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Six Sigma with R

The document outlines the book 'Six Sigma with R,' covering key concepts and methodologies for statistical engineering in process improvement, including the DMAIC cycle and role categorization. It includes practical applications using the R programming language, discussing topics such as measurement system analysis, process capability analysis, and Pareto analysis. Additionally, the book provides resources and links for further exploration, including a dedicated website and available R package.

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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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 withR | 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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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 WithR (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