An introduction to Six Sigma

1. Not to be used
commercially without
written permission.
ABN 95 844 017 962
kanriconsulting@adam.com.au

2. 




In 1986, Motorola, a mass producer
of semiconductors was concerned
with the quality of its product.
Motorola developed a toolset named
Six Sigma to measure defects per
million opportunities (DPMO).
The name ‘Six Sigma’ reflects a
scientific and structured method for
improvements.
Six Sigma is a powerful quality and
change tool that can trace its roots
back to Total Quality Management.
Define
Measure
Analyse
Improve
Control
Six Sigma does not use lean’s PDCA
cycle, instead using DMAIC.
シックスシグマ
(c) Ewan Pettigrew
2

3. 

Many of the tools used in Six Sigma
such as SIPOCs and VSMs are shared
with lean. However, Six Sigma uses
additional statistical tools to measure
quality.
0.45
Six Sigma measures variation within a
normal distribution.
0.25
◦
◦
◦
◦
◦
◦
◦
Normal distribution is bell shaped
The Six Sigma equation is Y=f(X) + ε
3.4 million defects per million opportunities
(worst case with 1.5 SD drift in process). We
allow for the 1.5 Sigma shift in calculating this
(discussed later).
USL and LSL are 6 standard deviations above
and below the mean
Measures the number of standard deviations
which we can fit inside customers requirements
Variation means there is a different Y each time
the process is completed.
Variation is bad whilst manufacturing.
0.4
0.35
0.3
0.2
0.15
0.1
0.05
0
0
20
40
シックスシグマ
(c) Ewan Pettigrew
3

4. 
Statistical measurement

Source
◦
5
◦
Frame – A section of the population
◦
Sample – A section of the frame
4
-1

Scale
◦
Nominal Scale – categories or names are used to
separate data.
◦
NEG2STDDEV
NEG3STDDEV
Ordinal Scale – Ordered by rank, but with no relative
degree of difference.
◦
-2
1153
NEG1STDDEV
1025
0
897
Continuous Data – decimal value
3STDDEV
769
◦
1
641
Variable Data – Discrete (whole number), Count
2STDDEV
513
◦
2
385
Attribute Data – Yes /No (Qualitative)
STDDEV
257
◦
3
129
Data
MEAN
1

Population – All items of interest under study
Interval Scale – Shows the degree of difference, but
not the ratio.
-3
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4

5. 
Measuring Location or central
tendency
◦
Mean
◦
Median
◦
Mode
120
100
Measuring Variation
80
◦
60
◦
Inter quartile range
standard deviation
40
◦
◦
Variance
4.05471786
3.489361366
2.924004871
2.358648377
99.7% of data falls within 3 SD of the mean.
1.793291882
◦
1.227935388
95% of data falls within 2 SD of the mean
0.662578893
◦
0.097222398
68% of data falls within 1 SD of the mean
-0.468134096
◦
0
-1.033490591
The empirical rule states that within
the normal distribution
20
-1.598847085

Range
-2.16420358

シックスシグマ
(c) Ewan Pettigrew
5

6. 


Define
During the define stage, the project is
scoped, a business case, and project
charter are developed. A team is
formed and customers are
documented.
Outputs of the define phase
◦
Project Charter
◦
Project plan with stage gates and milestones
◦
VOB
◦
VOC
◦
SIPOC
◦
Current State Process Map
◦
Find the Y
◦
COPQ
Analyse
Business Case
◦
Measure
CTQ
◦
Define
Improve
Control
シックスシグマ
(c) Ewan Pettigrew
6

7. 


Measure
The measure phase is used to
investigate and perform
measurements to confirm the
requirements of the customer. In this
phase, we measure statistics of the
existing process, create a data
collection method to measure
performance of the process, and
collect data on process performance.
Outputs of the measure phase
◦
Input Measures
◦
Process Measures
◦
Output Measures
◦
Measure process capability
◦
FMEA
◦
Improve
Data Collection Plan
◦
Analyse
Establishment of process baseline
◦
Measure
Identify measures from SIPOC
◦
Define
CTQ
Control
シックスシグマ
(c) Ewan Pettigrew
7

8. 


