Six Sigma with R: A Guide to Implementation, Process Improvement, and Problem Solving
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This document discusses using R software to support Six Sigma methodology. It introduces reproducible research approaches for statistical training, provides examples using Sweave documents to integrate R code and LaTeX, and outlines an EADAPU training program covering Six Sigma phases and tools. The document also describes using R for process mapping, loss function analysis, and measurement system analysis for quality improvement projects.
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Six Sigma with R: A Guide to Implementation, Process Improvement, and Problem Solving
- 1. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Seis Sigma con R Emilio L. Cano Departamento de Estad´ıstica e Investigaci´on Operativa Universidad Rey Juan Carlos (Madrid) December 5, 2012 E.T.S. Ingenieros Industriales Universidad de Castilla-La Mancha Seminario EIO UCLM 1/66
- 2. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Contents 1 Statistical Training Approaches Examples Application 2 Six Sigma with R Six Sigma R Packages Seminario EIO UCLM 2/66
- 3. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Elements of Statistical Training Seminario EIO UCLM 3/66
- 4. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Copy-paste Approach Inconsistencies Errors Out-of-date non-reproducible Painful changes Seminario EIO UCLM 4/66
- 5. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Reproducible Research Approach Reproducible Research The goal of reproducible research is to tie specific instructions to data analysis and experimental data so that scholarship can be recreated, better understood and verified Literate Programming Literate programming is a methodology that combines a programming language with a documentation language Seminario EIO UCLM 5/66
- 6. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Reproducible Research Workflow Seminario EIO UCLM 6/66
- 7. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Sweave Documents Sweave A Sweave document is a plain-text file which merges LATEX code and R code. The R function Sweave() converts the Sweave document (*.Rnw) into a LATEX file (*.tex). The code chunks are executed and the results embedded into the LATEX file. Seminario EIO UCLM 7/66
- 8. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Sweave Example documentclass [a4paper ]{ article} usepackage{Sweave} title{Design of Experiments} author{EL Cano and JM Moguerza and A Rechuk} begin{document} maketitle section{ Introduction } Design of experiments is the most important took in the I DMAIC cycle ldots. <<>>= library(SixSigma) doe.model1 <- lm(score ~ flour + salt + bakPow + flour * salt + flour * bakPow + salt * bakPow + flour * salt * bakPow , data = ss.data.doe1) summary(doe.model1) @ This is the general model: begin{equation} label{eq:doe:model} y_{ijkl }=mu+ alpha_i + beta_j + gamma_k +( alphabeta)_{ij} ( alphagamma)_{ik }+( betagamma)_{kl }+( alphabetagamma Seminario EIO UCLM 8/66
- 9. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Sweave Example (cont.) varepsilon_{ijkl}, end{equation} And here we have a plot of effects: <<maineff , echo=FALSE , fig=TRUE >>= plot(c(-1, 1), ylim = range(ss.data.doe1$score), coef(doe.model1 )[1] + c(-1, 1) * coef(doe type ="b", pch =16) abline(h=coef(doe.model1 )[1]) @ %input{section2} end{document} Seminario EIO UCLM 9/66
- 10. Design of Experiments EL Cano and JM Moguerza and A Rechuk April 10, 2012 1 Introduction Design of experiments is the most important took in the Improve phase of the DMAIC cycle . . . . > library(SixSigma) > doe.model1 <- lm(score ~ flour + salt + bakPow + + flour * salt + flour * bakPow + + salt * bakPow + flour * salt * bakPow, + data = ss.data.doe1) > summary(doe.model1) Call: lm(formula = score ~ flour + salt + bakPow + flour * salt + flour * bakPow + salt * bakPow + flour * salt * bakPow, data = ss.data.doe1) Residuals: Min 1Q Median 3Q Max -0.5900 -0.2888 0.0000 0.2888 0.5900 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 