# 1 - BSI - 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.
What is Six Sigma?

LSL   USL

• A systematic approach to process
improvement.
• Processes can be related to design,
• It involves the use of statistical tools and      LSL   USL
techniques to analyse & improve processes.
• The relentless pursuit of variability reduction
and defect elimination.
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)
The Six Sigma Metric

σ       =      Sigma
Used in statistics as a measure of variation

Standard Deviation

The central philosophy of 6 Sigma is the reduction
of variation in all our work processes
The Normal Distribution

Lower                             Upper
Spec.                             Spec.
Limit                             Limit         y ± 1σ = 68.26%
σ
y ± 2σ = 95.44%
σ
y ± 3σ = 99.73%
σ

-3σ
σ    -2σ
σ   -1σ y
σ         +1σ +2σ +3σ
σ   σ   σ
(Target)

The 3 Sigma mentality means 2700 defectives per million!
The 6 Sigma Metric
Normal Distribution
Lower               Centred on Target                    Upper
Specification                                            Specification
Limit                                                    Limit

-6σ -5σ -4σ -3σ
σ   σ   σ   σ   -2σ
σ     -1σ
σ   y    +1σ +2σ +3σ +4σ +5σ +6σ
σ   σ   σ   σ   σ   σ

Specification     Percent within Specification         Defects Per Million
Limit            (Centred Distribution)           (Centred Distribution)

±3σ
σ                       99.73                         2700
±4σ
σ                      99.9937                         63
±5σ
σ                      99.99994                       0.6
±6σ
σ                    99.999999999                    0.002
From 3 Sigma to 6 Sigma

Lower            Upper    Defects per Million
Spec.            Spec.
Limit            Limit

2700

Lower            Upper
Spec.            Spec.
Limit            Limit        0.002
Motorola’s 6 Sigma Metric

±1.5σ Shift
σ

Lower                                              Upper
Spec.                                              Spec.
Limit                                              Limit

-6σ -5σ -4σ -3σ -2σ
σ σ     σ   σ   σ   -1σ
σ   y   +1σ +2σ +3σ +4σ +5σ +6σ
σ   σ   σ   σ   σ   σ
Motorola’s 6 Sigma Metric

Percent within   Percent within    Defects       Defects
Specification      Specification    Specification    per million   per million
Limit             (Centred)       (1.5 σ shift)   (Centred)     (1.5σ shift)
σ

± 1σ             68.26           30.23          317400        697700
± 2σ
σ              95.44          69.13           45600         308700
± 3σ             99.73           93.32           2700          66810
± 4σ
σ            99.9937          99.38            63            6210
± 5σ
σ            99.99994         99.98            0.6           233
± 6σ           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.
6 Sigma & Defect Rates

A Process with 10 Steps

Each Process Step has a 3σ Quality Level = 93.32% Yield
σ
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

Another Process with 10 Steps

Each Process Step has a 6σ Quality Level = 99.99966% Yield
σ
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)
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….
• It must be reworked and then checked or scrapped and disposed
of…
• Often this non-value added activity is not shown within the factory
metrics - the “hidden” factory
Process Yield

Raw                                                Finished
Mixing       Forming      Cooling
Materials                                           Product

This process has 100% yield. Our                      Final
0% Fail      Inspection
Should we be just as happy?

100% Pass
Rolled Throughput Yield

Raw                                                          Finished
Mixing           Forming         Cooling
Materials                                                     Product

Rework
& Repair                                          Final
Inspection   0% Fail
0%
Rework
7.5% of Units       & Repair
Rework
6% of Units          & Repair
5% of Units   100% Pass

RTY = 0.925               x    0.94      x      0.95 = 0.826 = 82.6%
DMAIC Improvement Process

Define

Measure
Identify
Opportunity                      Analyse
Identify Key y’s
(Outputs)                      Improve
Identify
Critical x’s
Control

y = f(x)                          (Inputs)      Optimise
x’s
Control
x’s
DMAIC Improvement Process
Define               Measure                           Analyse                           Improve                               Control
Select Project        Define Measures (y’s)           Identify Potential x’s           Characterise x’s                       Control Critical x’s
Define Project

.. .. .
C1 C2 C3                                                          10.2
Objective                                                                              y                                                    Upper Control Limit

