Graphing using Minitab L. Goch – February 2011. A GENDA Why Graph Data? Under STAT Run Chart...
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Transcript of Graphing using Minitab L. Goch – February 2011. A GENDA Why Graph Data? Under STAT Run Chart...
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Graphing using Graphing using MinitabMinitab
L. Goch – February 2011
AGENDA Why Graph Data? Under STAT
Run ChartPareto ChartMulti-Vari Chart
Under GRAPHScatterplotHistogramBoxplot Individual Value PlotBar ChartPie Chart3D Scatterplot
All Minitab Tutorial Worksheets are located in the folder ‘C:\Program Files\Minitab 16\English\Sample Data’
Graphing using Minitab.mtb
Source: Donald Wheeler: Understanding Variation
WHY GRAPH THE DATA? Graphs help us understand the nature of
variation Graphs make the nature of data more
accessible to the human mind Graphs help display the context of the data Graphs should be the primary presentation tool
in data analysis If you can’t show it graphically, you
probably don’t have a good conclusion Graphs help separate the signal from the noise
Graphical Analysis is also Called Graphical Analysis is also Called DATA MINING!DATA MINING!
Graphical Analysis is also Called Graphical Analysis is also Called DATA MINING!DATA MINING!
RULES FOR EFFECTIVE DATA COLLECTION
Team must follow sampling plan consistently
Do a short Pilot Run to test your procedures
Note changes in operating conditions that are not part of the normal or initial operating conditions
Maintain monitors on gauges for key process inputs
Record any events that are out of the ordinary
Log data into database quickly
Keep a log book
AVAILABLE GRAPH TOOLS
RUN CHART: RUN CHART:
STAT > QUALITY TOOLS > RUN CHART
RUN CHART: STAT > QUALITY TOOLS > RUN CHART
Tests for Process Stability by applying some statistical diagnostic tests to the series
Open worksheet Radon.mtwRadon.mtw
RUN CHART
10987654321
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Sample
Mem
bra
ne
Number of runs about median: 3Expected number of runs: 6.0Longest run about median: 5Approx P-Value for Clustering: 0.022Approx P-Value for Mixtures: 0.978
Number of runs up or down: 5Expected number of runs: 6.3Longest run up or down: 3Approx P-Value for Trends: 0.135Approx P-Value for Oscillation: 0.865
Run Chart of Membrane
PARETO CHART: PARETO CHART:
STAT > QUALITY TOOLS > PARETO CHART
PARETO CHART: STAT > QUALITY TOOLS > PARETO CHART Pareto Charts are an
essential tool to help prioritize improvement targets
Pareto’s allow us to focus on the 20% of the problems that cause 80% of the poor performance
Open worksheet EXH_QC.MTWEXH_QC.MTW
Counts 274 59 43 19 10 8 6 4Percent 64.8 13.9 10.2 4.5 2.4 1.9 1.4 0.9Cum % 64.8 78.7 88.9 93.4 95.7 97.6 99.1 100.0
Defects
Scr
ap
Missing S
tuds
Unco
nnec
ted W
ir
Inco
mple
te P
art
Def
ectiv
e H
ousi
Leak
y G
asket
Missing C
lips
Missing S
crew
s300
250
200
150
100
50
0
Counts
Pareto Chart of Defects
PARETO CHART
Defects CountsMissing Screws 274Missing Clips 59Defective Housing 19Leaky Gasket 43Scrap 4Unconnected Wire 8Missing Studs 6Incomplete Part 10
SECOND LEVEL PARETOS
We can generate a second level Pareto using the ByBy statement
This breaks down the overall Pareto by time of day
SECOND LEVEL PARETOFlaws PeriodScratch DayScratch DayPeel DayPeel DaySmudge DayScratch DayOther DayOther EveningPeel EveningPeel EveningPeel EveningPeel EveningScratch EveningScratch EveningPeel NightScratch NightSmudge NightScratch NightPeel NightPeel NightPeel NightPeel NightOther NightOther NightScratch NightScratch NightPeel NightScratch NightSmudge NightScratch NightOther NightScratch NightScratch NightPeel WeekendPeel WeekendPeel WeekendSmudge WeekendSmudge WeekendSmudge WeekendOther Weekend
8
6
4
2
0
SmudgeOtherScratchPeel
8
6
4
2
0SmudgeOtherScratchPeel
Period = Day
Flaws
Count
Period = Evening
Period = Night Period = Weekend
PeelScratchOtherSmudge
Flaws
11
3
2
0
1
2
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2
3
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6
3
1
0
3
Pareto Chart of Flaws by Period
MULTI-VARI CHART: MULTI-VARI CHART:
STAT > QUALITY TOOLS > MULTI-VARI CHART
MULTI-VARI CHART: STAT > QUALITY TOOLS > MULTI-VARI CHART
Multi-vari charts are a way of presenting analysis of variance data in a graphical form. The chart displays the means at each factor level for every factor.
