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
SIX SIGMA
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)
SIX SIGMA
Six Sigma as a Metric
(xi x)2
=
Sigma = = Deviation n1
( 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
SIX SIGMA
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
SIX SIGMA
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
SIX SIGMA
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
Zshift 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’
SIX SIGMA
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