8765

45

40

35

LINE

DO

T S

IZE

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

45

40

35

30

25

20

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

4

2

3

8

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

321

24

23

22

21

20

19

18

17

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?

603602601600599598597

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10

5

0

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?

602601600599598597596

25

20

15

10

5

0

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

35

30

25

20

15

10

5

0

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

603.0601.5600.0598.5597.0

35

30

25

20

15

10

5

0603.0601.5600.0598.5597.0

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

4321

22.5

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

90

80

70

60

50

40

30

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

210

90

80

70

60

50

40

30

Additive

Elast

ic

012

Additive

42.8

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

9

8

7

6

5

4

3

2

1

0

Count

3

2

0

1

0

8

2

33

6

4

2

1

3

11

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

1400

1200

1000

800

600

400

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

160

140

120

100

80

60

40

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!!