SIX SIGMA

Ruben Guajardo
MS&E 269

Deepak Navnith

Victor Torres

Kuan Zhang

Professor:

Neil Kane

A STRATEGY FOR PERFORMANCE
EXCELLENCE

March 16th, 2001

SIX SIGMA
How good is good enough?

99.9% is already VERY GOOD

But what could happen at a quality level of 99.9% (i.e., 1000 ppm),

in our everyday lives (about 4.6)?

• 4000 wrong medical prescriptions each year

• More than 3000 newborns accidentally falling
from the hands of nurses or doctors each year

• Two long or short landings at American airports each day

• 400 letters per hour which never arrive at their destination

SIX SIGMA
How can we get these results

• 13 wrong drug prescriptions per year

• 10 newborn babies dropped by
doctors/nurses per year

• Two short or long landings per year in all
the airports in the U.S.

• One lost article of mail per hour

SIX SIGMA
The answer is:

Six Sigma

SIX SIGMA
What is Six Sigma

 A Vision and Philosophical commitment
to our consumers to offer the highest quality,
lowest cost products

 A Metric that demonstrates quality levels at
99.9997% performance for products and
processs

 A Benchmark of our product and process
capability for comparison to ‘best in class’

 A practical application of statistical Tools
and Methods to help us measure, analyze,
improve, and control our process

SIX SIGMA
Six Sigma as a Philosophy

 is a measure of how much
Internal &

Prevention & variation exists in a process
External

Appraisal
Failure

Costs
Costs

Old Belief
Old Belief

4 High Quality = High Cost

Quality

Internal & Prevention &
External Appraisal
Failure Costs Costs

New Belief 4

New Belief
High Quality = Low Cost 5

6

Quality

Costs

Costs

SIX SIGMA
3 Sigma Vs. 6 Sigma

The 3 sigma Company The 6 sigma Company
• Spends 15~25% of sales dollars • Spends 5% of sales dollars on
on cost of failure cost of failure

• Relies on inspection to find • Relies on capable process that
defects don’t produce defects

• Does not have a disciplined • Use Measure, Analyze, Improve,
approach to gather and analyze Control and Measure, Analyze,
data Design

• Benchmarks themselves • Benchmarks themselves
against their competition against the best in the world

• Believes 99% is good enough • Believes 99% is unacceptable

• Define CTQs internally • Defines CTQs externally

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Focus: The End User

• Customer: Internal or External

• Consumer: The End User

the “Voice of the Consumer” (Consumer Cue)

must be translated into

the “Voice of the Engineer” (Technical Requirement)

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Six Sigma as a Metric


(xi  x)2

   =
Sigma =  = Deviation n1
( Square root of variance )

Axis graduated in Sigma

between + / – 1 68.27 % result: 317300 ppm outside
(deviation)

between + / – 2 95.45 % 45500 ppm

between + / – 3 99.73 % 2700 ppm

between + / – 4 99.9937 % 63 ppm

between + / – 5 99.999943 % 0.57 ppm

between + / – 6 99.9999998 % 0.002 ppm

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

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3-sigma Process Spec Limits

(centered)
Cp = 1.0
Cpk = 1.0
2,700 ppm

SIX SIGMA
3-sigma Process Spec Limits

(shifted 0.5 std. dev.)
Cp = 1.0

Cpk = 0.833
ppm = 6,442

(about 2.72-sigma)

SIX SIGMA
3-sigma Process Spec Limits

(shifted 1.0 std. dev.)
Cp = 1.0

Cpk = 0.667
ppm = 22,782

(about 2.28-sigma)

SIX SIGMA
3-sigma Process Spec Limits

(shifted 1.5 std. dev.)
Cp = 1.0

Cpk = 0.5
ppm = 66,811

(about 1.83-sigma)

