3                                                                                                                                                          q
                         var




                                                                                                                                                                                                q
                                                                                            q                                              q                           q
                                                                                                                                                                       q                        q                 q
                                                                                                                                                                                                q
                                   0.2                                                                                                                         1.2
                                                                                                                   q                                                   q                        q                 q
                                                                                                                                                                       q
Backmatter                         0.1
                                                           q                      q
                                                                                                         q
                                                                                                                                                               1.0
                                                                                                                                                                       q
                                                                                                                                                                                                q
                                                                                                                                                                                                                  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                                                                                                                         1.4
                         var




                                   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




                         Book Presentation UCM                                                                                                                                                                            22/59
Six Sigma With R
  (Springer, 2012)       6. Pareto Analysis with R
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter
                         Ovidio
Mainmatter
I Basics
                         Causa latet: vis est notissima. [The cause is
II Define
III Measure
                         hidden, but the result is known.]
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                           23/59
Six Sigma With R
  (Springer, 2012)       Pareto Principle (80/20 rule)
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
                         Examples
III Measure
IV Analyze
V Improve
                                 20 % of customers make 80 % of incomes
VI Control
VII Further and Beyond           20 % of students get 80 % of good marks
Backmatter
                                 80 % of cost of quality is due to 20 % of
                                 the possible causes




                         Book Presentation UCM                         24/59
Six Sigma With R
  (Springer, 2012)       Cause-and-effect diagram
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e                                  Six Sigma Cause−and−effect Diagram

Frontmatter

Mainmatter
I Basics
                                         Operator         Environment                   Tools
                                                 operator #1           height                   scissors
II Define
                                                   operator #2           cleaning                  tape
III Measure                                           operator #3
IV Analyze
V Improve
VI Control
VII Further and Beyond
                                                                                                                              Flight Time
Backmatter



                                                                                                                  paperclip
                                                              model                    marks                  rotor.width2
                                                           calibrate                thickness              rotor.length

                                             Measure.Tool Raw.Material                             Design




                                                                       Paper Helicopter Project




                         Book Presentation UCM                                                                                              25/59
Six Sigma With R
  (Springer, 2012)       Pareto Chart
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e                                                                    Pareto Chart for b.vector

                                                                                                                                                               q
Frontmatter                                                                                                                         q
                                                                                                                                                  q
                                                                                                                           q
                                                                                                                    q

Mainmatter                                                                                                  q




                                                                                                                                                                           80%
                                                                                                   q




                                                  60
I Basics




                                                                                                                                                                                 Cumulative Percentage
                                                                                        q
II Define
                                                                             q
III Measure
IV Analyze                            Frequency

                                                  40
V Improve
                                                                 q
VI Control
VII Further and Beyond

Backmatter
                                                  20



                                                        q
                                                  0


                                                       Delays

                                                                Materials

                                                                            Customer

                                                                                       Training

                                                                                                  Rework

                                                                                                           Errors

                                                                                                                    Rain

                                                                                                                           Wind

                                                                                                                                  Permissions

                                                                                                                                                Inadequate

                                                                                                                                                             Temperature
                         Book Presentation UCM                                                                                                                                                           26/59
Six Sigma With R
  (Springer, 2012)       7. Process Capability Analysis
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter
                         Johann Wolfgang von Goethe
Mainmatter               One cannot develop taste from what is of
I Basics
II Define
III Measure
                         average quality but only from the very best.
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                      27/59
Six Sigma With R
  (Springer, 2012)       Capability Analysis Output
      November, 2012


  Emilio L. Cano
Javier M. Moguerza                            Six Sigma Capability Analysis Study
  Andr´s Redchuk
       e
                                                      Histogram & Density                                  Density Lines Legend
Frontmatter                                                                 Target                                   Density ST
                                                                                                                     Theoretical Dens. ST
Mainmatter                                                                                                           Density LT
                                                                                                                     Theoretical Density LT
I Basics
II Define
III Measure                                       LSL                                USL                        Specifications
IV Analyze                                                                                                         LSL: 740
                                                                                                                 Target: 750
V Improve
                                                                                                                   USL: 760
VI Control
VII Further and Beyond

Backmatter                                                                                              Short Term   Process Long Term
                                             740         745              750   755      760             Mean: 749.7625 Mean: 753.7239
                                                         Check Normality                                   SD: 2.1042     SD: 2.6958
                                                                                                             n: 20          n: 40
                                                                                Shapiro−Wilk Test           Zs: 3.14       Zs: 2.33
                                                                           q
                                                                                p−value: 0.07506                        DPMO: 9952.5
                                                                      q                                 Short Term    Indices Long Term
                                                                 qq             Lilliefors (K−S) Test      Cp: 1.5841          Pp: 1.2365
                                                            qq
                                                         qqq                     p−value: 0.2291            CI: [1.4,1.7]       CI: [1.1,1.3]
                                                       qq
                                                    qqq
                                                  qq
                                             qq                                                            Cpk: 1.5465         Ppk: 0.7760
                                         q
                                     q
                                                                                                            CI: [1.4,1.7]       CI: [0.7,0.8]
                                         Normality accepted when p−value > 0.05

                                                                                  Winery Project


                         Book Presentation UCM                                                                                                  28/59
Six Sigma With R
  (Springer, 2012)       8. Charts with R
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e
                         John Tukey
Frontmatter

Mainmatter
                           “The greatest value of a picture is when it
I Basics
II Define
                         forces us to notice what we never expected to
III Measure
IV Analyze                                    see.”
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                     29/59
Six Sigma With R
  (Springer, 2012)       Multi-vari chart
      November, 2012


  Emilio L. Cano                                Multi−vari chart for Volume by color and operator
Javier M. Moguerza
  Andr´s Redchuk
       e
                                                                        batch
                                           1    q           2   q                 3       q       4       q