5.5150 0.3434 16.061 2.27e-07 *** flour+ 1.8350 0.4856 3.779 0.005398 ** salt+ -0.8350 0.4856 -1.719 0.123843 bakPow+ -2.9900 0.4856 -6.157 0.000272 *** flour+:salt+ 0.1700 0.6868 0.248 0.810725 flour+:bakPow+ 0.8000 0.6868 1.165 0.277620 salt+:bakPow+ 1.1800 0.6868 1.718 0.124081 flour+:salt+:bakPow+ 0.5350 0.9712 0.551 0.596779 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.4856 on 8 degrees of freedom Multiple R-squared: 0.9565, Adjusted R-squared: 0.9185 F-statistic: 25.15 on 7 and 8 DF, p-value: 7.666e-05 This is the general model: yijkl = µ + αi + βj + γk + (αβ)ij + (αγ)ik + (βγ)kl + (αβγ)ijk + εijkl, (1) 1
- 11. And here we have a plot of effects: q q −1.0 −0.5 0.0 0.5 1.0 34567 c(−1, 1) coef(doe.model1)[1]+c(−1,1)*coef(doe.model1)[2] 2
- 12. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Project Example Strategies Partial Sweave files can be compiled to get partial LATEX files. R scripts can Sweave .Rnw files and“source”.R files. The final document is obtained by compiling the“master” LATEX file. > source("code/myoptions.R") > source("code/myfunctions.R") > source("code/mydata.R") > Sweave("rnw/theorem01.Rnw") > Sweave("rnw/lesson01.Rnw") > Sweave("rnw/exercises01.Rnw") > ... > texi2pdf("master.tex")Seminario EIO UCLM 12/66
- 13. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages EADAPU Seminario EIO UCLM 13/66
- 14. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages EADAPU - Programa Sesi´on 1 (4 horas) 1 Introducci´on a la Metodolog´ıa Seis Sigma.a 2 Herramientas de la fase de definici´on. 3 Herramientas de la fase de medida. a Incluye introducci´on a RStudio Seminario EIO UCLM 14/66
- 15. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages EADAPU - Programa (cont.) Sesi´on 2 (4 horas) 1 La importancia de experimentar. 2 Introducci´on al dise˜no de experimentos. 3 Dise˜no de experimentos como herramienta de mejora. 4 Dise˜no robusto. 5 Dise˜nos avanzados. Seminario EIO UCLM 15/66
- 16. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Contents 1 Statistical Training Approaches Examples Application 2 Six Sigma with R Six Sigma R Packages Seminario EIO UCLM 16/66
- 17. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Publisher http://www.springer.com/statistics/book/978-1-4614-3651-5 Seminario EIO UCLM 17/66
- 18. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Book website http://www.sixsigmawithr.com/ Seminario EIO UCLM 18/66
- 19. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages R Package http://cran.r-project.org/web/packages/SixSigma/index.html Seminario EIO UCLM 19/66
- 20. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Contents Foreword (Thanks David R´ıos) Preface Part I: Basics Part II: R Tools for the Define Phase Part III: R Tools for the Measure Phase Part IV: R Tools for the Analyze Phase Part V: R Tools for the Improve Phase Part VI: R Tools for the Control Phase Part VII: Further and Beyond Seminario EIO UCLM 20/66
- 21. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages 1. Six Sigma in a Nutshell Herbert Spencer “Science is organised knowledge” Seminario EIO UCLM 21/66
- 22. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages 2. R from the Beginning Linus Torvalds “Software is like sex; it’s better when it’s free” Seminario EIO UCLM 22/66
- 23. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages 3. Process Mapping with R Charles Franklin Kettering “A problem well stated is a problem half solved” Seminario EIO UCLM 23/66
- 24. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages A Process Map Six Sigma Process Map Paper Helicopter Project INPUTS X operators tools raw material facilities INSPECTION INPUTS sheets ... Param.(x):width NC operator C Measure pattern P discard P Featur.(y):ok ASSEMBLY INPUTS sheets Param.(x):operator C cut P fix P rotor.width C rotor.length C paperclip C tape C Featur.(y):weight TEST INPUTS helicopter Param.(x):operator C throw P discard P environment N Featur.(y):time LABELING INPUTS helicopter Param.(x):operator C label P Featur.(y):label OUTPUTS Y helicopterLEGEND (C)ontrollable (Cr)itical (N)oise (P)rocedure Seminario EIO UCLM 24/66