SIX SIGMA
Non-Liner Decrease

 PPM

2 308,537
80 800000

70 From 5 to 6 700000

3 66,811 60 600000

50 500000
PPM % Change

40 400000

4 6,210
30 From 4 to 5 300000

20 200000
From 3 to 4

5 233 10 100000
From 1 to 2

0 0

6 3.4 1 2 3 4 5 6

Process Sigma

Process Defects per Million
Capability Opportunities

* Includes 1.5 shift

Focusing on  requires thorough process
understanding and breakthrough thinking

% Change

PPM

SIX SIGMA
Six Sigma as a Tool

Process Mapping Tolerance Analysis

Structure Tree Components Search

Pareto Analysis Hypothesis Testing

Gauge R & R Regression

Rational Subgrouping DOE

Baselining SPC

Many familiar quality tools applied in a
structured methodology

SIX SIGMA
Six Sigma as a Method

To get results, should we focus our behavior on the Y or X

•Y •X1…Xn

•Dependent •Independent

•Output •Input-Process

•Effect •Cause

•Symptom •Problem

•Monitor •Control

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A Traditional View

Market Share

Sales Growth
• Output Variables

Profitability

Manage the outputs.

A NonS-ITXr aSdIGitiMonAal View

Product Quality

COQ Service

• Input Variables On-Time Delivery

Relationships
Credit Terms

Customer
Training

Customer Satisfaction

Market Share

Sales Growth
• Output Variables

Profitability

Manage the inputs; respond to the outputs.

DistinSIgXu SisIhG “MVAital Few”
from “Trivial Many”

Material Environment

Measurements

Methods Process
Output

(Parameters)
Machine

People

Define the Problem / Defect Statement

Y = f ( x *
1 , x2, x3, x

*
4 , x5. . . Xn)

Y = Dependent Variable Output, Defect
x = Independent Variables Potential Cause
x* = Independent Variable Critical Cause

Measure

SIX SIGMA
Strategy by Phase –

Improvement

Phase Step Focus

Process Characterization
Measure What is the frequency of Defects? Measure

(What) • Define the defect Y
• Define performance standards Y
• Validate measurement system Y

Improve

• Establish capability metric Y
Measure

Analyze Where, when and why do Defects occur?

(Where, When, Why) • Identify sources of variation X
• Determine the critical process parameters Vital X

Improve

Process Optimization
Improve How can we improve the process? Measure

(How) • Screen potential causes X
• Discover relationships Vital X
• Establish operating tolerances Vital X

Improve

Were the improvements effective?
• Re-establish capability metric Y, Vital X

Measure

Control How can we maintain the improvements? Y, Vital X

(Sustain, Leverage) • Implement process control mechanisms
• Leverage project learning’s Improve

• Document & Proceduralize

Analyze Analyze Analyze Analyze

Control Control Control Control

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Six Sigma Organization

SIX SIGMA
A Black Belt has…, and will…

Leadership Driving the Use

BlaScIXk SBIeGlMt TAraining
Time on

Related
Task Consulting/ Mentoring

Projects
Training

Green Utilize
Find one

Statistical/
2%~5% new green 2 / year

Belt Quality
belt

technique

Lead use
of

Black technique
Two green

and 5%~10% 4 / year
Belt belts

communic-
ate new
ones

Master
Consulting/

Five Black
Black Mentoring/ 80~100% 10 / year

Belts
Training

Belt

Core Statistical Skills Core Six Sigma Quality Skills Core Interpersonal Skills

GBM Statistical Software (JMP, MiSnitab) G
MIN101 IXBM ASIEG IQMGS MA GBM Communication (oral, written)

AEC722, DDI121

GBM Numerical and Graphical Techniques GBM QS 9000 GBM Team Facilitation
MIN101, IBM548 AEC279 DDI170

GBM Statistical Process Control GBM Customer Satisfaction GBM Coaching and Mentoring
AEC506, AEC661, AEC662, AEC663 SSG100, TCS100 LDR380, PER119

GBM Process Capability GBM Six Steps to Six Sigma GBM Managing Change
AEC661, AEC662, SCP201 SSG100, SSG102CD MGT564, MGT124, PDE532

GBM Comparative Tests GBM Concurrent Engineering BM Leadership
MIN101, SPC201 MGT561, MGT562, DDI180

GBM Analysis of Variance (ANOVA) GBM TCS BM Team Building
ENG998, AEC603 TCS100 MGT560, MGT562, EC727, MGT155

