Graphing using Minitab
DOT SIZE
45
40
35
5
6
7
8
LINE
L. Goch – February 2011
AGENDA
 Why Graph Data?
 Under STAT



Run Chart
Pareto Chart
Multi-Vari Chart
 Under







GRAPH
Scatterplot
Histogram
Boxplot
Individual Value Plot
Bar Chart
Pie Chart
3D Scatterplot
All Minitab Tutorial
Worksheets are located
in the folder ‘C:\Program
Files\Minitab
16\English\Sample Data’
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
DATA MINING!
Source: Donald Wheeler: Understanding Variation
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:
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.mtw
RUN CHART
Run Chart of Membrane
45
Membrane
40
35
30
25
20
1
2
3
4
5
6
7
8
Sample
Number of runs about median:
Expected number of runs:
Longest run about median:
Approx P-Value for Clustering:
Approx P-Value for Mixtures:
3
6.0
5
0.022
0.978
Number of runs up or down:
Expected number of runs:
Longest run up or down:
Approx P-Value for Trends:
Approx P-Value for Oscillation:
5
6.3
3
0.135
0.865
9
10
PARETO CHART:
STAT > QUALITY TOOLS >
PARETO CHART
PARETO CHART: STAT > QUALITY TOOLS >
PARETO CHART  Pareto Charts are an essential
Open worksheet
EXH_QC.MTW
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
Defects
Counts
Missing Screws
274
Missing Clips
59
Defective Housing 19
Leaky Gasket
43
Scrap
4
Unconnected Wire 8
Missing Studs
6
Incomplete Part
10
PARETO CHART
Pareto Chart of Defects
300
250
150
100
43
10.2
88.9
19
4.5
93.4
10
2.4
95.7
8
1.9
97.6
Scrap
59
13.9
78.7
Missing Studs
Incomplete Part
274
64.8
64.8
Unconnected Wir
Defectiv e Housi
Counts
Percent
Cum %
Leak y Gask et
0
Defects
Missing Clips
50
Missing Screws
C ounts
200
6
1.4
99.1
4
0.9
100.0
SECOND LEVEL PARETOS
We can generate a second level Pareto using the By
statement
 This breaks down the overall Pareto by time of day

Period
Day
Day
Day
Day
Day
Day
Day
Evening
Evening
Evening
Evening
Evening
Evening
Evening
Night
Night
Night
Night
Night
Night
Night
Night
Night
Night
Night
Night
Night
Night
Night
Night
Night
Night
Night
Weekend
Weekend
Weekend
Weekend
Weekend
Weekend
Weekend
SECOND LEVEL PARETO
Pareto Chart of Flaws by Period
Period = Day
Period = Evening
F law s
P eel
S cratch
O ther
S mudge
8
6
4
4
2
Count
Flaws
Scratch
Scratch
Peel
Peel
Smudge
Scratch
Other
Other
Peel
Peel
Peel
Peel
Scratch
Scratch
Peel
Scratch
Smudge
Scratch
Peel
Peel
Peel
Peel
Other
Other
Scratch
Scratch
Peel
Scratch
Smudge
Scratch
Other
Scratch
Scratch
Peel
Peel
Peel
Smudge
Smudge
Smudge
Other
3
2
1
1
1
0
0
Period = Night
Period = Weekend
8
8
6
2
6
4
3
3
3
2
2
1
0
0
P eel
S cratch
O ther
S mudge
P eel
Flaws
S cratch
O ther
S mudge
MULTI-VARI CHART:
STAT > QUALITY TOOLS >
MULTI-VARI CHART
MULTI-VARI CHART: STAT > QUALITY TOOLS >
MULTI-VARI CHART
Open worksheet
Sinter.MTW

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.
MULTI-VARI CHART
Multi-Vari Chart for Strength by SinterTime - MetalType
24
S interTime
100
150
200
23
Strength
22
21
20
19
18
17
1
2
MetalType
3
SCATTERPLOT:
GRAPH > SCATTERPLOT
SCATTERPLOT: STAT > SCATTERPLOT

Scatterplots study the relationship between
two variables
Open worksheet
Batteries.MTW
SCATTERPLOT
Scatterplot of FlashRecov vs VoltsAfter
7.5
7.0
6.5
FlashRecov
6.0
5.5
5.25
5.0
4.5
4.0
3.5
0.9
1.0
1.1
1.2
VoltsAfter
1.3
1.4
1.5
SCATTERPLOT – BY A VARIABLE
Scatterplot of FlashRecov vs VoltsAfter
7.5
F ormulation
N ew
O ld
7.0
6.5
FlashRecov
6.0
5.5
5.25
5.0
4.5
4.0
3.5
0.9
1.0
1.1
1.2
VoltsAfter
1.3
1.4
1.5
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.MTW
SMOOTHED (NORMAL) DISTRIBUTION
Histogram of Length
Normal
Mean
StDev
N
25
600.1
1.335
100
Frequency
20
15
10
5
0
597
598
599
600
Length
601
602
603
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?
SMOOTHED (SKEWED) DISTRIBUTION
Histogram of Length
Smallest Extreme Value
Loc
Scale
N
25
600.7
1.068
100
Frequency
20
15
10
5
0
596
597
598
599
Length
600
601
602
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?
CREATING A HISTOGRAM WITH GROUPS
Graph > Histogram > With Outline
and Groups
 Data for the 2 different suppliers is
available.