Analyse
The analyse phase is where the
problem is investigated and root
cause(s) are identified. This is where
the statistical analysis first occurs. For
example, the capability of the process
is analysed and confirmed and
reasons for specific variation and
central tendency are investigated.
Outputs of the analyse stage
◦
Hypothesis testing
◦
Control charts
◦
Draft Action Plan
Improve
Run charts
◦
Analyse
Histograms
◦
Measure
Regression analysis
◦
Define
Control
シックスシグマ
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8

9. 



Improve
This phase is where actual
improvements are made. It is crucial
that we have identified the vital few
‘x’s that are causing variation or shift
in central tendency.
Sometimes we experiment (DOE) or
implement on a small scale before
implementing on a larger scale.
Outputs of the improve phase
◦
5s (from lean methodology)
◦
Design of Experiments
◦
Improve
Control charts
◦
Analyse
Standardised work
◦
Measure
Action plan
◦
Define
Visual Management Board
Control
シックスシグマ
(c) Ewan Pettigrew
9

10. 



Control
The control phase is where
improvements in quality and
efficiency should be sustained
through standard work, error
proofing, and statistical process
control.
Most importantly, we must reward
and acknowledge the team.
Outputs of the control phase
◦
Control charts
◦
PCMs
◦
Improve
Project Report
◦
Analyse
Control Plan
◦
Measure
Error proofing
◦
Define
Lessons learnt
Control
シックスシグマ
(c) Ewan Pettigrew
10

11. 
RACI Charts graphically display the
roles of stakeholders in a project.
Define
Measure
Analyse
Improve
Control
Sponsor



Responsible – Are the people carrying
out the work.
Accountable – The one person who
shall ensure completion of the work.
Consulted –Are people providing
input and receiving output. Two way
information.
A
A
A
A
Black Belt
R
R
R
R
R
Green Belt
C
R
R
C
R
Process Owner
C
C
C
C
C
Manager
C
C
C
C
C
Operators
C
I
I
I
I
CEP

A
C
C
C
C
C
Informed –Are being provided with
one way information.
(c) Ewan Pettigrew
11

12. 
Pareto charts display relative
importance of different categories.
120

The counts for each category are
presented as a descending bar chart.
However, the cumulative percentage
is presented as an increasing line
chart.
100.00%
90.00%
100
80.00%
70.00%
80
60.00%
60


Vilfredo Pareto came up with the
80:20 rule, where he found that 80%
of problems were caused by the top
20% of categories
Pareto charts are a useful tool for
project selection.
50.00%
40.00%
40
30.00%
Frequency
Percentage
20.00%
20
10.00%
0
0.00%
パレート図
(c) Ewan Pettigrew
12

13. 
Run Charts are used for measurement
of a process’ output to be plotted in
order of time.
25

Patterns can indicate variability.
20


The run chart can show horizontal
trend lines detailing customer
specification limits.
Do not confuse specification limits
with control limits.
15
10
5
0
1

3
5
7
9
11 13 15 17 19 21 23 25
Run charts can easily be drawn in
Excel without any knowledge of
formulas or Macros.
パレート図
(c) Ewan Pettigrew
13

14. 
Are run charts with calculated
statistical limits
◦
◦
UCL – Upper control limit
LCL – Lower control limit
100
80


Are used for Statistical Process Contol
(SPC).
Mainly used in control phase, but can
also be used in measure and analyse.
40
Average
20
LCL
UCL
-20
1
2
3
4
5
6
7
8
9 10
-40
We look at the distribution of data to
determine variation.
◦
◦

I
0

60
Common Cause Variation – Natural variation
Special Cause Variation – Non natural variation
Control charts do not show customer
determined specifications.
◦
◦
USL - NO
LSL - NO
管理図
(c) Ewan Pettigrew
14

15. 
There are a number of control charts
around.
100
80
Also called Shewart charts after Walter
Shewart.





A large number of control charts used
in Six Sigma have control limits set at
3 standard deviations (3 Sigma on
each side of mean).
I-MR
X Bar – R
C Chart
U Chart
60
I
40
Average
20

LCL
0
UCL
-20
1
2
3
4
5
6
7
8
9 10
-40
(continuous data)
(attribute data)
(attribute data)
(attribute data)
管理図
(c) Ewan Pettigrew
15

16. 
I
I-MR
100

We start with this chart combination
as it is one of the simplest and
universally suitable control charts.
80

