Chapter 8 Making Sense of Data in Six Sigma and Lean
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Transcript of Chapter 8 Making Sense of Data in Six Sigma and Lean
Chapter 8
Making Sense of Data in
Six Sigma and Lean
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
How to tell “story” from dataset?Qualitative Data
– Pie Charts– Bar Charts– Pareto Analysis with Lorenz Curve
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
How to tell “story” from dataset?Multi-Vari Data
• Graphical Methods– Multi-Vari Charts
Summarizing Quantitative Data:Dot Plots
• Dot plot is one of the most simple types of plots
Example 8.1
MinitabGraphDotplotSimple
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.
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treediagram.png
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
Summarizing Quantitative Data:
Histogram
www.statcan.gc.ca/.../ch9/images/histo1.gif
Summarizing Quantitative Data:Run Charts
• A line graph of data points plotted in chronological order that helps detect special causes of variation
MinitabGraphTime Series PlotSimple
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.
MinitabGraphTime Series PlotSimple
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
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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
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Summarizing Quantitative Data:Descriptive Statistics
Measures of Variation• Coefficient of Variation (CV)
• Interquartile Range (IQR)
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13 QQIQR
Minitab:Stat
Basic StatisticsDisplay Descriptive..•Boxplot
• Minimum• Maximum• Median
• First Quartile• Third Quartile
Summarizing Quantitative Data:Descriptive Statistics
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
)5.1(1 IQRQ
)5.1(3 IQRQ
)0.3(1 IQRQ )0.3(3 IQRQ
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)
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Summarizing Qualitative Data:Graphical Displays
• Pie Chart
http://techie-teacher-wanna-be.wikispaces.com/file/view/SocialPieChart.png/96606670/SocialPieChart.png
Summarizing Qualitative Data:Graphical Displays
• Bar Graph
www.creationfactor.net/images/graph-bar.jpg
Summarizing Qualitative Data:Graphical Displays
• Pareto Analysis with Lorenz Curve
www.spcforexcel.com/files/images/ccpareto.gif
Summarizing Bivariate Data:Scatterplot
Minitab:Graph
ScatterplotSimple
• Pearson Correlation Coefficient
Summarizing Bivariate Data:Correlation Coefficient
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Minitab:Stat
RegressionRegression
• 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
Summarizing Bivariate Data:Correlation Coefficient
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• Spearman’s Rho () Example
Summarizing Bivariate Data:Correlation Coefficient
667.)18(8
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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
• 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
Summarizing Bivariate Data:Correlation Coefficient
1)1(
4
nn
Pr
• Kendall’s Tau () Example• Example
Summarizing Bivariate Data:Correlation Coefficient
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
50.1)18(8
)21(41
)1(
4
nn
Pr
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
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 = small2 = large
Product: 1 = Consumer2 = Manuf.
Cus. Type: 1 = Gov’t2 = Commercial3 = Education
http://www.qimacros.com/qiwizard/multivari-chart.html
Graphical Tool: Multi-Vari Charts
Minitab:StatQuality ToolsMulti Vari Chart