Still using worksheet
Camshaft.MTW
SMOOTHED (SKEWED) DISTRIBUTION
Histogram of Camshaft Lengths
Camparison of Supplier 1 vs Supplier 2
35
V ariable
S upp1
S upp2
30
Frequency
25
20
15
10
5
0
597.0
100 P arts P lotted for E ach S upplier
598.5
600.0
Data
601.5
603.0
SMOOTHED (SKEWED) DISTRIBUTION
Histogram of Camshaft Lengths
Camparison of Supplier 1 vs Supplier 2
Supp1
35
Supp2
30
Frequency
25
20
15
10
5
0
597.0
598.5
100 P arts P lotted for E ach S upplier
600.0
601.5
603.0
597.0
598.5
600.0
601.5
603.0
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!


The center of the Boxplot is the MEDIAN, not the MEAN
Open worksheet
Carpet.MTW
BOXPLOTS
Boxplot of Durability
22.5
75% to
100%
20.0
75th
Percentile
Durability
17.5
15.0
Average
12.5
50th
Percentile
or Median
10.0
7.5
5.0
NOTE:
Outliers will be
displayed as *
0% to
25%
We can also generate boxplots by a variable to
look at the variation due to that variable
25th
Percentile
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.MTW
BOXPLOTS W/ GROUPS
Boxplot of Durability
22.5
20.0
18.115
Durability
17.5
15.0
14.4825
12.8075
12.5
10.0
9.735
7.5
5.0
1
2
Carpet
3
4
INDIVIDUAL VALUE 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.MTW
INDIVIDUAL VALUE PLOT
Individual Value Plot of Elastic
90
80
Elastic
70
60
Average
50
40
30
We can also generate Individual Value Plots by a
variable to look at the variation due to that variable
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.MTW
INDIVIDUAL VALUE PLOT W/ GROUPS
Individual Value Plot of Elastic
Additive
0
1
2
90
80
75.9
Elastic
70
60
54.2
50
42.8
40
30
0
1
Additive
2
BAR CHART:
GRAPH > BAR CHART
BAR CHART: GRAPH > BAR CHART

Bar Charts can be
created from:
1)
2)
3)
Data that needs
to be counted
Functions of
data(e.g. avg,
min, max) OR
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.MTW
Flaws
3
2
Weekend
Night
Evening
0
Smudge
1
Day
8
Weekend
Night
2
Evening
3
Scratch
3
Day
6
Weekend
Night
1
Evening
2
Day
3
Weekend
Night
Evening
4
Peel
0
Period
1
Other
1
Day
Count
BAR CHART: GRAPH > BAR CHART (COUNTS OF
UNIQUE VALUES)
Chart of Flaws, Period
9
8
7
6
5
4
3
2
1
0
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.MTW
BAR CHART: GRAPH > BAR CHART (A
FUNCTION OF A VARIABLE)
Chart of Mean( LightOutput )
1386
1400
1313
Mean of LightOutput
1200
1087.33
1035 1054.67
1000
886.667
800
600
572.667 553 573.333
400
200
GlassType
Temperature
0
1
2
100
3
1
2
125
3
1
2
150
3
BAR CHART: GRAPH > BAR CHART (VALUES
FROM A TABLE)

asdfa
Open worksheet
Tires.MTW
BAR CHART: GRAPH > BAR CHART (VALUES
FROM A TABLE)
Chart of Repairs
160
140
Repairs
120
100
80
60
40
20
Q1
Q2
Leak From Seating
Q3
Q4
Q1
Q2
Damaged Liner
Q3
Q4
Q1
Q2
Valve Core Leak
Q3
Q4
Q1
Q2
Damaged Sidewall
Q3
Q4
Q1
Q2
Valve Stem Leak
Q3
Q4
CausesB
0
Q1
Q2
Puncture
Q3
Q4
Qtr
We can easily switch the X-axis so that CauseB is
plotted within Qtr.
CausesB
Damaged Liner
Puncture
Valve Core Leak
Valve Stem Leak
Valve Core Leak
Valve Stem Leak
Damaged Liner
Damaged Sidewall
Leak From Seating
Q4
Puncture
Valve Stem Leak
Damaged Sidewall
Leak From Seating
Q3
Puncture
Valve Core Leak
Q2
Damaged Liner
Damaged Sidewall
Leak From Seating
Valve Stem Leak
Damaged Sidewall
Leak From Seating
Q1
Puncture
Valve Core Leak
Qtr
Damaged Liner
Repairs
BAR CHART: GRAPH > BAR CHART (VALUES
FROM A TABLE)
Chart of Repairs
160
140
120
100
80
60
40
20
0
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)
Chart of Repairs
C ausesB
V alv e S tem Leak
V alv e C ore Leak
P uncture
Leak F rom S eating
Damaged S idew all
Damaged Liner
400
200
100
Q4
Q1
0
Q2
Qtr
Q3
Repairs
300
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.MTW
PIE CHART: GRAPH > PIE CHART
Pie Chart of CausesA
Leak F rom S eating
7.0%
Damaged Liner
9.2%
P uncture
28.8%
V alv e C ore Leak
12.8%
Damaged S idew all
14.6%
V alv e S tem Leak
27.6%
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.MTW
3D SCATTERPLOT: GRAPH > 3D SCATTERPLOT
3D Scatterplot of Quality vs Time vs Temp
O perator
A
B
7.5
Q uality
5.0
2.5
40
35
0.0
30
350
400
Temp
Time
25
450
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 = 1 defect
x
xxxx
xx
x
x
x
x
x
x
x
x xx
xx
x
x
x
xxx
xxx
xx xxx
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 format
 Make sense from an 3) Engineering standpoint

Good Conclusions Require
Data and Hard Evidence!!