                                                                                      1       2       3
Frontmatter
                                                           3                                  3
Mainmatter
                                                           B                                  C
I Basics                                   18
II Define                                   17
III Measure                                16                                         q               q
                                                    q               q
                                                    q       q
                                                            q                                 q
                                                                                              q
IV Analyze                                 15                       q
                                                                    q                 q
                                                                                      q               q
                                                    q
                                                    q               q                         q       q
                                                            q                         q       q       q
V Improve                                  14
VI Control                                                 2                                  2
VII Further and Beyond                                     B                                  C
                                                                                      q       q               18
                                                                    q
Backmatter
                                  Volume




                                                    q                                         q               17
                                                                                      q               q
                                                            q       q                                 q
                                                    q
                                                                                              q               16
                                                    q       q                         q               q
                                                            q       q
                                                                    q                 q                       15
                                                            q                                 q
                                                    q
                                                                                                              14
                                                           1                                  1
                                                           B                                  C
                                                            q
                                           18       q       q
                                                                                              q
                                           17       q               q                 q       q
                                                                                                      q
                                                                                                      q
                                           16       q
                                                                    q
                                                                                      q               q
                                                            q                         q               q
                                           15       q                                 q
                                                                    q                         q
                                           14               q


                                                    1       2       3

                                                                         Filler


                         Book Presentation UCM                                                                     30/59
Six Sigma With R
  (Springer, 2012)       9. Statistics and Probability with R
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter               Aaron Levenstein
I Basics
II Define                 “Statistics are like bikinis. What they reveal is
III Measure
IV Analyze
V Improve
                           suggestive, but what they conceal is vital.”
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                         31/59
Six Sigma With R
  (Springer, 2012)       Distributions
      November, 2012


  Emilio L. Cano                                                     Hypergeometric                                                         Geometric                                        Negative Binomial                                                        Poison
Javier M. Moguerza




                                 Probability




                                                                                                 Probability




                                                                                                                                                             Probability




                                                                                                                                                                                                                         Probability
                                                                                                                                                                                   0.06




                                                                                                                                                                                                                                               0.15
                                                                                                                         0.00 0.10
  Andr´s Redchuk
       e




                                                       0.3




                                                                                                                                                                                   0.00




                                                                                                                                                                                                                                               0.00
                                                       0.0
Frontmatter                                                          0      1     2    3     4                                          0    10    30                                               10 20 30 40                                              0        5   10    20

                                                                     Elements in class A                               Items extracted until first success                         Number of trials until 3 events
                                                                                                                                                                                                                 Number of successful experiments per unit
Mainmatter
I Basics                                                                 Exponential                                                        Lognormal                                                   Uniform                                                       Gamma
                                 Probability Density




                                                                                                 Probability Density




                                                                                                                                                             Probability Density




                                                                                                                                                                                                                         Probability Density
II Define




                                                                                                                         0.0 0.4 0.8




                                                                                                                                                                                   0.0 0.6 1.2




                                                                                                                                                                                                                                               0.0 0.2 0.4
III Measure                                            0.6

IV Analyze
                                                       0.0



V Improve
                                                                     0 1 2 3 4 5                                                        0     2   4     6                                        −0.5     0.5      1.5                                       0 2 4 6 8
VI Control
                                                                     Random Variable X                                                 Random Variable X>0                                        Random Variable X                                          Random Variable X
VII Further and Beyond

Backmatter                                                                      Beta                                                         Weibul                                                 t−Student                                                Chi−squared
                                 Probability Density




                                                                                                 Probability Density




                                                                                                                                                             Probability Density




                                                                                                                                                                                                                         Probability Density
                                                       0.0 1.0 2.0




                                                                                                                         0.0 0.3 0.6




                                                                                                                                                                                                                                               0.06
                                                                                                                                                                                   0.3
                                                                                                                                                                                                          95%
                                                                                                                                                                                                              5%                                                      95% 5%




                                                                                                                                                                                                                                               0.00
                                                                                                                                                                                   0.0
                                                                                                                                                                                                            1.73                                                        30.14
                                                                     0.0        0.4    0.8                                              0     2   4     6                                          −4      0 2 4                                                 10       30    50

                                                                     Random Variable X                                                  Random Variable X                                         Random Variable X                                          Random Variable X



                                                                                  F
                                 Probability Density

                                                       0.6




                                                                           95%
                                                                                     5%
                                                       0.0




                                                                                  2.34
                                                                     0      1     2    3     4

                                                                     Random Variable X




                         Book Presentation UCM                                                                                                                                                                                                                                       32/59
Six Sigma With R
  (Springer, 2012)       10. Statistical Inference with R
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e
                         George E.P. Box
Frontmatter

Mainmatter
                             “All models are wrong; some models are
I Basics
II Define
                                             useful.”
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                        33/59
Six Sigma With R
  (Springer, 2012)       Confidence Interval Example
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e                                                 Confidence Interval for the Mean

Frontmatter
                                      Mean:                    950.016
                                                                                     95% CI:            [949.967, 950.064]
Mainmatter                            StdDev:                    0.267
                                                                                     P−Var:                       unknown
I Basics                              n:                           120
                                                                                     t:                               1.98
II Define                              Missing:                       0
III Measure
IV Analyze
V Improve
VI Control                                               Histogram & Density Plot                       Shapiro−Wilks
                                                 1.5
VII Further and Beyond                                                                                  Normality Test

Backmatter                                                                                                  0.985
                                                                                                         p−value: 0.19
                                                 1.0
                                       density