GBM Measurement System Analysis GBM Systemic Approach to Problem M Instructional/Teaching
AEC663 Solving MOT132

QUA392

GBM Design of Experiments (e.g. Full, GBM Team Oriented Problem Solving M Managing Projects
Fractional, Taguchi Designs) (8D, 7D, 5P)
ENG998, QUA389 AEC471, MGT839

GBM Regression (e.g. linear, nonlinear) BM Quality System Review
QUA590

GBM Statistical Process Characterization BM Team Problem Solving Non-
Strategies and Techniques Manufacturing
ENG227 CES103

BM Statistical Inference BM Design for Manufacturability
MIN101, SPC201

ENG123, ENG123CD

BM Confidence Intervals BM Financial/Economic Quality Issues
MIN101, SPC201

BM Probability Concepts and M Quality Function Deployment
Distributions
SPC201 QUA200A, QUA200B, QUA200C

BM Response Surface Methods M Total Quality Management
QUA393

BM Screening DOE M Benchmarking
QUA391 BMK220

M Advanced Problem Solving M Product Development Assessment
Strategies and Technologies
ENG998

M Acceptance Sampling
SPC201

M Sample Size Estimation

M Robust Design of Processes and
Products

M Survival Analysis / Reliability

SIX SIGMA
Corporate Commitment

Motorola is committed to developing these leaders…

We provide these people with extensive training in statistical
and interpersonal tools, skilled guidance and management
support…

Once their development has achieved a level worthy of
recognition, we even have a term for those exceptional
individuals :

Six Sigma Black Belts

Chris Galvin

SIX SIGMA
Corporate Commitment (Cont’d)

• Motto:

– Quality is our job

– Customer satisfaction is our duty

– Customer loyalty is our future

SIX SIGMA
Barrier Breakthrough Plan

Pareto, Brainstorming, C&E, BvC
SIGMA

100.00 8D, 7D, TCS Teams, SPC
5.3

DOE, DFM, PC
5.4

RenewBlack Belt Program (Internal Motorola)
5.5

5.6
5.65

Black Belt Program (External Suppliers)
10.00

Proliferation of Master Black Belts
6 Sigma

6

MY95 MY96 MY97 MY98
1.00

J94 J95 J96 J97

DPMOp

Other CSoIXm SpIaGnMieAs have Black
Belts Program

• GE has very successfully instituted this program
– 4,000 trained Black Belts by YE 1997
– 10,000 trained Black Belts by YE 2000
– “You haven’t much future at GE unless they are selected to

become Black Belts” – Jack Welch

• Kodak has instituted this program
– CEO and COO driven process
– Training includes both written and oral exams
– Minimum requirements: a college education, basic statistics,

presentation skills, computer skills

• Other companies include:
– Allied Signal -Texas Instruments
– IBM – ABB
– Navistar – Citibank

SIX SIGMA

Measure
Characterize Process

Evaluate Control
Understand Process Maintain New Process

Improve
Improve and Verify Process

SIX SIGMA

Measure Phase

Define Understand Collect Process
Problem Process Data Performance

 Defect  Define Process-  Data Types  Process Capability
Statement Process Mapping – Defectives – Cp/Cpk

 Project  Historical – Defects – Run Charts
Goals Performance – Continuous  Understand Problem

 Brainstorm  Measurement (Control or
Potential Defect Systems Evaluation Capability)
Causes (MSE)

Understand the Process and Potential Impact

SIX SIGMA

Problem Definition
 What do you want to improve?
 What is your ‘Y’?

Reduce
Complaints

(int./ext.)

Reduce Reduce
Defects Cost

What are the Goals?

Problem Definitions need to be based on
quantitative facts supported by analytical data.

SIX SIGMA

Baselining:
Quantifying the goodness (or badness!) of the current
process, before ANY improvements are made, using
sample data. The key to baselining is collecting
representative sample data

Sampling Plan
– Size of Subgroups
– Number of Subgroups
– Take as many “X” as possible into consideration

SIX SIGMA

How do we know our process?