- 25. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages 4. Loss Funtion Analysis with R W. Edwards Deming Defects are not free. Somebody makes them, and gets paid for making them Seminario EIO UCLM 25/66
- 26. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages A Loss Function Example Loss Function Analysis 10 mm. Bolts Project 0e+00 1e−04 2e−04 3e−04 4e−04 5e−04 LSL USL T 9.6 9.8 10.0 10.2 10.4 Observed Value CostofPoorQuality L = 0.002 ⋅ (Y − 10)2 Data CTQ: diameter Y0 = 10 ∆ = 0.5 L0 = 0.001 Size = 1e+05 Mean = 10.0308 k = 0.002 MSD = 0.0337 Av.Loss = 1e−04 Loss = 6.7441 Seminario EIO UCLM 26/66
- 27. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages 5. Measurement System Analysis Lord Kelvin “If you cannot measure it, you cannot improve it.” Seminario EIO UCLM 27/66
- 28. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages MSA with R Six Sigma Gage R&R Study Helicopter Project Components of Variation Percent 0 20 40 60 80 G.R&R Repeat Reprod Part2Part %Contribution %Study Var Var by Part var 1.0 1.2 1.4 1.6 1.8 prot #1 prot #2 prot #3 q q q q q q q q q qq q q q q qq q q q q q qq q q q Var by appraiser var 1.0 1.2 1.4 1.6 1.8 op #1 op #2 op #3 q q q q q q q q q qq q q q q qq q q q q q qq q q q Part*appraiser Interaction var 1.1 1.2 1.3 1.4 1.5 1.6 1.7 prot #1 prot #2 prot #3 q q q q q q q q q op #1 op #2 op #3 x Chart by appraiser part var 1.1 1.2 1.3 1.4 1.5 1.6 1.7 prot #1 prot #2 prot #3 q q q op #1 prot #1 prot #2 prot #3 q q q op #2 prot #1 prot #2 prot #3 q q q op #3 R Chart by appraiser part var 0.1 0.2 0.3 0.4 0.5 prot #1 prot #2 prot #3 q q q op #1 prot #1 prot #2 prot #3 q q q op #2 prot #1 prot #2 prot #3 q q q op #3 Seminario EIO UCLM 28/66
- 29. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages 6. Pareto Analysis with R Ovidio Causa latet: vis est notissima. [The cause is hidden, but the result is known.] Seminario EIO UCLM 29/66
- 30. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Cause-and-effect diagram Six Sigma Cause−and−effect Diagram Paper Helicopter Project Flight Time Operator operator #1 operator #2 operator #3 Environment height cleaning Tools scissors tape Design rotor.length rotor.width2 paperclip Raw.Material thickness marks Measure.Tool calibrate model Seminario EIO UCLM 30/66
- 31. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Pareto Chart Delays Materials Customer Training Rework Errors Rain Wind Permissions Inadequate Temperature Pareto Chart for b.vector Frequency 0204060 q q q q q q q q q q q 80% CumulativePercentage Seminario EIO UCLM 31/66
- 32. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages 7. Process Capability Analysis Johann Wolfgang von Goethe One cannot develop taste from what is of average quality but only from the very best. Seminario EIO UCLM 32/66
- 33. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Capability Analysis Output Six Sigma Capability Analysis Study Winery Project Histogram & Density LSL Target USL 740 745 750 755 760 Check Normality q q q q qq qqq qq qqqqq q q q q Shapiro−Wilk Test p−value: 0.07506 Lilliefors (K−S) Test p−value: 0.2291 Normality accepted when p−value > 0.05 Density Lines Legend Density ST Theoretical Dens. ST Density LT Theoretical Density LT Specifications LSL: 740 Target: 750 USL: 760 ProcessShort Term Mean: 749.7625 SD: 2.1042 n: 20 Zs: 3.14 Long Term Mean: 753.7239 SD: 2.6958 n: 40 Zs: 2.33 DPMO: 9952.5 IndicesShort Term Cp: 1.5841 CI: [1.4,1.7] Cpk: 1.5465 CI: [1.4,1.7] Long Term Pp: 1.2365 CI: [1.1,1.3] Ppk: 0.7760 CI: [0.7,0.8] Seminario EIO UCLM 33/66
- 34. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages 8. Charts with R John Tukey “The greatest value of a picture is when it forces us to notice what we never expected to see.” Seminario EIO UCLM 34/66
- 35. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Multi-vari chart Multi−vari chart for Volume by color and operator Filler Volume 14 15 16 17 18 1 2 3 q q q q q q q q q q q q B 1 q q qq q q q q q q q q C 1 q q q q q q q q q q q q B 2 14 15 16 17 18 q q q q q qq q q q q q C 2 14 15 16 17 18 q q q q q qq q q q q q B 3 1 2 3 q q q q q q q q q q q q C 3 batch 1 2 3 4q q q q Seminario EIO UCLM 35/66