                                                                                                     Normal q−q Plot
                                                 0.5                                                                                        q
                                                                                                                                     qq q
                                                                                                                               qq
                                                                                                                              qq qq q
                                                                                                                                qq q
                                                                                                                                 qq
                                                                                                                              qq
                                                                                                                             qq
                                                                                                                             qq
                                                                                                                            qq
                                                                                                                           qq
                                                                                                                           qq
                                                                                                                           qq
                                                                                                                          qq
                                                                                                                          qq
                                                                                                                         qq
                                                                                                                         qq
                                                                                                                        qq
                                                                                                                        qq
                                                                                                                       q
                                                                                                                       q
                                                                                                                      qq
                                                                                                                     qq
                                                                                                                     qq
                                                                                                                    qq
                                                                                                                  qq
                                                                                                                 qq
                                                                                                                 qq
                                                                                                                   q
                                                 0.0                                                            qq
                                                                                                               qq
                                                                                                              qqqq
                                                                                                              qq
                                                                                                             qq
                                                                                                             qq
                                                                                                              q
                                                                                                            qq
                                                                                                           qq
                                                                                                           qq
                                                                                                          qq
                                                                                                             q
                                                                                                         qq
                                                                                                         qq
                                                                                                        qq
                                                       949.0   949.5   950.0     950.5                 q
                                                                                                       q
                                                                                                      q
                                                                                                     q
                                                                  Value of len                 q
                                                                                                   qq




                         Book Presentation UCM                                                                                                  34/59
Six Sigma With R
  (Springer, 2012)       11. Design of Experiments with R
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter
                         R.A. Fisher
Mainmatter                      “Sometimes the only thing you can
I Basics
II Define                        do with a poorly designed
III Measure
IV Analyze
V Improve
                                experiment is to try to find out what
VI Control
VII Further and Beyond
                                it died of”
Backmatter




                         Book Presentation UCM                         35/59
Six Sigma With R
  (Springer, 2012)       The Importance of Experimenting
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter
                                 “An engineer who does not know
Mainmatter                       experimental design is not an
I Basics
II Define
III Measure
                                 engineer”
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter
                         Comment made by to one
                         of the authors [of “Statistics
                         for experimenters” by an
                                            ]
                         executive of the Toyota
                         Motor Company.


                          Book Presentation UCM                   36/59
Six Sigma With R
  (Springer, 2012)       12.Process Control with R
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
                         Walter A. Shewhart
I Basics
II Define
                         “Special causes of variation may be found and
III Measure
IV Analyze                                eliminated.”
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                     37/59
Six Sigma With R
  (Springer, 2012)       Control Chart Plotting
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e                                                                                                   p Chart
                                                                                                        for stockouts




                                                                 0.25
Frontmatter                                                                                                     q
                                                                                                                q



                                                                                                                                                                      UCL
Mainmatter                                                                  q
                                                                                    q




                                                                 0.20
I Basics




                                      Group summary statistics
II Define
                                                                                                                         q
III Measure



                                                                 0.15
                                                                                                                                           q             q
                                                                        q                   q
IV Analyze
                                                                                                                                  q

V Improve                                                                                                                              q        q


VI Control
                                                                 0.10
                                                                                q
                                                                                                            q
                                                                                                                                                                      CL
                                                                                                                                                    q
VII Further and Beyond
                                                                                                    q
                                                                                                                                                             q

Backmatter                                                                                      q                                                                 q
                                                                 0.05




                                                                                                        q
                                                                                                                     q        q



                                                                                        q
                                                                                                                                                                      LCL
                                                                 0.00




                                                                        1       3       5       7       9       11       13       15       17       19       21

                                                                                                                Group

                                                                    Number of groups = 22
                                                                    Center = 0.1212294    LCL is variable                         Number beyond limits = 1
                                                                    StdDev = 0.3263936    UCL is variable                         Number violating runs = 0




                         Book Presentation UCM                                                                                                                              38/59
Six Sigma With R
  (Springer, 2012)       13. Other Tools and
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
                         Methodologies
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
                         Johann Wolfgang von Goethe
I Basics
II Define                 Instruction does much, but encouragement
III Measure
IV Analyze
V Improve
                         everything.
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM                      39/59
Six Sigma With R
  (Springer, 2012)       Other topics
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
                                 Failure Mode, Effects, and Criticality
II Define
III Measure
                                 Analysis
IV Analyze
V Improve
VI Control
                                 Design for Six Sigma
VII Further and Beyond

Backmatter
                                 Lean
                                 Gantt Chart
                                 Some Advanced R Topics




                         Book Presentation UCM                           40/59
Six Sigma With R
  (Springer, 2012)       Contents
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e                 1   Frontmatter
Frontmatter

Mainmatter
                         2   Mainmatter
I Basics
II Define                      I Basics
III Measure
IV Analyze
V Improve
                              II Define
VI Control
VII Further and Beyond
                              III Measure
Backmatter                    IV Analyze
                              V Improve
                              VI Control
                              VII Further and Beyond
                         3   Backmatter

                         Book Presentation UCM         41/59
Six Sigma With R
  (Springer, 2012)       Case Study
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM   42/59
Six Sigma With R
  (Springer, 2012)       Helicopter Template
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter



                         > ss . heli ()

                         null device
                                   1

                         > # vignette (" H e l i c o p t e r I n s t r u c t i o n s ") to get
                              instructions


                         Book Presentation UCM                                                   43/59
Six Sigma with R | Paper Helicopter template
                                                                                   max
                                                                                   (9.5cm)


                                                                                   std
                                                                                   (8cm)


                                                                                   min
                                                                                   (6.5cm)




                                                                                ← wings length →
                                              cut
                                         ?
                                     pe
            fold ↑                                             fold ↓




                                    ta
cut




      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)
Six Sigma With R
  (Springer, 2012)       Enjoy the Case Study!
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM   45/59
Six Sigma With R
  (Springer, 2012)       Enjoy the Case Study!
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM   45/59
Six Sigma With R
  (Springer, 2012)       So what?
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM   46/59
Six Sigma With R
  (Springer, 2012)       So what?
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e                 The Scientific Method
Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM   46/59
Six Sigma With R
  (Springer, 2012)       The Scientific Method and Six
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
                         Sigma
  Andr´s Redchuk
       e