The I-MR chart is used where we are
measuring individual items or batches
of continuous data where we wish for
the subgroup size to equal one.
The chart is split into two sub-charts
being Individual and Moving Range.
◦
◦
I - detects trends and shifts in the process. Does
not have to be normally distributed.
MR - shows short term variability and stability in
process.
I
40
Average
20

60
LCL
0
UCL
-20
1
2
3
4
-40
5
6
7
8
9 10
MR
100
80
60
mR
40
Average
UCL
20
0
1
2
3
4
5
6
(c) Ewan Pettigrew
7
8
9 10
16

17. 
I
I
◦
◦
The Individuals chart measured values and
observation scales make the two axis. The centreline
is calculated from the average value of all
measurements.
The control limits are calculated as 3 standard
deviations of the data+ or - mean. We will use this
assumption from now on.


Shewart used mean + or - 2.66 * mean of moving range as
we are using sample and not population data. However, it is
more common to use the 3 Sigma method these days, even if
technically incorrect.
MR
◦
100
80
60
I
40
Average
20
LCL
0
UCL
-20
1
2
3
4
-40
The moving range chart uses artificially created
subgroup sizes of two to calculate the variation
between point. The centreline is calculated by ?????
5
6
7
8
9 10
MR
100
80
◦
The control limits are calculated as mean + - 3
standard deviations.


See above note.
Uses for I-MR
◦
Cycle time
◦
Limited number of measurements
60
mR
40
Average
UCL
20
0
1
2
3
4
5
6
7
8
9 10
管理図
(c) Ewan Pettigrew
17

18. 
x̄
◦
The X Bar chart looks at data which uses rational
subgroups. The chart analyses consistency of
averages for each subgroup. The centreline is
calculated as the average of the average of each
subgroup.
X
14.00
13.50
13.00
12.50

R
◦
◦

12.00
The R chart describes each subgroups ranges. The R
chart plots variation. Or the Max take min of each
subgroup. Therefore the centreline is calculated as
the mean of each subgroup’s variation.
11.50
11.00
1
3
The control Limits
Uses for X Bar – R
◦
When data is collected in groups
◦
Sfsafsf
◦
Sfsfsf
◦
sfsf
4.0
5
7
9
11 13 15 17 19 21 23 25
R
3.0
2.0
1.0
0.0
1 3 5 7 9 11 13 15 17 19 21 23 25
管理図
(c) Ewan Pettigrew
18

19. 
Western Electric Rules for symmetric
control limits.
◦
◦
Two out of three consecutive points fall beyond the
2σ limit on the same side of the centreline
◦
Four out of five consecutive points fall beyond the 1σ
limit on the same side of the centreline
◦

Any single data point falls outside the control limit
Seven consecutive points fall on the same side of the
centreline
Additional contemporary rules
◦
Seven points in a row going up or seven points in a
row going down
管理図
(c) Ewan Pettigrew
19

20. 
Histograms measure relative
frequency. In other words, which
frequencies occur most. Can look at
shape of histogram to see if it looks
like a normal distribution. Can see
spread and centring of data.
Pareto charts, run charts and control
charts look at the time domain.
Histogram
800
700
600
Frequency

500
400
300
200
More
87.74886017
73.06164513
58.37443009
29
43.68721504
Excel can not draw control lines or
mean on histograms without a plugin.
0
14.31278496

Each bin should have a count of
values which fall within that bin.
100
-0.374430086

The range of data is broken into bins.
-15.06164513

Bin
度数分布図
(c) Ewan Pettigrew
20

21. Used for descriptive statistics
Plots quartiles, Mean, and Median
Upper Adjacent Value
Also known as box and whisker
diagram where Whiskers can extend
outside.
Q3
Median
Show differences between populations.
Usually used to compare two or more
sets of data.
Mean
95% confidence of
mean
Q1
Show dispersion of data
Lower Adjacent Value
Show skewness of data
Excel can’t draw box plots. Must use
Minitab.
箱ひげ図
(c) Ewan Pettigrew
21

22. 