Form the Team
Evaluate Measurement
System
Effect         .. .
. ..
10.0

9.8                 Lower Control Limit
x
C4 C5 C6                              y=f(x1,x2,..)                9.6
1    5   10        15        20

Analyse x’s                      Optimise x’s                           Monitor y’s
Run 1    2   3   4   5   6   7
Map the Process
Determine Process               1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
Identify Customer     Stability                       3   1   2   2   1   1   2   2
4   1   2   2   2   2   1   1
Requirements                                          5   2   1   2   1   2   1   2                                                           y
Determine Process               6   2   1   2   2   1   2   1
7   2   2   1   1   2   2   1
Capability                      8   2   2   1   2   1   1   2

Set Tolerances for x’s                 Validate Control
LSL        USL         Select Critical x’s
Verify Improvement                     Plan
xx
x x
x x                                LSL        USL
15    20   25   30    35
x x
Identify Priorities                                               x
Set Targets for                            x
Update Project File   Measures                                                                                                Close Project
x
15    20   25   30    35

Phase Review           Phase Review                     Phase Review                       Phase Review                         Phase Review
1. Define the Problem

8. Standardise and Future Actions                            2. Interim Actions

Problem Solving
7. Verify the Results
Process                            3. Acquire and Analyse Data

6. Action Plan and Implement                           4. Determine Root Cause
5. Evaluate Possible Solutions
A Few of the Six Sigma Tools!
Review                                                                                                                                                           Accuracy                        Analysis of Variance
Cause & Effect
Templates                                                                                                                                                                         Calibration
Diagram                                                                                                              Measurement                                                           Stability
M
System
Man Machine              A                                                                                                                                                              Reproducibility
Variation
I                                                                                                                                                                               Gauge R&R

Effect       C                                                                                                                                                             Repeatability                           A1 A2

Minitab Software                                                                                                                                                                                Customer
Maint. Method                                                                  D e s c rip tive S ta tis tic s                                                                               Process                                     Focus
V a ria b le : S A T

A n d e r s o n - D a r lin g N o r m a lity T e s t
A- S q u a r e d :
P - V a lu e :
0 .3 2 9
0 .5 1 2
Validation                      Flow
M ea n                          5 9 0 .2 4 0
S tD e v                          6 5 .1 0 1

Chart
Va r ia n c e                   4 2 3 8 .0 8
Sk ew n e ss                  2 .6 3 E - 0 2
K u r to s is                  - 4 .0 E - 0 1
N                                      10 0
44 0      5 00            5 60           620            6 80       74 0

Regression                                  9 5 % C o n fid e n c e In te r v a l fo r M u
M in im u m
1 s t Q u a r tile
M e d ia n
3 r d Q u a r tile
M a x im u m
4 2 6 .0 0 0
5 4 2 .2 5 0
5 9 8 .0 0 0
6 4 0 .0 0 0
7 4 0 .0 0 0

Analysis
9 5 % C o n fid e n c e In te r v a l fo r M u
5 7 7 .3 2 3                   6 0 3 .1 5 7
568           5 78                     5 88                59 8                 60 8       9 5 % C o n fid e n c e In te rv a l fo r S ig m a
5 7 .1 5 9                       7 5 .6 2 6
9 5 % C o n fid e n c e In te r v a l fo r M e d ia n
9 5 % C o n fid e n c e In te r v a l fo r M e d ia n
5 7 0 .7 1 1                   6 0 5 .0 0 0

y      y=f(x)
Design of Experiments                                                                                                                                          Robust Design
Run            A                B                    C                     D                 E          F                     G                           y   Tolerance Design
1              1                1                    1                     1                 1         1                      1                   y1
2              1                1                    1                     2                 2         2                      2                   y2
3              1                2                    2                     1                 1         2                      2                   y3
x
4              1                2                    2                     2                 2         1                      1                   y4
Scatter             FMEA
5              2                1                    2                     1                 2         1                      2                   y5
6              2                1                    2                     2                 1         2                      1                   y6                                    Diagram
7              2                2                    1                     1                 2         2                      1                   y7
8              2                2                    1                     2                 1         1                      2                   y8
Process                                                                                                                                                                                                               x
Mistake                 x x
Capability
Pareto                                                                                    Histogram                                                           Proofing            x
x x x
x
x x
x x

```
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 views: 18 posted: 5/13/2011 language: English pages: 19
Description: BSI: Standards, Training, Testing, Assessment & Certification