Frontmatter

Mainmatter                                 DMAIC Cycle       Scientific Method
I Basics
II Define                                                   Ask a question
III Measure                                      Define
IV Analyze
V Improve                                                  Do some background
VI Control
                                                 Measure   research
VII Further and Beyond

Backmatter
                                                           Construct a hypothesis
                                                 Analyze
                                                           Test the hypothesis
                                                           with an experiment
                                                 Improve
                                                           Analyze the data and
                                                           draw conclusions
                                                 Control
                                                           Communicate results



                         Book Presentation UCM                                      47/59
Six Sigma With R
  (Springer, 2012)       The Key to Success
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
                         “Six Sigma speaks the language of business”
  Andr´s Redchuk
       e

Frontmatter                                         ISO 13053-1:2011
Mainmatter
I Basics
II Define
III Measure
IV Analyze
                         Six Sigma methodology is a quality paradigm
V Improve
VI Control
                         that translates the involved scientific
VII Further and Beyond

Backmatter
                         methodology into a simple way to apply the
                         scientific method within every organization.




                         Book Presentation UCM                     48/59
Six Sigma With R
  (Springer, 2012)       Opportunities
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter
                                 For Today’s Graduate, Just One Word: Statistics
Mainmatter                       (The New York Times, August 2009)
I Basics
II Define                              “I keep saying that the sexy job in the
III Measure
IV Analyze                            next 10 years will be statisticians”
V Improve
VI Control
VII Further and Beyond

Backmatter                       Data Scientist: The Sexiest Job of the 21st
                                 Century (Harvard Business Review, October 2012)
                                      . . . the “data scientist.” It’s a
                                      high-ranking professional with the
                                      training and curiosity to make
                                      discoveries in the world of big data . . .


                         Book Presentation UCM                                49/59
Six Sigma With R
  (Springer, 2012)       Opportunities (cont.)
      November, 2012


  Emilio L. Cano                 Gartner Sees 4.4M Big Data Jobs by 2015
Javier M. Moguerza
  Andr´s Redchuk
       e                         (Information Management, October 2012)
Frontmatter                      Lack of data scientists could derail big data
Mainmatter
I Basics
                                 projects: IBM (CIO, October 2012)
II Define
III Measure
IV Analyze
                                 Son las matem´ticas, est´pido (El Pa´
                                              a          u           ıs,
V Improve
VI Control
                                 Noviembre 2012)
VII Further and Beyond

Backmatter
                                          La econom´ del conocimiento exige
                                                    ıa
                                          una educaci´n sustentada en tres
                                                     o
                                          fundamentos: un nivel avanzado en
                                          matem´tica y estad´
                                                 a           ıstica, una
                                          capacidad elevada para escribir un
                                          argumento y un nivel avanzado de
                                          ingl´s
                                              e

                         Book Presentation UCM                                   50/59
Six Sigma With R
  (Springer, 2012)       R Final Remarks
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond
                                                 kdnuggets.com
Backmatter                                       (2012) link




                         Book Presentation UCM                   51/59
Six Sigma With R
  (Springer, 2012)       R Final Remarks (cont.)
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
                         Community
  Andr´s Redchuk
       e
                                 4131 packages at CRAN (18/11/2012)
Frontmatter

Mainmatter                       Task views
I Basics
II Define
III Measure
                                 Manuals
IV Analyze
V Improve                        Publications
VI Control
VII Further and Beyond

Backmatter               http:
                         //cran.r-project.org/web/packages/




                         Book Presentation UCM                    52/59
Six Sigma With R
  (Springer, 2012)       R Final Remarks (cont.)
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e
                         Customization
                         A company can develop a package that fits its
Frontmatter

Mainmatter
                         inner procedures and methods.
I Basics
II Define
III Measure
IV Analyze
V Improve
                         Innovation
VI Control
VII Further and Beyond
                         A company can develop and deploy an
Backmatter               innovative method from its R&D department,
                         or from the result of other published
                         researches.




                         Book Presentation UCM                    53/59
Six Sigma With R
  (Springer, 2012)       R Final Remarks (cont.)
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter              Business
Mainmatter
I Basics
                                 http:
II Define
III Measure
                                 //www.revolutionanalytics.com/
IV Analyze
V Improve
VI Control
                                 http://www.openanalytics.eu/
VII Further and Beyond

Backmatter
                                 http://www.fellstat.com/
                                 http://www.rstudio.com/ide/
                                 http://www.datanalytics.com/
                                 ...


                         Book Presentation UCM                    54/59
Six Sigma With R
  (Springer, 2012)       R Final Remarks (cont.)
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
                         GUI, IDE
II Define
III Measure
                                 RStudio
IV Analyze
V Improve
VI Control
                                 Eclipse + StatET
VII Further and Beyond

Backmatter
                                 EMACS + EES
                                 Deducer
                                 ...




                         Book Presentation UCM      55/59
Six Sigma With R
  (Springer, 2012)       R Final Remarks (cont.)
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                         Book Presentation UCM     56/59
Six Sigma With R
  (Springer, 2012)

      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                                                 http://r-es.org/


                         Book Presentation UCM                      57/59
Six Sigma With R
  (Springer, 2012)

      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e

Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter




                           http://www.r-project.org/useR-2013

                         Book Presentation UCM              58/59
Six Sigma With R
  (Springer, 2012)       Discussion
      November, 2012


  Emilio L. Cano
Javier M. Moguerza
  Andr´s Redchuk
       e




                                                 Thanks !
Frontmatter

Mainmatter
I Basics
II Define
III Measure
IV Analyze
V Improve
VI Control
VII Further and Beyond

Backmatter                                       emilio.lopez@urjc.es
                                                   @emilopezcano