Process Map

Fishbone

Historical Data

SIX SIGMA
RATIONAL SUBGROUPS

Minimize variation within subroups

BLACK NOISE Maximize variation between subrgoups
(Signal)

WHITE NOISE
(Common
Cause Variation)

TIME

RATIONAL SUBROUPING Allows samples to be taken that
include only white noise, within the samples. Black noise

occurs between the samples.

PROCESS
RESPONSE

SIX SIGMA

SIX SIGMA

Visualizing the Causes
Within Group

Time 1

Time 2

Time 3

Time 4

•Called  short term (st)

 st + shift = •Our potential – the best

 we can be
total

•The s reported by all 6
sigma companies

•The trivial many

SIX SIGMA

Visualizing the Causes

Time 1

Time 2

Time 3

Time 4
•Called shift (truly a
measurement in sigmas of how
far the mean has shifted)

•Indicates our process control
 st + shift = total •The vital few

Between Groups

SIX SIGMA

Assignable Cause
• Outside influences

• Black noise

• Potentially controllable

• How the process is actually performing
over time

Fishbone

SIX SIGMA

Common Cause Variation
• Variation present in every process

• Not controllable

• The best the process can be within the
present technology

Data within subgroups (Z.st) will contain only Common Cause
Variation

SIX SIGMA

Gauge R&R

2
Total = 2

Part-Part + 2
R&R

Recommendation:

Resolution 10% of tolerance to measure
Gauge R&R  20% of tolerance to measure

R&R
Part-Part

• Repeatability (Equipment variation)
Variation observed with one measurement device when used several times by one operator
while measuring the identical characteristic on the same part.

• Reproducibility (Appraised variation)
Variation Obtained from different operators using the same device when measuring the
identical characteristic on the same part.

•Stability or Drift
Total variation in the measurement obtained with a measurement obtained on the same
master or reference value when measuring the same characteristic, over an extending time
period.

SIX SIGMA

Map the Process

Identify the variables – ‘x’

Measure the Process

Understand the Problem –
’Y’ = function of variables -’x’

Y=f(x)

To understand where you want to be,
you need to know how to get there.v

SIX SIGMA

Measure
Characterize Process

Evaluate Control
Understand Process Maintain New Process

Improve
Improve and Verify Process

SIX SIGMA

In many cases, the data sample can be transformed so that it is approximately normal.
For example, square roots, logarithms, and reciprocals often take a positively skewed
distribution and convert it to something close to a bell-shaped curve

SIX SIGMA
What do we Need?

LSL USL LSL USL

Off-Target, Low Variation On Target
High Potential Defects High Variation
Good Cp but Bad Cpk High Potential Defects

No so good Cp and Cpk
LSL USL

 Variation reduction and process
centering create processes with
less potential for defects.
 The concept of defect reduction
applies to ALL processes (not just

On-Target, Low Variation manufacturing)
Low Potential Defects
Good Cp and Cpk

SIX SIGMA

Eliminate “Trivial Many”

 Qualitative Evaluation
 Technical Expertise
 Graphical Methods
 Screening Design of Experiments Identify “Vital Few”

 Pareto Analysis
 Hypothesis Testing
 Regression

Quantify
 Design of Experiments

Opportunity

 % Reduction in Variation Our Goal:
 Cost/ Benefit

Identify the Key Factors (x’s)

SIX SIGMA

Graph>Box plot Graph>Box plot

DBP

Without X values 10

9

75% 10

DBP
4

109 99 Day DBP

10
104 94

50% 9

99
10

94
DBP 4

25%
10 99 Operator

9 94

10

4

99 Shift

Box plots help to see th94e data distribution

SIX SIGMA

Statistical Analysis
Apply statistics to validate actions & improvements

Hypothesis Testing

7 30

6

5
20

4

3

10
2

1

0 0

0.000 0.005 0.010 0.015 0.020 0.025 0.000 0.005 0.010 0.015 0.020 0.025

New Machine Machine 6 mths

RegressiRoegnre sAsionn Palotlysis
Y = 2.19469 + 0.918549X  Is the factor really important?

R-Sq = 86.0 %

60

50  Do we understand the impact for
40 the factor?
30

20

10 Regression  Has our improvement made an
95% PI

0

impact
5 15 25 35 45 55

X

 What is the true impact?