Open worksheet Sinter.MTWSinter.MTW
MULTI-VARI CHART
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MetalType
Str
ength
100150200
SinterTime
Multi-Vari Chart for Strength by SinterTime - MetalType
SCATTERPLOT: SCATTERPLOT:
GRAPH > SCATTERPLOT
SCATTERPLOT: STAT > SCATTERPLOT Scatterplots study the relationship
between two variablesOpen worksheet Batteries.MTWBatteries.MTW
SCATTERPLOT
1.51.41.31.21.11.00.9
7.5
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
VoltsAfter
Fla
shRec
ov
5.25
Scatterplot of FlashRecov vs VoltsAfter
SCATTERPLOT – BY A VARIABLE
1.51.41.31.21.11.00.9
7.5
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
VoltsAfter
Fla
shRec
ov
5.25
NewOld
Formulation
Scatterplot of FlashRecov vs VoltsAfter
HISTOGRAM: HISTOGRAM:
GRAPH > HISTOGRAM
CREATING A HISTOGRAM WITH A NORMAL CURVE Graph > Histogram > With Fit
Histograms examine the shape and spread of data
Open worksheet Camshaft.MTWCamshaft.MTW
SMOOTHED (NORMAL) DISTRIBUTION
We can view the data as a smoothed distribution (red line), in this example using the “normal distribution” assumption. It provides an approximation of how the data might look if we were to collect an infinite number of data points. DOES THE DATA FIT THE CURVE??? If not, does another type of distribution fit the data?
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Length
Freq
uenc
yMean 600.1StDev 1.335N 100
Histogram of LengthNormal
SMOOTHED (SKEWED) DISTRIBUTION
We can view the data as a smoothed distribution (red line), in this example using the “skewed distribution” assumption. It provides an approximation of how the data might look if we were to collect an infinite number of data points. DOES THE DATA FIT THE CURVE??? If not, look for groups that may explain the shape of the data?
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Length
Fre
quen
cy
Loc 600.7Scale 1.068N 100
Histogram of LengthSmallest Extreme Value
CREATING A HISTOGRAM WITH GROUPS Graph > Histogram > With Outline
and Groups Data for the 2 different suppliers is
available.
Still using worksheet Camshaft.MTWCamshaft.MTW
SMOOTHED (SKEWED) DISTRIBUTION
603.0601.5600.0598.5597.0
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Data
Fre
quen
cy
Supp1Supp2
Variable
Histogram of Camshaft LengthsCamparison of Supplier 1 vs Supplier 2
100 Parts Plotted for Each Supplier
SMOOTHED (SKEWED) DISTRIBUTION
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Supp1
Fre
quen
cy
Supp2
Histogram of Camshaft LengthsCamparison of Supplier 1 vs Supplier 2
100 Parts Plotted for Each Supplier
BOXPLOT: BOXPLOT:
GRAPH > BOXPLOT
BOXPLOTS: GRAPH > BOXPLOT There is another method of looking at the data that
may be easier to see differences in the distributions Boxplots show the spread and center of the data BE CAREFUL!BE CAREFUL!
The center of the Boxplot is the MEDIANMEDIAN, not the MEANMEAN
Open worksheet Carpet.MTWCarpet.MTW
22.5
20.0
17.5
15.0
12.5
10.0
7.5
5.0
Dura
bility
Boxplot of Durability
75th Percentile
50th Percentile or Median
25th Percentile
NOTE: Outliers will be
displayed as *
BOXPLOTS
We can also generate boxplots by a variable to look at the variation due to that variable
75% to 100%
0% to 25%
Average
BOXPLOTS W/ GROUPS We can also generate boxplots by a variable to look at
the variation due to that variable Data for 4 Experimental Carpet types is available.