Hypothesis testing in its simplest
form is a selection of tests to
determine central
tendency, variance, or analyse
variance in sample data.
We use sample data as it is easier and
cheaper to collect than population
data.
We use the tools to test whether it is
likely that there are differences in the
parameters of the population, or
whether the distance may come from
sample variation.
Do not reject H0
(-1.96<z<1.96)
Converts a problem to a statistical
problem.
仮説検定
(c) Ewan Pettigrew
22

23. 
H0 – null hypothesis, no difference

H1 – alternate hypothesis, difference



H0 must be rejected if P value is less
than alpha level.
Type I error – Alpha Risk, probability
that we are wrong in saying that there
is a difference.
Do not reject H0
(-1.96<z<1.96)
Type II error – Beta Risk – probability
that we are wrong in saying that there
is no difference.
(c) Ewan Pettigrew
23

24. 



First if using T Tests or F Tests, we
must ensure that our data is normal.
We can use the histogram function in
Excel, or Minitab has a myriad of tools
to perform a Z test.
Measuring differences in the mean
Two sample T tests measure the
differences between the means of two
sets of normally distributed data. The
T test is used for continuous data.
Z Test for
normality
Test Mean
1 Sample T
Test
Test
Variance
F Test
2 Sample T
Test
Paired T
Test
仮説検定
(c) Ewan Pettigrew
24

25. 
1 sample t test compares expected
mean of population to target mean.
Therefore 1 sample t with an alpha
risk of .05 gives us 95% confidence
interval of where population mean
is. H0 is that sample is same as
target. If p-value is >0.05 fail to
reject H0.


Two sample T tests measure the
differences between the means of
two sets of normally distributed
data.


Paired T test for before and after

Z Test for
normality
Test Mean
1 Sample T
Test
Test
Variance
F Test
2 Sample T
Test
Paired T
Test
The T test is used for continuous data.
仮説検定
(c) Ewan Pettigrew
25

26. 
Excel command for T Test is
=TTEST(array1,array2,tails,type)






Where type =
1 Paired
2 Two-sample equal variance
(homoscedastic)
3 Two-sample unequal variance
(heteroscedastic)
.
Z Test for
normality
Test Mean
1 Sample T
Test
Test
Variance
F Test
2 Sample T
Test
Paired T
Test
(c) Ewan Pettigrew
26

27. 

Ranks failures by the severity of
resulting effects.
Proactively prevents failures from
happening before the event

Cl
a
ss
P
ot
e
nt
ia
l
C
a
u
s
e
s
of
F
ai
lu
re
O
cc
u
rr
e
n
c
e
C
u
rr
e
nt
C
o
nt
r
ol
s
D
et
R
P
N
A
ct
io
n
Pr
io
ri
ty
R
e
c
o
m
m
e
n
d
e
d
A
ct
io
n
s
R
e
s
p
o
n
si
bi
lit
y
a
n
d
T
ar
g
et
C
o
m
pl
et
io
n
D
at
e
A
ct
io
n
s
T
a
k
e
n
S
e
v
er
it
y
O
cc
u
rr
e
n
c
e
D
et
R
P
N
Then new RPN is issued.

S
e
v
er
it
y
Calls for corrective action.

P
ot
e
nt
ia
l
Ef
fe
ct
s
of
F
ai
lu
re
Output is a risk priority number (RPN).

P
ot
e
nt
ia
l
F
ai
lu
re
M
o
d
e
Risk management

It
e
m
/
F
u
n
ct
io
n
PFMEA and DFMEA
故障モード影響解析
(c) Ewan Pettigrew
27

28. 






Where we optimise the process
through experimentation.
We must have already identified the
critical few Xs.
We wish to find the effects that the Xs
have on the Y.
Fractional Factorials
Full Factorials
Response Surface Methods
This is all we will learn here. More
DOE shall be covered in a deeper
course.
(c) Ewan Pettigrew
28

29. 








Developed by Taiichi Ohno from
Toyota
Transportation
Inventory
Motion
Waiting
Over processing
Over production
Defects
Transportation
Motion
Inventory
Muda
Over Production
Remember these by thinking of the
name TIMWOOD.
Motion
Over Processing
Waiting
無駄
29

30. 



Whilst consulting for Kawasaki in the
1960s Dr. Ishikawa developed
fishbone diagrams as a simple cause
and effect tool.
The fishbone diagram is designed to
show causes of an unwanted event.
Effect
Most commonly in the manufacturing
environment, there are six major fish
bones being;
Methods, Machinery, Management, Ma
terials, Manpower, and Environment.
Secondary Level
Tertiary Level
From each major bone connects a
minor bone, which can again connect
to a smaller bone to flow back as far
as we wish to investigate. All bones or
causes shall flow to the effect.
根本原因分析
(c) Ewan Pettigrew
30

31. 