                                  http://www.sixsigmawithr.com


                         Book Presentation UCM                          59/59

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Six Sigma with R

  • 1. Six Sigma With R (Springer, 2012) November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Six Sigma with R Frontmatter Statistical Engineering for Process Mainmatter Improvement I Basics II Define III Measure IV Analyze V Improve VI Control Emilio L. Cano, Javier M. Moguerza VII Further and Beyond Backmatter and Andr´s Redchuk e November 20, 2012 Facultad de Estudios Estad´ ısticos Universidad Complutense de Madrid Book Presentation UCM 1/59
  • 2. Six Sigma With R (Springer, 2012) Contenido November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e 1 Frontmatter Frontmatter Mainmatter 2 Mainmatter I Basics II Define I Basics III Measure IV Analyze V Improve II Define VI Control VII Further and Beyond III Measure Backmatter IV Analyze V Improve VI Control VII Further and Beyond 3 Backmatter Book Presentation UCM 2/59
  • 3. Six Sigma With R (Springer, 2012) Contents November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e 1 Frontmatter Frontmatter Mainmatter 2 Mainmatter I Basics II Define I Basics III Measure IV Analyze V Improve II Define VI Control VII Further and Beyond III Measure Backmatter IV Analyze V Improve VI Control VII Further and Beyond 3 Backmatter Book Presentation UCM 3/59
  • 4. Six Sigma With R (Springer, 2012) Publisher November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter http://www.springer.com/statistics/book/978-1-4614-3651-5 Book Presentation UCM 4/59
  • 5. Six Sigma With R (Springer, 2012) Book website November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter http://www.sixsigmawithr.com/ Book Presentation UCM 5/59
  • 6. Six Sigma With R (Springer, 2012) R Package November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter http://cran.r-project.org/web/packages/SixSigma/index.html Book Presentation UCM 6/59
  • 7. Six Sigma With R (Springer, 2012) Frontmatter November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Foreword Frontmatter Preface Mainmatter Why Six Sigma with R I Basics II Define Who is this book for III Measure Conventions IV Analyze V Improve Production VI Control VII Further and Beyond Resources Backmatter About the Authors Acknowledgements Contents List of Tables and Figures Acronyms http://link.springer.com/book/10.1007/978-1-4614-3652-2//page/1 Book Presentation UCM 7/59
  • 8. Six Sigma With R (Springer, 2012) Contents November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e 1 Frontmatter Frontmatter Mainmatter 2 Mainmatter I Basics II Define I Basics III Measure IV Analyze V Improve II Define VI Control VII Further and Beyond III Measure Backmatter IV Analyze V Improve VI Control VII Further and Beyond 3 Backmatter Book Presentation UCM 8/59
  • 9. Six Sigma With R (Springer, 2012) 1. Six Sigma in a Nutshell November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Herbert Spencer Mainmatter I Basics “Science is organised knowledge” II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 9/59
  • 10. Six Sigma With R (Springer, 2012) The DMAIC Cycle November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 10/59
  • 11. Six Sigma With R (Springer, 2012) Six Sigma Roles November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter In Six Sigma, everyone in the organization has Mainmatter I Basics a role in the project. Six Sigma methodology II Define III Measure IV Analyze uses an intuitive categorization of these roles. V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 11/59
  • 12. Six Sigma With R (Springer, 2012) Six Sigma Roles November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter In Six Sigma, everyone in the organization has Mainmatter I Basics a role in the project. Six Sigma methodology II Define III Measure IV Analyze uses an intuitive categorization of these roles. V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 11/59
  • 13. Six Sigma With R (Springer, 2012) 2. R from the Beginning November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Linus Torvalds Mainmatter I Basics “Software is like sex; it’s better when it’s free” II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 12/59
  • 14. Six Sigma With R (Springer, 2012) The R Project November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter http://www.r-project.org Book Presentation UCM 13/59
  • 15. Six Sigma With R (Springer, 2012) The R Environment November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 14/59
  • 16. Six Sigma With R (Springer, 2012) 3. Process Mapping with R November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Charles Franklin Kettering Mainmatter I Basics “A problem well stated is a problem half II Define III Measure solved” IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 15/59
  • 17. Six Sigma With R (Springer, 2012) A Process Map November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Six Sigma Process Map Frontmatter operators INPUTS tools Mainmatter X raw material I Basics facilities II Define INSPECTION ASSEMBLY TEST LABELING III Measure sheets sheets helicopter helicopter IV Analyze ... INPUTS INPUTS INPUTS INPUTS V Improve VI Control VII Further and Beyond Param.(x): width NC Param.(x): operator C Param.(x): operator C Param.(x): operator C Backmatter 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 Book Presentation UCM 16/59
  • 18. Six Sigma With R (Springer, 2012) 4. Loss Funtion Analysis with R November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter W. Edwards Deming Mainmatter I Basics II Define Defects are not free. Somebody makes them, III Measure IV Analyze and gets paid for making them V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 17/59