Still using worksheet Carpet.MTWCarpet.MTW
BOXPLOTS W/ GROUPS
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20.0
17.5
15.0
12.5
10.0
7.5
5.0
Carpet
Dura
bility
18.115
12.8075
9.735
14.4825
Boxplot of Durability
INDIVIDUAL VALUE INDIVIDUAL VALUE PLOT: PLOT: GRAPH > INDIVIDUAL VALUE PLOT
INDIVIDUAL VALUE PLOT: GRAPH > INDIVIDUAL VALE PLOT
Individual Value Plots also show the spread and center of the data
Open worksheet Billiards.MTWBilliards.MTW
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Elast
icIndividual Value Plot of Elastic
INDIVIDUAL VALUE PLOT
We can also generate Individual Value Plots by a variable to look at the variation due to that variable
Average
INDIVIDUAL VALUE PLOT W/ GROUPS We can also generate Individual Value Plots by a
variable to look at the variation due to that variable Data for 2 Additives is available.
Still using worksheet Billiards.MTWBilliards.MTW
INDIVIDUAL VALUE PLOT W/ GROUPS
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Additive
Elast
ic
012
Additive
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75.9
54.2
Individual Value Plot of Elastic
BAR CHART: BAR CHART:
GRAPH > BAR CHART
BAR CHART: GRAPH > BAR CHART
Bar Charts can be created from:1) Data that
needs to be counted
2) Functions of data(e.g. avg, min, max) OR
3) a Table
BAR CHART: GRAPH > BAR CHART (COUNTS OF UNIQUE VALUES)
Use to chart counts of unique values, clustered by grouping variables.
Open worksheet Exh_QC.MTWExh_QC.MTW
BAR CHART: GRAPH > BAR CHART (COUNTS OF UNIQUE VALUES)
Flaws
Period
Sm
udge
Scr
atc
h
Peel
Oth
er
Week
end
Nig
ht
Evenin
g
Day
Week
end
Nig
ht
Evenin
g
Day
Week
end
Nig
ht
Evenin
g
Day
Week
end
Nig
ht
Evenin
g
Day
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1
0
Count
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1
0
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1
3
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Chart of Flaws, Period
BAR CHART: GRAPH > BAR CHART (A FUNCTION OF A VARIABLE)
Use to chart counts of unique values, clustered by grouping variables.
Still using worksheet Exh_AOV.MTWExh_AOV.MTW
BAR CHART: GRAPH > BAR CHART (A FUNCTION OF A VARIABLE)
TemperatureGlassType
150125100321321321
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1000
800
600
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200
0
Mean o
f Li
ghtO
utp
ut
886.667
1313
1386
1054.6710351087.33
573.333553572.667
Chart of Mean( LightOutput )
BAR CHART: GRAPH > BAR CHART (VALUES FROM A TABLE)
asdfa
Open worksheet Tires.MTWTires.MTW
BAR CHART: GRAPH > BAR CHART (VALUES FROM A TABLE)
CausesB
Qtr
Leak F
rom
Seating
Dam
aged L
iner
Valv
e C
ore
Leak
Dam
aged S
idew
all
Valv
e S
tem
Leak
Punct
ure
Q4
Q3
Q2
Q1
Q4
Q3
Q2
Q1
Q4
Q3
Q2
Q1
Q4
Q3
Q2
Q1
Q4
Q3
Q2
Q1
Q4
Q3
Q2
Q1
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20
0
Repairs
Chart of Repairs
We can easily switch the X-axis so that CauseB is plotted within Qtr.
