Chapter 8 Making Sense of Data in Six Sigma and Lean

1. Chapter 8Making Sense of Data inSix Sigma and Lean

2. How to tell “story” from dataset?Quantitative Data • Graphical Methods • Dot Plots • Stem-and-Leaf Plots • Frequency Tables • Histograms and Performance Histograms • Run Charts • Time-Series Plots • Numerical Methods: Descriptive Statistics

3. How to tell “story” from dataset?Qualitative Data • Pie Charts • Bar Charts • Pareto Analysis with Lorenz Curve

4. How to tell “story” from dataset?Bivarite Data • Graphical Methods • Scatter Plots • Numerical Methods: Correlation Coefficient • Pearson Coefficient • Spearman’s Rho () • Kendall’s Tau () Rank Correlation

5. How to tell “story” from dataset?Multi-Vari Data • Graphical Methods • Multi-Vari Charts

6. Summarizing Quantitative Data:Dot Plots • Dot plot is one of the most simple types of plots Example 8.1 Minitab Graph Dotplot Simple

7. Summarizing Quantitative Data:Stem-and-Leaf Plots • Stem-and-Leaf Plots are a method for showing the frequency with which certain classes of values occur. i160.photobucket.com/.../treediagram.png

8. Summarizing Quantitative Data:Frequency Tables • constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies. • Absolute frequencies or relative frequencies (%) www.sci.sdsu.edu/.../Weeks/images/Frequency.png

9. Summarizing Quantitative Data: Histogram www.statcan.gc.ca/.../ch9/images/histo1.gif

10. Summarizing Quantitative Data:Run Charts • A line graph of data points plotted in chronological order that helps detect special causes of variation Minitab Graph Time Series Plot Simple

11. Summarizing Quantitative Data: Time-Series Plots • A time series plot is a graph showing a set of observations taken at different points in time and charted in a time series. Minitab Graph Time Series Plot Simple

12. Summarizing Quantitative Data:Descriptive Statistics Measures of Center • Sample mean • Population mean • Median: the "middle" value in the dataset • Mode: the value that occurs most often

13. Summarizing Quantitative Data:Descriptive Statistics Measures of Variation • Range: the difference between the largest and the smallest values in the dataset • Sample variance • Sample standard deviation • Population variance • Population standard deviation

14. Summarizing Quantitative Data:Descriptive Statistics Measures of Variation • Coefficient of Variation (CV) • Interquartile Range (IQR)

15. Summarizing Quantitative Data:Descriptive Statistics • Minimum • Maximum • Median • First Quartile • Third Quartile • Minitab: • Stat • Basic Statistics • Display Descriptive.. • Boxplot

16. Summarizing Quantitative Data:Descriptive Statistics Identifying Potential Outliers • Lower inner fence (LIF) = • Upper inner fence (UIF) = • Lower outer fence (LOF) = • Upper outer fence (UOF) = • Mild outliers: data fall between the two lower fences and between the two upper fences • Extreme outliers: data fall below the LOF or above the UOF

17. Summarizing Quantitative Data:Descriptive Statistics Measures of Positions • Percentiles • Percentiles divide the dataset into 100 equal parts • Percentiles measure position from the bottom • Percentiles are most often used for determining the relative standing of an individual in a population or the rank position of the individual. • z scores • Standard normal distribution ( = 0 and  = 1)

18. Summarizing Qualitative Data:Graphical Displays • Pie Chart http://techie-teacher-wanna-be.wikispaces.com/file/view/SocialPieChart.png/96606670/SocialPieChart.png

19. Summarizing Qualitative Data:Graphical Displays • Bar Graph www.creationfactor.net/images/graph-bar.jpg

20. Summarizing Qualitative Data:Graphical Displays • Pareto Analysis with Lorenz Curve www.spcforexcel.com/files/images/ccpareto.gif

21. Summarizing Bivariate Data:Scatterplot Minitab: Graph Scatterplot Simple

22. Summarizing Bivariate Data:Correlation Coefficient • Pearson Correlation Coefficient Minitab: Stat Regression Regression

23. Summarizing Bivariate Data:Correlation Coefficient • Spearman’s Rho () • A measure of the linear relationship between two variables. • It differs from Pearson's correlation only in that the computations are done after the numbers are converted to ranks. • When converting to ranks, the smallest value on X becomes a rank of 1, etc. • D (Difference) is calculated between the pair of ranks

24. Summarizing Bivariate Data:Correlation Coefficient • Spearman’s Rho () Example

25. Summarizing Bivariate Data:Correlation Coefficient • Kendall’s Tau () • A measure of the linear relationship between two variables. • It differs from Pearson's correlation only in that the computations are done after the numbers are converted to ranks. • When converting to ranks, the smallest value on X becomes a rank of 1, etc. • P is # of pairs with both ranks higher

26. Summarizing Bivariate Data:Correlation Coefficient • Kendall’s Tau () Example • Example

27. Summarizing Multi-Vari Data: Multi-Vari Charts • Show patterns of variation from several possible causes on a single chart, or set of charts • Obtains a first look at the process stability over time. Can be constructed in various ways to get the “best view”. • Positional: variation within a part or process • Cyclical: variation between consecutive parts or process steps • Temporal: Time variability

28. Graphical Tool: Multi-Vari Charts Cus. Size: 1 = small 2 = large Product: 1 = Consumer 2 = Manuf. Cus. Type: 1 = Gov’t 2 = Commercial 3 = Education http://www.qimacros.com/qiwizard/multivari-chart.html

29. Graphical Tool: Multi-Vari Charts Minitab: Stat Quality Tools Multi Vari Chart