Y
Frequency

Frequency

SIX SIGMA

poor 2.5 A B
2.0

1.5

1.0
Zshift C D

0.5

1 2 3 4 5 6
good poor TECHNOLOGY good

ZSt

A- Poor Control, Poor Process

B- Must control the Process better, Technology is fine

C- Process control is good, bad Process or technology

D- World Class

CONTROL

SIX SIGMA
M.A.D

Six Sigma Design Process
Stop

Adjust

Technical process &
design

Requirement

Con- Preliminary Identify
Obtain Data on Calculate Z Rev 0

sumer Drawing/Database Critical
Similar Process values Drawings

Cue Process
Identity
CTQs

Stop
Fix process

1st piece & design
inspection

Z<3

Prepilot Recheck
Data Obtain data ‘Z’ levels

Z>= Design Intent
M.A.I.C

Pilot data

SIX SIGMA
Reliability (Level)
Time to install
Total Electricity Usage Req’d for System
Time to Repair
Floor space occupied NO INPUT IN THIS AREA
Sensor Resolution
Response time to power loss
Voltage
Power
Time to supply Backup Power
backup power capacity (time)
Sensor Sensitivity
Floor Loading
Time Between maintenance
Time between equipment replacement
Safety Index Rating
Cost of investment
Cost of maintenace
Cost of installation
Years in Mainstream market
Customer Support Rating
Dependency on weather conditions
ECO-rating
Hours of training req’d

Preferred up dwn dwn dwn dwn dwn dwn tgt tgt dwn dwn tgt dwn up up

Engineering Metrics

Customer Requirements
1 Fast Response 9
2 Long time of backup power supply 9
3 Low environmental impact 9
4 Safe to operate 9
5 Meet power requirements 9
6 Low investment cost 3
7 Occupies small floor space 3
8 Easy to upgrade 3
9 Low upgrading costs 3

10 Low time to implement 3
11 Cheap to maintain 3
12 Low recovery or cycle time 3
13 Long life cycle of the system/component 1
14 Cheap to operate 1
15 Cheap to install 1
16 Long Existing proven technology 1

• #1 Define the customer Cue and technical requirement we
need to satisfy

Consumer Cue: Blocks Cannot rattle and must not
interfere with box

Technical Requirement: There must be a positive Gap

Customer Weights

Reliability (Level)

Time to install

Total Electricity Usage Req’d for System

Time to Repair

Floor space occupied

Sensor Resolution

Response time to power loss

Voltage

Power

Time to supply Backup Power

backup power capacity (time)

Sensor Sensitivity

Floor Loading

Time Between maintenance

Time between equipment replacement

Safety Index Rating

Cost of investment

Cost of maintenace

Cost of installation

Years in Mainstream market

SIX SIGMA

• #2 Define the target dimensions (New designs) or
process mean (existing design) for all mating Parts

Gap

Gap Must Be T=.011, LSL=.001 and USL = .021

SIX SIGMA

(+) Gap Requirements

(-) (-) (-) (-)
mT = .010
USL = .020
LSL = .001

Step #3

• Gather process capability data.

• Use actual or similar part data to calculate SS of
largest contributors.

• May use expert data for minimal contributors

• Do not calculate s from current tolerances

SIX SIGMA

(+) From process:
Average st

(-) (-) (-) (-)
Cube 1.250 .001
Box 5.080 .001

mgap= mbox – mcube1 – mcube2 – mcube3 – mcube4 Zshift = 1.6

gap = 2
box + 2

cube1 + 2
cube2 + 2

cube3 + 2
cube4

Short Term

mgap= 5.080 – 1.250 – 1.250 – 1.250 – 1.250.016

gap = (.001)2 + (.001)2 + (.001)2 + (.001)2 + (.001)2 = .00224

Long Term

gap = (.0015)2 + (.0015)2 + (.0015)2 + (.0015)2 + (.0015)2 = .00335

SIX SIGMA

Measure
Characterize Process

Evaluate Control
Understand Process Maintain New Process

Improve
Improve and Verify Process

SIX SIGMA

What Do I need to do to improve my Game?

6

GUTTER!

