Module 1 - Six Sigma Introduction
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Module 1 - Six Sigma Introduction
History of Six Sigma
• Established by Motorola in the 1980’s and still being developed. Seen as a cornerstone to the company’s culture.
• Companies adopting 6 Sigma include General Electric, Allied Signal, ABB, Sony, Lockheed Martin, Ford, Nissan and many others
• It is essential for companies to take responsibility for their own (unique) programme.
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What is Six Sigma?
• A systematic approach to process improvement.
• Processes can be related to design, manufacturing or administrative functions.
• It involves the use of statistical tools and techniques to analyse & improve processes.
• The relentless pursuit of variability reduction and defect elimination.
LSL USL
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LSL USL
Where can Six Sigma be applied?
• Six Sigma can be applied to all company processes
• A distinction is often made between:
• Design applications (Design for Six Sigma)
• Manufacturing applications (Operational Six Sigma)
• Administrative and Service applications (Transactional Six Sigma)
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Used in statistics as a measure of variation
σσσσ Sigma=
The Six Sigma Metric
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Standard Deviation
The central philosophy of 6 Sigma is the reduction
of variation in all our work processes
Lower
Spec.
Limit
Upper
Spec.
Limit y ±±±± 1σσσσ = 68.26%
y ±±±± 2σσσσ = 95.44%
y ±±±± 3σσσσ = 99.73%
The Normal Distribution
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The 3 Sigma mentality means 2700 defectives per million!
-1σσσσ +1σσσσ +2σσσσ-2σσσσ-3σσσσ +3σσσσ
y ±±±± 3σσσσ = 99.73%
y
(Target)
Lower
Specification
Limit
Upper
Specification
Limit
Normal Distribution
Centred on Target
The 6 Sigma Metric
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-6σσσσ -5σσσσ -4σσσσ -3σσσσ -2σσσσ -1σσσσ y +1σσσσ +2σσσσ +3σσσσ +4σσσσ +5σσσσ +6σσσσ
±±±±6σσσσ 99.999999999 0.002
±±±±5σσσσ 99.99994 0.6
±±±±4σσσσ 99.9937 63
Specification
Limit
Percent within Specification
(Centred Distribution)
Defects Per Million
(Centred Distribution)
±±±±3σσσσ 99.73 2700
Lower
Spec.
Limit
Upper
Spec.
Limit
2700
Defects per Million
From 3 Sigma to 6 Sigma
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Lower
Spec.
Limit
Upper
Spec.
Limit 0.002
±±±±1.5σσσσ Shift
Lower
Spec.
Limit
Upper
Spec.
Limit
Motorola’s 6 Sigma Metric
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Limit Limit
-6σσσσ -5σσσσ -4σσσσ -3σσσσ -2σσσσ -1σσσσ y +1σσσσ +2σσσσ +3σσσσ +4σσσσ +5σσσσ +6σσσσ
Calculating Sigma LevelNumber of defects or error opportunities per unit
O 4
Number of Units Processed N 100
Total No. of defects D 16
Defects per Unit DPU D / N 0.16
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Defects per Unit DPU D / N 0.16
Defects per opportunity DPO (DPU/O) D . N x O
0.04
Defects per Million Opportunity DPMO DPO x 10,00,000 40,000
Sigma Level 3.25
Yield 1-DPO 96%
SpecificationLimit
Percent withinSpecification
(Centred) σσσσ
Percent withinSpecification(1.5 shift)
Defectsper million(Centred)
Defectsper million(1.5σσσσ shift)
± 1σσσσ 68.26 30.23 317400 697700
± 2σσσσ 95.44 69.13 45600 308700
± 3σσσσ 99.73 93.32 2700 66810
Motorola’s 6 Sigma Metric
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± 3σσσσ 99.73 93.32 2700 66810
± 4σσσσ 99.9937 99.38 63 6210
± 5σσσσ 99.99994 99.98 0.6 233
± 6σσσσ 99.9999998 99.9997 0.002 3.4
Motorola’s definition of a 6 Sigma process is one
which achieves 3.4 defects per million or less.
• A Process with 10 Steps
• Each Process Step has a 3σ Quality Level = 93.32% Yield
• The probability of success (non-defective) at each step = 0.9332
• The probability of overall success = 0.933210 = 0.5008
• Overall Process Yield = 50.08% (499200 dpm)
6 Sigma & Defect Rates
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• Another Process with 10 Steps
• Each Process Step has a 6σ Quality Level = 99.99966% Yield
• The probability of success (non-defective) at each step = 0.9999966
• The probability of overall success = 0.999996610 = 0.999966
• Overall Process Yield = 99.9966% (34 dpm)
6 Sigma & Defect Rates
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•
The Hidden Factory
• To produce a defect uses production time, production capacity, energy, raw material….
