SPC tools and techniques– part 2 & Fundamentals of Statistics—Part 1
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Lecture 7: SPC tools and
techniques– part 2
Chapter 4
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Magnificent seven quality tools
Process flow diagram
Pareto diagram
Cause and effect diagram
Check sheet
Scatter diagram
Histogram
Control charts (include run chart)
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Check sheet— for paint non-conformities
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Check sheet– for plastic mold nonconformities
××××
××
× ××××
×
××
× ×
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Check sheet example– pin diameter
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Check sheet example-- for car door painting process
The Quality Toolbook from
http://syque.com/quality_tools/toolbook/Check/example.htm
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Key points in using check sheet
Check sheet should be well designed, easy to read, and clearly labeled.
Record only necessary information. Don’t attempt to collect data not specifically related to the issues being studied.
Keep it simple
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Scatter diagram (scatterplot)
Display the relationship between two variables
Gas mileage and speed
Cutting speed and tool life
Feed rate and surface roughness
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Constructing scatter diagram
Two measurements on each unit
Plot using coordinate axes
Vertical: response
Horizontal: explanatory or predictor
Explanatory variable
R e s p o n s e v
a ri a b le
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Interpretation-- scatter plot
Positive
Negative
No association
Curvilinear
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Interpretation-- scatter plot
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Scatter diagram example
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Scatter diagram example
Fig. 22-17, cutting speed and tool life,
from Materials and Processes in Mfg, by DeGarmo, Black, & Kohser, 9th ed 14
Scatter diagram example
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Scatter diagram examples
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Histogram
Pictorial representation (summary) of a set of data
measurement
fr e q u e n c y
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Interpret histograms
By graphic (qualitative) features
Symmetry
Mounted, flat
Skew
Right, left
By analytical (quantitative) features
Center: mean, medium, mode
Dispersion: range, standard deviation
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symmetric Skew- right
Skew- left
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Histogram
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Constructing a stem-leaf chart (one type of histogram)
Order data from smallest to largest
Determine cell intervals– equal width
Construct a frequency table
Draw bar chart
Vertical: frequency by %
Horizontal: cell intervals
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How many intervals (cells, categories) should be formed?
Number of cells is based on judgment
General rule of thumb is the number of cells should be between 5 and 20
5 to 9 when observations are < 100
8 to 17 observations are between 100 & 500
15 to 20 when observations are > 500
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Stem-and-leaf chart-- octane ratings
The following data on motor octane ratings are excerpted from an article in Technometrics Vol.19 p425
93.3 91.8 92.3 90.4 90.1 93.0 88.7 89.9
89.8 89.6 87.4 88.4 88.9 91.2 89.3 94.4
92.7 91.8 91.6 90.4 91.1 92.6 89.3 90.6
91.1 90.4 89.3 89.7 90.3 91.6 90.5 93.7
92.7 92.2 92.2 91.2 91.0 92.2 90.0 90.7
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Stem-and-leaf chart-- octane ratings 86
87 4
88 4 9 7
89 8 6 3 7 3 3 9
90 4 4 4 1 3 5 0 6 7
91 1 8 8 6 2 1 0 2 6
92 7 7 2 3 2 6 2
93 3 0 7
94 4
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Stem-and-leaf chart-- octane ratings
86
87 4
88 4 7 9
89 3 3 3 6 7 8 9
90 0 1 3 4 4 4 5 6 7
91 0 1 1 2 2 3 6 8 8
92 2 2 2 3 6 7 7
93 0 3 7
94 4
95
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Octane Rating –frequency table
Class interval Freq. Freq.% Cumu. %
87.0≤Y<88.0 1 2.5 2.5
88.0≤Y<89.0 3 7.5 10
89.0≤Y<90.0 7 17.5 27.5
90.0≤Y<91.0 9 22.5 50
91.0≤Y<92.0 9 22.5 72.5
92.0≤Y<93.0 7 17.5 90
93.0≤Y<94.0 3 7.5 97.5
94.0≤Y<95.0 1 2.5 100
40 100
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Histogram—octane rating
Histogram—octane rating (created from Excel)
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3
7
9 9
7
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0
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Frequency
Frequency
Linear (Frequency)
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Cautions (limitations)
Choice of intervals can affect the picture you get
Histograms can hide trends over time or other patterns
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Run chart
A graphic representation of process performance data tracked over time
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Run chart
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Control chart
A graphic display of the results of a process over time and against established control limits
Control chart— Run chart with control limits
A statistical tool used to detect excessive process variability due to specific assignable causes that can be corrected.
Two purposes
To see if special causes are present
To test or evaluate if a solution works
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Control chart Assignment today
InClass Practice 5
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