SIX SIGMA

Design of Experiments (DOE)

• To estimate the effects of independent Variables on
Responses.

X Y
PROCESS

• Terminology
Factor – An independent variable
Level – A value for the factor.
Response – Outcome

SIX SIGMA
THE COFFEE EXAMPLE

Level
Factor

Low High
Coffee Brand Maxwell House Chock Full o Nuts

Water Spring Tap

Coffee Amount 1 2

SIX SIGMA
Main Effects: Effect of each individual factor on response

3.7

ME

2.2

Bean ‘A’ Bean ‘B’

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Concept of Interaction

Bean ‘A’ Bean ‘B’
Temp ‘X’ Temp ‘Y’

SIX SIGMA

Why use DoE ?

• Shift the average of a process.
x1 x2

• Reduce the variation.

• Shift average and reduce variation

SIX SIGMA

DoE techniques

• Full Factorial.
4

2 = 16 trials

2 is number of levels

4 is number of factors

• All combinations are tested.

• Fractional factorial can reduce number of

trials from 16 to 8.

SIX SIGMA

DoE techniques….contd.
• Fractional Factorial

• Taguchi techniques

• Response Surface Methodologies

• Half fraction

SIX SIGMA
Mini Case – NISSAN MOTOR COMPANY

Level
Factor

High Low

Adhesion Area (cm2) 15 20
Type of Glue Acryl Urethan
Thickness of Foam Styrene Thick Thin
Thickness of Logo Thick Thin
Amount of pressure Short Long
Pressure application time Small Big
Primer applied Yes No

SIX SIGMA

Design Array

No A B C D Gluing Str

1 + + + – 9.8
2 + + – – 8.9

A – Adhesion Area (cm2)
3 + – + +

B – Type of Glue 9.2
4 + – – +

C – Thickness of Foam ` 8.9
Styrene 5 – + + – 12.3
D – Thickness of Logo 6 – + – – 13

7 – – + + 13.9
8 – – – + 12.6

Effect Tabulation

A B C D
+ 4.60 5.50 5.65 5.58
– 6.48 5.58 5.43 5.50

SIX SIGMA

Factor Effect Plot

6.5
5.58 5.65 5.58

5.5 5.43 5

4.6

＋ – ＋ – ＋ – ＋ –

Adhesion Thk of logo
Area Type of Glue Thk of Foam

Styrene

SIX SIGMA

STEPS IN PLANNING AN EXPERIMENT

1. Define Objective.

2. Select the Response (Y)

3. Select the factors (Xs)

4. Choose the factor levels

5. Select the Experimental Design

6. Run Experiment and Collect the Data

7. Analyze the data

8. Conclusions

9. Perform a confirmation run.

SIX SIGMA

“….No amount of experimentation can prove
me right; a single experiment can prove me

wrong”.

“….Science can only ascertain what is, but
not what should be, and outside of its domain

value judgments of all kinds remain
necessary.”

– Albert Einstein

SIX SIGMA

Measure
Characterize Process

Evaluate Control
Understand Process Maintain New Process

Improve
Improve and Verify Process

SIX SIGMA

CONTROL PHASE – SIX SIGMA

Control Phase Activities:

-Confirmation of Improvement
-Confirmation you solved the practical problem
-Benefit validation
-Buy into the Control plan
-Quality plan implementation
-Procedural changes
-System changes
-Statistical process control implementation
-“Mistake-proofing” the process
-Closure documentation
-Audit process
-Scoping next project

SIX SIGMA

CONTROL PHASE – SIX SIGMA

How to create a Control Plan:

1. Select Causal Variable(s). Proven vital few X(s)
2. Define Control Plan

– 5Ws for optimal ranges of X(s)
3. Validate Control Plan

– Observe Y
4. Implement/Document Control Plan
5. Audit Control Plan
6. Monitor Performance Metrics

SIX SIGMA

CONTROL PHASE – SIX SIGMA

Control Plan Tools:

1. Basic Six Sigma control methods.
– 7M Tools: Affinity diagram, tree diagram, process

decision program charts, matrix diagrams,
interrelationship diagrams, prioritization matrices,
activity network diagram.