BAR CHART: GRAPH > BAR CHART (VALUES FROM A TABLE)
Qtr
CausesB
Q4
Q3
Q2
Q1
Valv
e S
tem
Leak
Valv
e C
ore
Leak
Punct
ure
Leak
Fro
m S
eati
ng
Dam
aged S
idew
all
Dam
aged L
iner
Valv
e S
tem
Leak
Valv
e C
ore
Leak
Punct
ure
Leak
Fro
m S
eati
ng
Dam
aged S
idew
all
Dam
aged L
iner
Valv
e S
tem
Leak
Valv
e C
ore
Leak
Punct
ure
Leak
Fro
m S
eati
ng
Dam
aged S
idew
all
Dam
aged L
iner
Valv
e S
tem
Leak
Valv
e C
ore
Leak
Punct
ure
Leak
Fro
m S
eati
ng
Dam
aged S
idew
all
Dam
aged L
iner
160
140
120
100
80
60
40
20
0
Repairs
Chart of Repairs
We can easily stack the Causes B into one bar on the X-axis still plotted within Qtr.
BAR CHART: GRAPH > BAR CHART (VALUES FROM A TABLE)
QtrQ
4
Q1
Q2
Q3
400
300
200
100
0
Repairs
Valve Stem LeakValve Core LeakPunctureLeak From SeatingDamaged SidewallDamaged Liner
CausesB
Chart of Repairs
PIE CHART: PIE CHART:
GRAPH > PIE CHART
PIE CHART: GRAPH > PIE CHART
Use to display the proportion of each data category relative to the whole data set.
Open worksheet Tires.MTWTires.MTW
PIE CHART: GRAPH > PIE CHART
Leak From Seating7.0%
Damaged Liner9.2%
Valve Core Leak12.8%
Damaged Sidewall14.6%
Valve Stem Leak27.6%
Puncture28.8%
Pie Chart of CausesA
3D SCATTERPLOT: 3D SCATTERPLOT:
GRAPH > 3D SCATTERPLOT
3D SCATTERPLOT: GRAPH > 3D SCATTERPLOT
Use to evaluate relationships between three variables at once by plotting data on three axes.
Open worksheet Reheat.MTWReheat.MTW
3D SCATTERPLOT: GRAPH > 3D SCATTERPLOT
0.0
2.5
5.0
7.5
350400
450
30
40
35
25450
Quality
Time
Temp
AB
Operator
3D Scatterplot of Quality vs Time vs Temp
Us the 3D Graph Tools to Enlarge & Rotate Graph (Check Tools >Toolbars >3D Graph Tools).
CONCENTRATION DIAGRAMS CANNOT BE CREATED IN MINITAB Concentration Diagrams provide a visual
display of occurrences to identify trends Usually a pictorial representation (drawing) of
the product is used as the basis Occurrences are marked on the drawing where
they were noticed for all units reviewed Take a look at the following examples…
A Concentration Diagram is a great tool to Investigate the nature of surface defects
LOOKING FOR PAINT DEFECTS Top View of a Cooktop
x
X = 1 defect
xxx
xx
x xx xx x
x
xxxx
xx
xx
x
x
x
x
xx
x
x
xx
xx
x
ANNOTATING GRAPHS: ANNOTATING GRAPHS: • To Change Title: Double click on Title, Change Font or
Text, Click ‘OK’.• To Add Subtitle or Footnote: Left Click anywhere on
Graph, Click Add, Select Option to be added. • To Underline Legend Title: Double Click on Legend
box, Left click on ‘Header Font’ tab, Check Underline.• To add data labels: Right Click anywhere on graph,
Left click on ‘Add’, Left click on ‘Data Labels’, Left click on ‘OK’.
• To add Groups to data: Double Click on any Data Point, Select Groups tab, Select column to group by
• To Delete Legend Box: Right click on Legend box, Left Click on ‘Delete’.
• To move the position of a Label: Right Click to select the label you want to move. You may have to Right Click more than once. Right Click, hold and drag the label to the new position.
• To Unslant X-axis Labels: Double click X-axis, select Alignment tab, enter 90 for text angle, Click on ‘OK’.
• To Add Jitter to Data Points: Double click any Data Point, select the Jitter tab, Check Add jitter to direction, Click on ‘OK’.
CONCLUSIONS
Results need to be Supported by data Not based on conjecture or intuition Shown in 1) Graphical & 2) Statistical 1) Graphical & 2) Statistical
formatformat Make sense from an 3) Engineering 3) Engineering
standpointstandpoint
Good Conclusions RequireGood Conclusions Require
Data and Hard Evidence!!Data and Hard Evidence!!
Good Conclusions RequireGood Conclusions Require
Data and Hard Evidence!!Data and Hard Evidence!!