  • 19. Six Sigma With R (Springer, 2012) A Loss Function Example November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e > ss . lfa ( ss . data . bolts , " diameter " , 0.5 , 10 , 0.001 , lfa . sub = " 10 mm . Bolts Project " , Frontmatter lfa . size = 100000 , lfa . output = " both " ) Mainmatter I Basics II Define $ lfa . k III Measure [1] 0.002 IV Analyze V Improve VI Control $ lfa . lf VII Further and Beyond expression ( bold ( L == 0.002 %. % ( Y - 10) ^2) ) Backmatter $ lfa . MSD [1] 0.03372065 $ lfa . avLoss [1] 6.74413 e -05 $ lfa . Loss [1] 6.74413 Book Presentation UCM 18/59
  • 20. Six Sigma With R (Springer, 2012) A Loss Function Example (cont.) November, 2012 Emilio L. Cano Javier M. Moguerza Loss Function Analysis Andr´s Redchuk e Frontmatter 5e−04 T Data Mainmatter I Basics 4e−04 CTQ: diameter II Define Y0 = 10 III Measure Cost of Poor Quality ∆ = 0.5 IV Analyze L0 = 0.001 3e−04 V Improve Size = 1e+05 VI Control VII Further and Beyond 2e−04 Backmatter Mean = 10.0308 k = 0.002 1e−04 MSD = 0.0337 LSL USL Av.Loss = 1e−04 Loss = 6.7441 0e+00 9.6 9.8 10.0 10.2 10.4 Observed Value L = 0.002 ⋅ (Y − 10) 2 10 mm. Bolts Project Book Presentation UCM 19/59
  • 21. Six Sigma With R (Springer, 2012) 5. Measurement System Analysis November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Lord Kelvin Mainmatter “If you cannot measure it, I Basics II Define you cannot improve it.” III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 20/59
  • 22. Six Sigma With R (Springer, 2012) Repeatability & Reproducibility November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics Repetible and Reproducible Repetible but non Reproducible Reproducible but non Repetible Non Repetible & Non Reproducible II Define q q III Measure qq q q q q q q q IV Analyze q q V Improve q qq q qq VI Control VII Further and Beyond q q q q q Backmatter Book Presentation UCM 21/59
  • 23. Six Sigma With R (Springer, 2012) MSA with R November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Six Sigma Gage R&R Study Components of Variation Var by Part 1.8 Frontmatter 80 q q q q q 1.6 60 q q Percent Mainmatter 1.4 var 40 q q q q q q 1.2 I Basics 20 q q q q q 1.0 q 0 II Define G.R&R Repeat Reprod Part2Part q prot #1 prot #2 prot #3 III Measure %Contribution %Study Var IV Analyze R Chart by appraiser Var by appraiser prot #1 prot #2 prot #3 V Improve 1.8 q q q op #1 op #2 op #3 0.5 q q q q q VI Control 1.6 0.4 q q q VII Further and Beyond q 1.4 var 0.3 q var q q q q q q q q 0.2 1.2 q q q q q Backmatter 0.1 q q q 1.0 q q 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 1.4 var 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 Book Presentation UCM 22/59
  • 24. Six Sigma With R (Springer, 2012) 6. Pareto Analysis with R November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Ovidio Mainmatter I Basics Causa latet: vis est notissima. [The cause is II Define III Measure hidden, but the result is known.] IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 23/59
  • 25. Six Sigma With R (Springer, 2012) Pareto Principle (80/20 rule) November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define Examples III Measure IV Analyze V Improve 20 % of customers make 80 % of incomes VI Control VII Further and Beyond 20 % of students get 80 % of good marks Backmatter 80 % of cost of quality is due to 20 % of the possible causes Book Presentation UCM 24/59
  • 26. Six Sigma With R (Springer, 2012) Cause-and-effect diagram November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Six Sigma Cause−and−effect Diagram Frontmatter Mainmatter I Basics Operator Environment Tools operator #1 height scissors II Define operator #2 cleaning tape III Measure operator #3 IV Analyze V Improve VI Control VII Further and Beyond Flight Time Backmatter paperclip model marks rotor.width2 calibrate thickness rotor.length Measure.Tool Raw.Material Design Paper Helicopter Project Book Presentation UCM 25/59
  • 27. Six Sigma With R (Springer, 2012) Pareto Chart November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Pareto Chart for b.vector q Frontmatter q q q q Mainmatter q 80% q 60 I Basics Cumulative Percentage q II Define q III Measure IV Analyze Frequency 40 V Improve q VI Control VII Further and Beyond Backmatter 20 q 0 Delays Materials Customer Training Rework Errors Rain Wind Permissions Inadequate Temperature Book Presentation UCM 26/59
  • 28. Six Sigma With R (Springer, 2012) 7. Process Capability Analysis November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Johann Wolfgang von Goethe Mainmatter One cannot develop taste from what is of I Basics II Define III Measure average quality but only from the very best. IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 27/59
  • 29. Six Sigma With R (Springer, 2012) Capability Analysis Output November, 2012 Emilio L. Cano Javier M. Moguerza Six Sigma Capability Analysis Study Andr´s Redchuk e Histogram & Density Density Lines Legend Frontmatter Target Density ST Theoretical Dens. ST Mainmatter Density LT Theoretical Density LT I Basics II Define III Measure LSL USL Specifications IV Analyze LSL: 740 Target: 750 V Improve USL: 760 VI Control VII Further and Beyond Backmatter Short Term Process Long Term 740 745 750 755 760 Mean: 749.7625 Mean: 753.7239 Check Normality SD: 2.1042 SD: 2.6958 n: 20 n: 40 Shapiro−Wilk Test Zs: 3.14 Zs: 2.33 q p−value: 0.07506 DPMO: 9952.5 q Short Term Indices Long Term qq Lilliefors (K−S) Test Cp: 1.5841 Pp: 1.2365 qq qqq p−value: 0.2291 CI: [1.4,1.7] CI: [1.1,1.3] qq qqq qq qq Cpk: 1.5465 Ppk: 0.7760 q q CI: [1.4,1.7] CI: [0.7,0.8] Normality accepted when p−value > 0.05 Winery Project Book Presentation UCM 28/59
  • 30. Six Sigma With R (Springer, 2012) 8. Charts with R November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e John Tukey Frontmatter Mainmatter “The greatest value of a picture is when it I Basics II Define forces us to notice what we never expected to III Measure IV Analyze see.” V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 29/59