2. Statistical Process Control (SPC)
– Used with various types of distributions
– Control Charts

•Attribute based (np, p, c, u). Variable based (X-R, X)
•Additional Variable based tools

-PRE-Control
-Common Cause Chart (Exponentially Balanced
Moving Average (EWMA))

SIX SIGMA

AFFINITY DIAGRAM

INNOVATION
CHARACTERISTICS:

PRODUCT
MANAGEMENT • Organizing ideas into meaningful

OVERALL categories
GOAL OF

SOFTWARE • Data Reduction. Large numbers of qual.
Inputs into major dimensions or categories.

KNOWLEDGE OF
COMPETITORS

METHODS TO MAKE
EASIER FOR USERS

PRODUCT PRODUCT OUTPUT SUPPORT
DESIGN MANAGEMENT

PRODUCT PRODUCT INTUITIVE
DESIGN MANAGEMENT ANSWERS

SUPERVISION DIRECTORY
ORGANIZATION

SIX SIGMA

MATRIX DIAGRAM

HOWS

RELATIONSHIP
MATRIX

CUSTOMER
WHATS IMPORTANCE

MATRIX

Arrive at scheduled time 5 5 5 5 1 5 0 0 0 0 0
Arrive with proper equipment 4 2 0 0 5 0 0 0 0 0 0
Dressed properly 4 0 0 0 0 0 0 0 0 0 0
Delivered via correct mode 2 3 0 0 1 0 0 0 0 0 0
Take back to room promptly 4 0 0 0 0 0 0 5 5 5 5

IMPORTANCE SCORE 39 25 25 27 25 0 20 20 20 20
RANK 1 3 3 2 3 7 6 6 6 6

5 = high importance, 3 = average importance, 1 = low importance

Patient scheduled

Attendant assigned

Attendant arrives

Obtains equipment

Transports patient

Provide Therapy

Notifies of return

Attendant assigned

Attendant arrives

Patient returned

SIX SIGMA

COMBINATION ID/MATRIX DIAGRAM

CHARACTERISTICS:

•Uncover patterns in
cause and effect
relationships.

(9) = Strong Influence
•Most detailed level in

(3) = Some Influence
tree diagram. Impact

(1) = Weak/possible influence
on one another

Means row leads to column item
evaluated.

Means column leads to row item

Add features 5 0 5 45
Make existing product faster 2 1 3 27
Make existing product easier to use 1 2 3 21
Leave as-is and lower price 0 3 3 21
Devote resources to new products 1 1 2 18
Increase technical support budget 0 2 2 18

Add features

Make existing product faster

Make existing product easier to use

Leave as-is and lower price

Devote resources to new products

Increase technical support budget

Out arrows

In arrows

Total arrows

Strength

SIX SIGMA

CONTROL PHASE – SIX SIGMA

Control Plan Tools:

1. Basic Six Sigma control methods.
– 7M Tools: Affinity diagram, tree diagram, process

decision program charts, matrix diagrams,
interrelationship diagrams, prioritization matrices,
activity network diagram.

2. Statistical Process Control (SPC)
– Used with various types of distributions
– Control Charts

•Attribute based (np, p, c, u). Variable based (X-R, X)
•Additional Variable based tools

-PRE-Control
-Common Cause Chart (Exponentially Balanced
Moving Average (EWMA))

SIX SIGMA

How do we select the correct Control Chart:

Attributes Variables
Type
Data

Measurement
Individuals

Defects Defectives of subgroups
Graph defects

Ind. Meas. or
of defectives

subgroups

Yes
Oport. Area Yes

Normally dist. Interest in Yes
constant from

data X, Rm sudden mean
sample to C, u

changes
sample

No No
No

If mean is big, X and
u R are effective too MA, EWMA or X – R

CUSUM and
Yes Rm

Size of the
subgroup p, np Use X – R chart with
constant

modified rules
More efective to

No detect gradual
Ir neither n nor p are

changes in long term
small: X – R, X – Rm

p are effective

SIX SIGMA

SIX SIGMA

Additional Variable based tools:
1. PRE-Control

•Algorithm for control based on tolerances
•Assumes production process with measurable/adjustable
quality characteristic that varies.
•Not equivalent to SPC. Process known to be capable of
meeting tolerance and assures that it does so.
•SPC used always before PRE-Control is applied.
•Process qualified by taking consecutive samples of individual
measurements, until 5 in a row fall in central zone, before 2
fall in cautionary. Action taken if 2 samples are in Cau. zone.
•Color coded

RED YELLOW GREEN YELLOW RED
ZONE ZONE ZONE ZONE ZONE

1/4 TOL. 1/2 TOL. 1/4 TOL.

