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Chapter 8 Making Sense of Data in Six Sigma and Lean

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Chapter 8Making Sense of Data inSix Sigma and Lean

- Graphical Methods
- Dot Plots
- Stem-and-Leaf Plots
- Frequency Tables
- Histograms and Performance Histograms
- Run Charts
- Time-Series Plots

- Numerical Methods: Descriptive Statistics

- Pie Charts
- Bar Charts
- Pareto Analysis with Lorenz Curve

- Graphical Methods
- Scatter Plots

- Numerical Methods: Correlation Coefficient
- Pearson Coefficient
- Spearman’s Rho ()
- Kendall’s Tau () Rank Correlation

- Graphical Methods
- Multi-Vari Charts

- Dot plot is one of the most simple types of plots

Example 8.1

Minitab

Graph

Dotplot

Simple

- Stem-and-Leaf Plots are a method for showing the frequency with which certain classes of values occur.

i160.photobucket.com/.../treediagram.png

- 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

www.statcan.gc.ca/.../ch9/images/histo1.gif

- A line graph of data points plotted in chronological order that helps detect special causes of variation

Minitab

Graph

Time Series Plot

Simple

- 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

Measures of Center

- Sample mean
- Population mean
- Median: the "middle" value in the dataset
- Mode: the value that occurs most often

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

Measures of Variation

- Coefficient of Variation (CV)
- Interquartile Range (IQR)

Summarizing Quantitative Data:Descriptive Statistics

- Minimum
- Maximum
- Median
- First Quartile
- Third Quartile

- Minitab:
- Stat
- Basic Statistics
- Display Descriptive..
- Boxplot

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

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)

- Pie Chart

http://techie-teacher-wanna-be.wikispaces.com/file/view/SocialPieChart.png/96606670/SocialPieChart.png

- Bar Graph

www.creationfactor.net/images/graph-bar.jpg

- Pareto Analysis with Lorenz Curve

www.spcforexcel.com/files/images/ccpareto.gif

Minitab:

Graph

Scatterplot

Simple

- Pearson Correlation Coefficient

Minitab:

Stat

Regression

Regression

- 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

- Spearman’s Rho () Example

- 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

- Kendall’s Tau () Example
- Example

- 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

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

Minitab:

Stat

Quality Tools

Multi Vari Chart