  • 31. Six Sigma With R (Springer, 2012) Multi-vari chart November, 2012 Emilio L. Cano Multi−vari chart for Volume by color and operator Javier M. Moguerza Andr´s Redchuk e batch 1 q 2 q 3 q 4 q 1 2 3 Frontmatter 3 3 Mainmatter B C I Basics 18 II Define 17 III Measure 16 q q q q q q q q q IV Analyze 15 q q q q q q q q q q q q q q V Improve 14 VI Control 2 2 VII Further and Beyond B C q q 18 q Backmatter Volume q q 17 q q q q q q q 16 q q q q q q q q 15 q q q 14 1 1 B C q 18 q q q 17 q q q q q q 16 q q q q q q q 15 q q q q 14 q 1 2 3 Filler Book Presentation UCM 30/59
  • 32. Six Sigma With R (Springer, 2012) 9. Statistics and Probability with R November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter Aaron Levenstein I Basics II Define “Statistics are like bikinis. What they reveal is III Measure IV Analyze V Improve suggestive, but what they conceal is vital.” VI Control VII Further and Beyond Backmatter Book Presentation UCM 31/59
  • 33. Six Sigma With R (Springer, 2012) Distributions November, 2012 Emilio L. Cano Hypergeometric Geometric Negative Binomial Poison Javier M. Moguerza Probability Probability Probability Probability 0.06 0.15 0.00 0.10 Andr´s Redchuk e 0.3 0.00 0.00 0.0 Frontmatter 0 1 2 3 4 0 10 30 10 20 30 40 0 5 10 20 Elements in class A Items extracted until first success Number of trials until 3 events Number of successful experiments per unit Mainmatter I Basics Exponential Lognormal Uniform Gamma Probability Density Probability Density Probability Density Probability Density II Define 0.0 0.4 0.8 0.0 0.6 1.2 0.0 0.2 0.4 III Measure 0.6 IV Analyze 0.0 V Improve 0 1 2 3 4 5 0 2 4 6 −0.5 0.5 1.5 0 2 4 6 8 VI Control Random Variable X Random Variable X>0 Random Variable X Random Variable X VII Further and Beyond Backmatter Beta Weibul t−Student Chi−squared Probability Density Probability Density Probability Density Probability Density 0.0 1.0 2.0 0.0 0.3 0.6 0.06 0.3 95% 5% 95% 5% 0.00 0.0 1.73 30.14 0.0 0.4 0.8 0 2 4 6 −4 0 2 4 10 30 50 Random Variable X Random Variable X Random Variable X Random Variable X F Probability Density 0.6 95% 5% 0.0 2.34 0 1 2 3 4 Random Variable X Book Presentation UCM 32/59
  • 34. Six Sigma With R (Springer, 2012) 10. Statistical Inference with R November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e George E.P. Box Frontmatter Mainmatter “All models are wrong; some models are I Basics II Define useful.” III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 33/59
  • 35. Six Sigma With R (Springer, 2012) Confidence Interval Example November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Confidence Interval for the Mean Frontmatter Mean: 950.016 95% CI: [949.967, 950.064] Mainmatter StdDev: 0.267 P−Var: unknown I Basics n: 120 t: 1.98 II Define Missing: 0 III Measure IV Analyze V Improve VI Control Histogram & Density Plot Shapiro−Wilks 1.5 VII Further and Beyond Normality Test Backmatter 0.985 p−value: 0.19 1.0 density Normal q−q Plot 0.5 q qq q qq qq qq q qq q qq qq qq qq qq qq qq qq qq qq qq qq qq qq q q qq qq qq qq qq qq qq q 0.0 qq qq qqqq qq qq qq q qq qq qq qq q qq qq qq 949.0 949.5 950.0 950.5 q q q q Value of len q qq Book Presentation UCM 34/59
  • 36. Six Sigma With R (Springer, 2012) 11. Design of Experiments with R November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter R.A. Fisher Mainmatter “Sometimes the only thing you can I Basics II Define do with a poorly designed III Measure IV Analyze V Improve experiment is to try to find out what VI Control VII Further and Beyond it died of” Backmatter Book Presentation UCM 35/59
  • 37. Six Sigma With R (Springer, 2012) The Importance of Experimenting November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter “An engineer who does not know Mainmatter experimental design is not an I Basics II Define III Measure engineer” IV Analyze V Improve VI Control VII Further and Beyond Backmatter Comment made by to one of the authors [of “Statistics for experimenters” by an ] executive of the Toyota Motor Company. Book Presentation UCM 36/59
  • 38. Six Sigma With R (Springer, 2012) 12.Process Control with R November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter Walter A. Shewhart I Basics II Define “Special causes of variation may be found and III Measure IV Analyze eliminated.” V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 37/59
  • 39. Six Sigma With R (Springer, 2012) Control Chart Plotting November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e p Chart for stockouts 0.25 Frontmatter q q UCL Mainmatter q q 0.20 I Basics Group summary statistics II Define q III Measure 0.15 q q q q IV Analyze q V Improve q q VI Control 0.10 q q CL q VII Further and Beyond q q Backmatter q q 0.05 q q q q LCL 0.00 1 3 5 7 9 11 13 15 17 19 21 Group Number of groups = 22 Center = 0.1212294 LCL is variable Number beyond limits = 1 StdDev = 0.3263936 UCL is variable Number violating runs = 0 Book Presentation UCM 38/59
  • 40. Six Sigma With R (Springer, 2012) 13. Other Tools and November, 2012 Emilio L. Cano Javier M. Moguerza Methodologies Andr´s Redchuk e Frontmatter Mainmatter Johann Wolfgang von Goethe I Basics II Define Instruction does much, but encouragement III Measure IV Analyze V Improve everything. VI Control VII Further and Beyond Backmatter Book Presentation UCM 39/59
  • 41. Six Sigma With R (Springer, 2012) Other topics November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics Failure Mode, Effects, and Criticality II Define III Measure Analysis IV Analyze V Improve VI Control Design for Six Sigma VII Further and Beyond Backmatter Lean Gantt Chart Some Advanced R Topics Book Presentation UCM 40/59
  • 42. Six Sigma With R (Springer, 2012) Contents November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e 1 Frontmatter Frontmatter Mainmatter 2 Mainmatter I Basics II Define I Basics III Measure IV Analyze V Improve II Define VI Control VII Further and Beyond III Measure Backmatter IV Analyze V Improve VI Control VII Further and Beyond 3 Backmatter Book Presentation UCM 41/59
  • 43. Six Sigma With R (Springer, 2012) Case Study November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 42/59