- 36. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages 9. Statistics and Probability with R Aaron Levenstein “Statistics are like bikinis. What they reveal is suggestive, but what they conceal is vital.” Seminario EIO UCLM 36/66
- 37. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Distributions 0 1 2 3 4 0.00.3 Hypergeometric Elements in class A Probability 0 10 30 0.000.10 Geometric Items extracted until first success Probability 10 20 30 40 0.000.06 Negative Binomial Number of trials until 3 events Probability 0 5 10 20 0.000.15 Poison Number of successful experiments per unit Probability 0 1 2 3 4 5 0.00.6 Exponential Random Variable X ProbabilityDensity 0 2 4 6 0.00.40.8 Lognormal Random Variable X>0 ProbabilityDensity −0.5 0.5 1.5 0.00.61.2 Uniform Random Variable X ProbabilityDensity 0 2 4 6 8 0.00.20.4 Gamma Random Variable X ProbabilityDensity 0.0 0.4 0.8 0.01.02.0 Beta Random Variable X ProbabilityDensity 0 2 4 6 0.00.30.6 Weibul Random Variable X ProbabilityDensity −4 0 2 4 0.00.3 t−Student Random Variable X ProbabilityDensity 1.73 95% 5% 10 30 50 0.000.06 Chi−squared Random Variable X ProbabilityDensity 30.14 95% 5% 0 1 2 3 4 0.00.6 F Random Variable X ProbabilityDensity 2.34 95% 5% Seminario EIO UCLM 37/66
- 38. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages 10. Statistical Inference with R George E.P. Box “All models are wrong; some models are useful.” Seminario EIO UCLM 38/66
- 39. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Confidence Interval Example Confidence Interval for the Mean Mean: StdDev: n: Missing: 950.016 0.267 120 0 95% CI: P−Var: t: [949.967, 950.064] unknown 1.98 Shapiro−Wilks Normality Test 0.985 p−value: 0.19 q qq q qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqq q Normal q−q Plot 0.0 0.5 1.0 1.5 949.0 949.5 950.0 950.5 Value of len density Histogram & Density Plot Seminario EIO UCLM 39/66
- 40. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages 11. Design of Experiments with R R.A. Fisher “Sometimes the only thing you can do with a poorly designed experiment is to try to find out what it died of” Seminario EIO UCLM 40/66
- 41. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages The Importance of Experimenting “An engineer who does not know experimental design is not an engineer” Comment made by to one of the authors [of“Statistics for experimenters”] by an executive of the Toyota Motor Company. Seminario EIO UCLM 41/66
- 42. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages 12.Process Control with R Walter A. Shewhart “Special causes of variation may be found and eliminated.” Seminario EIO UCLM 42/66
- 43. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Control Chart Plotting p Chart for stockouts Group Groupsummarystatistics 1 3 5 7 9 11 13 15 17 19 21 0.000.050.100.150.200.25 q q q q q q q q q q q q q q q q q q q q q q LCL UCL CL q Number of groups = 22 Center = 0.1212294 StdDev = 0.3263936 LCL is variable UCL is variable Number beyond limits = 1 Number violating runs = 0 Seminario EIO UCLM 43/66
- 44. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages 13. Other Tools and Methodologies Johann Wolfgang von Goethe Instruction does much, but encouragement everything. Seminario EIO UCLM 44/66
- 45. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Other topics Failure Mode, Effects, and Criticality Analysis Design for Six Sigma Lean Gantt Chart Some Advanced R Topics Seminario EIO UCLM 45/66
- 46. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Case Study Seminario EIO UCLM 46/66
- 47. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Helicopter Template > ss.heli() null device 1 > #vignette("HelicopterInstructions") t Seminario EIO UCLM 47/66
- 48. Six Sigma with R | Paper Helicopter template cut fold ↑ fold ↓ tape? cut fold↓↓ cut fold↑↑ cuttape? tape? clip? min (6.5cm) std (8cm) max (9.5cm) ←bodylength→ ← body width →min (4cm) min (4cm) max (6cm) max (6cm) min (6.5cm) std (8cm) max (9.5cm) ←wingslength→
