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Chapter 8 Making Sense of Data in Six Sigma and Lean

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Title: Chapter 8 Making Sense of Data in Six Sigma and Lean


1
Chapter 8 Making Sense of Data in Six 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
  • Spearmans Rho (?)
  • Kendalls 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.p
ng
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
  • Spearmans 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
  • Spearmans Rho (?) Example

GPA 3.99 3.97 3.93 3.92 3.91 3.85 3.84 3.77
Salary 57.7 61.2 57.3 54.6 64.7 55.3 52.2 54.1
GPA Rank 8 7 6 5 4 3 2 1
Salary Rank 6 7 5 3 8 4 1 2
D 2 0 1 2 -4 -1 1 -1
D2 4 0 1 4 16 1 1 1 ?28
25
Summarizing Bivariate Data Correlation
Coefficient
  • Kendalls 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
  • Kendalls Tau (?) Example
  • Example

GPA 3.99 3.97 3.93 3.92 3.91 3.85 3.84 3.77
Salary 57.7 61.2 57.3 54.6 64.7 55.3 52.2 54.1
GPA Rank 8 7 6 5 4 3 2 1
Salary Rank 6 7 5 3 8 4 1 2
P 0 0 2 3 0 4 6 6 ?21
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 Product Cus. Type Satis.
1 1 2 3.54
2 1 3 3.16
1 2 2 2.42
2 2 2 2.70
1 1 3 3.31
2 1 2 4.12
2 2 1 3.24
2 2 2 4.47
2 1 2 3.83
1 1 1 2.94
Cus. Size 1 small 2 large Product 1
Consumer 2 Manuf. Cus. Type 1 Govt 2
Commercial 3 Education
http//www.qimacros.com/qiwizard/multivari-chart.h
tml
29
Graphical Tool Multi-Vari Charts
Minitab Stat Quality Tools Multi Vari Chart
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