  • 44. Six Sigma With R (Springer, 2012) Helicopter Template November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter > ss . heli () null device 1 > # vignette (" H e l i c o p t e r I n s t r u c t i o n s ") to get instructions Book Presentation UCM 43/59
  • 45. Six Sigma with R | Paper Helicopter template max (9.5cm) std (8cm) min (6.5cm) ← wings length → cut ? pe fold ↑ fold ↓ ta cut 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)
  • 46. Six Sigma With R (Springer, 2012) Enjoy the Case Study! November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 45/59
  • 47. Six Sigma With R (Springer, 2012) Enjoy the Case Study! November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 45/59
  • 48. Six Sigma With R (Springer, 2012) So what? November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 46/59
  • 49. Six Sigma With R (Springer, 2012) So what? November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e The Scientific Method Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 46/59
  • 50. Six Sigma With R (Springer, 2012) The Scientific Method and Six November, 2012 Emilio L. Cano Javier M. Moguerza Sigma Andr´s Redchuk e Frontmatter Mainmatter DMAIC Cycle Scientific Method I Basics II Define Ask a question III Measure Define IV Analyze V Improve Do some background VI Control Measure research VII Further and Beyond Backmatter Construct a hypothesis Analyze Test the hypothesis with an experiment Improve Analyze the data and draw conclusions Control Communicate results Book Presentation UCM 47/59
  • 51. Six Sigma With R (Springer, 2012) The Key to Success November, 2012 Emilio L. Cano Javier M. Moguerza “Six Sigma speaks the language of business” Andr´s Redchuk e Frontmatter ISO 13053-1:2011 Mainmatter I Basics II Define III Measure IV Analyze Six Sigma methodology is a quality paradigm V Improve VI Control that translates the involved scientific VII Further and Beyond Backmatter methodology into a simple way to apply the scientific method within every organization. Book Presentation UCM 48/59
  • 52. Six Sigma With R (Springer, 2012) Opportunities November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter For Today’s Graduate, Just One Word: Statistics Mainmatter (The New York Times, August 2009) I Basics II Define “I keep saying that the sexy job in the III Measure IV Analyze next 10 years will be statisticians” V Improve VI Control VII Further and Beyond Backmatter Data Scientist: The Sexiest Job of the 21st Century (Harvard Business Review, October 2012) . . . the “data scientist.” It’s a high-ranking professional with the training and curiosity to make discoveries in the world of big data . . . Book Presentation UCM 49/59
  • 53. Six Sigma With R (Springer, 2012) Opportunities (cont.) November, 2012 Emilio L. Cano Gartner Sees 4.4M Big Data Jobs by 2015 Javier M. Moguerza Andr´s Redchuk e (Information Management, October 2012) Frontmatter Lack of data scientists could derail big data Mainmatter I Basics projects: IBM (CIO, October 2012) II Define III Measure IV Analyze Son las matem´ticas, est´pido (El Pa´ a u ıs, V Improve VI Control Noviembre 2012) VII Further and Beyond Backmatter La econom´ del conocimiento exige ıa una educaci´n sustentada en tres o fundamentos: un nivel avanzado en matem´tica y estad´ a ıstica, una capacidad elevada para escribir un argumento y un nivel avanzado de ingl´s e Book Presentation UCM 50/59
  • 54. Six Sigma With R (Springer, 2012) R Final Remarks November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond kdnuggets.com Backmatter (2012) link Book Presentation UCM 51/59
  • 55. Six Sigma With R (Springer, 2012) R Final Remarks (cont.) November, 2012 Emilio L. Cano Javier M. Moguerza Community Andr´s Redchuk e 4131 packages at CRAN (18/11/2012) Frontmatter Mainmatter Task views I Basics II Define III Measure Manuals IV Analyze V Improve Publications VI Control VII Further and Beyond Backmatter http: //cran.r-project.org/web/packages/ Book Presentation UCM 52/59
  • 56. Six Sigma With R (Springer, 2012) R Final Remarks (cont.) November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Customization A company can develop a package that fits its Frontmatter Mainmatter inner procedures and methods. I Basics II Define III Measure IV Analyze V Improve Innovation VI Control VII Further and Beyond A company can develop and deploy an Backmatter innovative method from its R&D department, or from the result of other published researches. Book Presentation UCM 53/59
  • 57. Six Sigma With R (Springer, 2012) R Final Remarks (cont.) November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Business Mainmatter I Basics http: II Define III Measure //www.revolutionanalytics.com/ IV Analyze V Improve VI Control http://www.openanalytics.eu/ VII Further and Beyond Backmatter http://www.fellstat.com/ http://www.rstudio.com/ide/ http://www.datanalytics.com/ ... Book Presentation UCM 54/59
  • 58. Six Sigma With R (Springer, 2012) R Final Remarks (cont.) November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics GUI, IDE II Define III Measure RStudio IV Analyze V Improve VI Control Eclipse + StatET VII Further and Beyond Backmatter EMACS + EES Deducer ... Book Presentation UCM 55/59
  • 59. Six Sigma With R (Springer, 2012) R Final Remarks (cont.) November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter Book Presentation UCM 56/59
  • 60. Six Sigma With R (Springer, 2012) November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter http://r-es.org/ Book Presentation UCM 57/59
  • 61. Six Sigma With R (Springer, 2012) November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter http://www.r-project.org/useR-2013 Book Presentation UCM 58/59
  • 62. Six Sigma With R (Springer, 2012) Discussion November, 2012 Emilio L. Cano Javier M. Moguerza Andr´s Redchuk e Thanks ! Frontmatter Mainmatter I Basics II Define III Measure IV Analyze V Improve VI Control VII Further and Beyond Backmatter emilio.lopez@urjc.es @emilopezcano http://www.sixsigmawithr.com Book Presentation UCM 59/59