Low

Tolerance
Limt

PRE-Control

Reference Line

NOMINAL

DIMENSION

PRE-Control

Reference Line

High

Tolerance
Limt

SIX SIGMA

2. Common Causes Chart (EWMA).
•Mean of automated manufacturing processes drifts because of
inherent process factor. SPC consideres process static.
•Drift produced by common causes.
•Implement a “Common Cause Chart”.
•No control limits. Action limits are placed on chart.

•Computed based on costs
•Violating action limit does not result in search for special
cause. Action taken to bring process closer to target value.

•Process mean tracked by EWMA
•Benefits:

•Used when process has inherent drift
•Provide forecast of where next process measurement will be.
•Used to develop procedures for dynamic process control

•Equation: EWMA = y^t +  (yt – y^t)  between 0 and 1

SIX SIGMA

Sand Temperature EWMA Error

EWMA chart of sand temperature
125 125.00 0.00
123 125.00 -2.00
118 123.20 -5.20 150
116 118.52 -2.52
108 116.25 -8.25
112 108.83 3.17 100
101 111.68 -10.68 Sand
100 102.07 -2.07

Temperature
92 100.21 -8.21

50 EWMA
102 98.22 3.78
111 101.62 9.38
107 110.60 -3.60
112 107.30 4.70 0
112 111.53 0.47
122 111.95 10.05
140 121.00 19.00 Observations
125 138.00 -13.00
130 126.31 3.69
136 129.63 6.37
130 135.36 -5.36
112 130.54 -18.54
115 113.85 1.15
100 114.89 -14.89
113 101.49 11.51
111 111.85 -0.85

Degrees

1

4

7

10

13

16

19

22

25

28

SIX SIGMA

Project Closure

•Improvement fully implemented and process re-baselined.
•Quality Plan and control procedures institutionalized.
•Owners of the process: Fully trained and running the process.
•Any required documentation done.
•History binder completed. Closure cover sheet signed.
•Score card developed on characteristics improved and reporting
method defined.

SIX SIGMA

Motorola ROI
1987-1994

• Reduced in-process defect levels by a factor of 200.

• Reduced manufacturing costs by $1.4 billion.

• Increased employee production on a dollar basis by 126%.

• Increased stockholders share value fourfold.

AlliedSignal ROI
1992-1996

• $1.4 Billion cost reduction.

• 14% growth per quarter.

• 520% price/share growth.

• Reduced new product introduction time by 16%.

• 24% bill/cycle reduction.

SIX SIGMA

General Electric ROI
1995-1998

• Company wide savings of over $1 Billion.

• Estimated annual savings to be $6.6 Billion by the year 2000.

SIX SIGMA
Bibliography

• Control Engineering On line, “Design for Six Sigma Capability”
http://www.controleng.com/, 1999

• Forrest W. Breyfogle III, “Implementing Six Sigma”, John Wiely & Sons, Inc,1999

• Infinity Performance Systems, “Six Sigma Overview”,
http://www.6sigmaworld.com/six_sigma.htm, 2000

• Motorola Inc., “What is 3 vs. 6 sigma”,
http://www.Motorola.com/MIMS/MSPG/Special/CLM/sld011.htm, 1997

• Sigma Holdings, Inc., “Six Sigma Breakthrough Strategy”,
http://www.6-sigma.com/Bts1.htm, 2000

• Six Sigma SPC / Jim Winings, “Six Sigma & SPC”,
http://www.sixsigmaspc.com/six_sigma.html, 2001

• StatPoint, LLC. “Six Sigma Tour”,
http://www.sgcorp.com/six-sigma_tour.htm, 2001