Another example is the 5 whys. The 5
whys involves asking why 5 times to
get to the root of the problem.
5 Whys Real Life Example

Speeding ticket

Why 1

Late for work

Why 2

Slept in

Why 3

Went to bed too late

Why 4

Soccer was on

Why5

Don’t have PVR

We can actually delve less or deeper.
However 5 levels seem to be a fair
depth.
根本原因分析
(c) Ewan Pettigrew
31

32. 

Poka Yoke is a Japanese term which
translates as mistake proofing. It is
sometimes mistakenly assumed to
translate as idiot proofing.
The innovators behind Poka Yoke
realised that the error was in the
process and not in the operator. Every
year, many highly regarded skilled
people make mistakes in their jobs.
Often this is through complacency
from zoning out, or after taking one
mistaken shortcut after 40 years.
ポカヨケ
(c) Ewan Pettigrew
32

33. 



Value stream maps are a type of
process map which detail data on
process performance. Value stream
mapping consists of creating three
maps being; the current state, ideal
state, and future state. The current
state can be based on the current
process map.
Value stream maps detail the full
value stream and may cross
organisational boundaries depending
on the level of detail required.
Value stream is all activities which
add value (and waste) to a product or
service
Simplified value stream map – car
servicing
Service
car
Enter in
log
book
Wash
car
50
S
10
s
30
s
Surf
internet
12
s
Check
log
book
34
s
Value streams show the movement of
information in one direction, and the
movement of material generally in the
opposite direction.
バリューストリームマッピング
(c) Ewan Pettigrew
33

34. 
Steps in the process are timed, and
marked as ‘Value Add, Business Value
Add, and Non Value Add’. The desired
end state is to remove the non value
add steps within the process.


Business value add (BVA) differs from
value add and non value add, as BVA
often cannot be removed from the
process, may be seen as inefficient by
the customer,. However BVA may be
required for regulatory requirements
or even to keep the business running.
バリューストリームマッピング
(c) Ewan Pettigrew
34

35. 
Even if a step is determined to be
value add, that does not mean that it
can not be modified to reduce time.
Title of VSM


Unlike traditional process maps, value
stream maps are most commonly
mapped backwards so as to be
starting from the customer’s
perspective.

We start with a current state VSM

Then we produce a future state VSM

Production
Control
Sup
plier
Custo
mer
Ste
p1
Ste
p2
I
V
A
NV
A
5
min
Ste
p4
I
I
7
min
20
min
Ste
p3
6
min
7
10
min
min
Total Lead Time =
277 Minutes
Value added time =
45 Minutes
Ste
p5
I
15
min
12
min
15
min
Must incorporate VOC requirements
Must incorporate VOB requirements
May use spaghetti diagram for layout
バリューストリームマッピング
(c) Ewan Pettigrew
35

36. 
The factory where the materials or
services are produced.

A step in the process or value stream.

Inventory.

The truck symbol to represent
movement of materials.

Push, where materials or services
move along a push system.

I
A human. Usually underneath a step
to show that a human is required to
control the relevant step.
バリューストリームマッピング
(c) Ewan Pettigrew
36

37. 
(manufacturing) supermarket.
C/T=

Data box symbol
C/O=
Batch=
Avail=

Physical pull symbol

Pull
バリューストリームマッピング
(c) Ewan Pettigrew
37

38. 
Manual information flow

Electronic information flow

Kaizen burst

Safety stock
バリューストリームマッピング
(c) Ewan Pettigrew
38

39. 
Steps to map current state









1. Gather voice of the customer
2. Walk through the process and
sketch the process
3. Enter the data boxes and
inventory levels
4. Document flow of goods to the
customer.
5. Gather information for the
suppliers.
6. Enter the information flows.
7. Sketch how material moves
between the processes.
8. Draw timelines for production
lead time and processing.
バリューストリームマッピング
(c) Ewan Pettigrew
39

40. 

Thank You
Hopefully we have satisfied your
requirements for a brief introduction
to Six Sigma.

More to come as time permits 

kanriconsulting@adam.com.au
(c) Ewan Pettigrew
40