• This all takes time, people, material, energy, floor space....
• It must be identified by testing and/or inspection, transported, stored, re-tested….
• Often this non-value added activity is not shown within the factory metrics - the “hidden” factory
• It must be reworked and then checked or scrapped and disposed of…
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Raw
MaterialsMixing Forming Cooling
Finished
Product
Final
Process Yield
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Final
Inspection
100% Pass
0% FailThis process has 100% yield. Our
customers would be very pleased.
Should we be just as happy?
0% Fail
7.5% of Units
Raw
MaterialsMixing Forming Cooling
Finished
Product
Final
Inspection0% Fail
Rework
& RepairRework
& Repair
Rolled Throughput Yield
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RTY = 0.925 x 0.94 x 0.95 = 0.826 = 82.6%
7.5% of Units
6% of Units
5% of Units 100% Pass
& RepairRework
& Repair
Define
Identify
Opportunity
Identify Key y’s
Measure
Analyse
DMAIC Improvement Process
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Identify Key y’s
(Outputs)
y = f(x)
Identify
Critical x’s
(Inputs) Optimise
x’s
Improve
Control
x’s
Control
Define ImproveMeasure Control� Control Critical x’s
� Monitor y’s
1 5 10 15 20
10.2
10.0
9.8
9.6
Upper Control Limit
Lower Control Limit
Analyse� Characterise x’s
� Optimise x’s
y=f(x1,x2,..)
y
x
. . .. . .. .. . .. . .
� Identify Potential x’s
� Analyse x’s
Run 1 2 3 4 5 6 7
1 1 1 1 1 1 1 1
Effect
C1 C2
C4
C3
C6C5
� Select Project
� Define Project Objective
� Form the Team
� Map the Process
� Define Measures (y’s)
� Evaluate Measurement System
� Determine Process
DMAIC Improvement Process
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� Validate Control Plan
� Close Project
y
Phase Review
� Set Tolerances for x’s
� Verify Improvement
15 20 25 30 35
LSL USL
Phase Review
� Select Critical x’s
Phase Review
1 1 1 1 1 1 1 12 1 1 1 2 2 2 23 1 2 2 1 1 2 24 1 2 2 2 2 1 15 2 1 2 1 2 1 26 2 1 2 2 1 2 17 2 2 1 1 2 2 18 2 2 1 2 1 1 2
x
xx
xx
xx
xx
x
x
� Identify Customer Requirements
� Identify Priorities
� Update Project File
Phase Review
� Determine Process Stability
� Determine Process Capability
� Set Targets for Measures
15 20 25 30 35
LSL USL
Phase Review
1. Define the Problem
2. Interim Actions8. Standardise and Future Actions
Problem Solving Process
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7. Verify the Results 3. Acquire and Analyse Data
4. Determine Root Cause
5. Evaluate Possible Solutions
6. Action Plan and Implement
A Few of the Six Sigma Tools!
Review Templates
FlowChart
Effect
Man
Maint. Method
Machine
Cause & EffectDiagram
y=f(x)y
RegressionAnalysis
MeasurementSystemVariation Reproducibility
Repeatability
Accuracy
StabilityCalibration
Gauge R&R
44 0 5 00 5 60 620 6 80 74 0
95 % C o n fide nc e In te rva l fo r M u
5 6 8 5 7 8 5 8 8 5 9 8 6 0 8
9 5% C on fid en ce In te rva l fo r M ed ian
V a ria b le : S A T
A-S q ua red :P -V a lu e :
M ea nS tD e vVa r ia n ceS k ew n e ssK u rtos isN
M in im um1s t Q u art i leM ed ian3rd Q ua rti leM ax im um
57 7.3 23
5 7 .1 59
57 0 .7 11
0 .32 90 .51 2
5 9 0 .24 0 6 5 .10 1
4 2 38 .0 82 .6 3 E -0 2-4 .0 E -0 1
10 0
4 2 6 .00 05 4 2 .25 05 9 8 .00 06 4 0 .00 07 4 0 .00 0
6 0 3 .15 7
7 5 .62 6
6 0 5 .00 0
A nd ers on -D ar l in g N o rm a lity T es t
9 5 % C on fid e nc e In te rv a l fo r M u
95 % C o n fide nc e In te rv a l fo r S ig m a
95 % C o n fide nc e In te rva l fo r M e d ia n
D e scrip tive S ta tis tic s
Minitab Software
A1 A2
Analysis of Variance
CustomerFocus
MAIC
ProcessValidation
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HistogramParetox
xxx
x
xx
xx
x
x
x
ScatterDiagram
y=f(x)y
x
ProcessCapability
FMEA
MistakeProofing
Control Charts
CRCL
Test Statistic
Value
Test Statistic
Distribution
Hypothesis Testing