- 49. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Enjoy the Case Study! Seminario EIO UCLM 49/66
- 50. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Enjoy the Case Study! Seminario EIO UCLM 49/66
- 51. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Book Production Reproducible Research Written applying reproducible research techniques. All figures (except screen captures) are generated while compiling the book using R code. Seminario EIO UCLM 50/66
- 52. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages The DMAIC Cycle Seminario EIO UCLM 51/66
- 53. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Six Sigma Roles In Six Sigma, everyone in the organization has a role in the project. Six Sigma methodology uses an intuitive categorization of these roles. Seminario EIO UCLM 52/66
- 54. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Six Sigma Roles In Six Sigma, everyone in the organization has a role in the project. Six Sigma methodology uses an intuitive categorization of these roles. Seminario EIO UCLM 52/66
- 55. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Why 6 and why Sigma Sigma refers to the Z-Score of the process: Z = min (USL − x) σ , (x − LSL) σ ; ZLT = ZST −1,5. CTQ Frequency Short Term Long Term 1.5σ 4.5σ > (1-pnorm(4.5))*(10^6) [1] 3.397673 DPMO Seminario EIO UCLM 53/66
- 56. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages So what? Seminario EIO UCLM 54/66
- 57. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages So what? The Scientific Method Seminario EIO UCLM 54/66
- 58. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages The Scientific Method and Six Sigma Define Ask a question Measure Analyze Improve Control Do some background research Construct a hypothesis Test the hypothesis with an experiment Analyze the data and draw conclusions Communicate results DMAIC Cycle Scientific Method Seminario EIO UCLM 55/66
- 59. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages The Key to Success “Six Sigma speaks the language of business” ISO 13053-1:2011 Six Sigma methodology is a quality paradigm that translates the involved scientific methodology into a simple way to apply the scientific method within every organization. Seminario EIO UCLM 56/66
- 60. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages The R Project http://www.r-project.org Seminario EIO UCLM 57/66
- 61. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages The R Environment Seminario EIO UCLM 58/66
- 62. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Reproducible Research knitr, pgfSweave: enhanced options for Sweave exams: Automatic generation of printable exams odfWeave: Open Document format documents generation More in the“Reproducible Research”Task View at CRAN. http://cran.r-project.org/web/views/ ReproducibleResearch.html Seminario EIO UCLM 59/66
- 63. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Package RGIFT Open format GIFT Integration with Moodle Automatic correction http://cran.r-project.org/web/ packages/RGIFT/ Seminario EIO UCLM 60/66
- 64. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Community Community 4131 packages at CRAN (18/11/2012)a Bioconductor, R-forge, Github, Omegahat. Task views Manuals Publications http: //cran.r-project.org/web/packages/ a 4181 04/12 Seminario EIO UCLM 61/66
- 65. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages R Interfaces GUI, IDE RStudio Eclipse + StatET EMACS + EES Deducer . . . Seminario EIO UCLM 62/66
- 66. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages R Interfaces (cont.) Seminario EIO UCLM 63/66
- 67. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages http://r-es.org/ Seminario EIO UCLM 64/66
- 68. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages http://www.r-project.org/useR-2013 Seminario EIO UCLM 65/66
- 69. Seis Sigma con R December, 2012 Emilio L. Cano Statistical Training Approaches Examples Application Six Sigma with R Six Sigma R Packages Discussion Thanks ! emilio.lopez@urjc.es @emilopezcano http://www.sixsigmawithr.com Seminario EIO UCLM 66/66