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1© 2001 ConceptFlow
Black Belt Refresher
2© 2001 ConceptFlow
SPACER
• Safety• Purpose• Agenda• Code of Conduct• Expectations• Roles
3© 2001 ConceptFlow
Safety
• Drills• Issues• • • • • • Emotional
4© 2001 ConceptFlow
Purpose
• Education: Review of the methodology and tools learned in Black Belt training
• Practical Exercises: Provide a refresher for use and interpretation of the tools
5© 2001 ConceptFlow
Agenda
Roadmap of the Phases
The 12 Step Process
Supporting tools
6© 2001 ConceptFlow
Administrivia
• Breaks• Lunch• Pagers, Blackberrys & Cell Phones• Facilities• • •
7© 2001 ConceptFlow
Code of Conduct
• Stay focused• Openness and trust • One person speaks at a time• No whining• Breaks as needed• Start and stop on time• Enjoy learning• Your turn....•
8© 2001 ConceptFlow
Your Expectations?
9© 2001 ConceptFlow
Roles
• Black Belts • Facilitator• Others
10© 2001 ConceptFlow
The Breakthrough Strategy
11© 2001 ConceptFlow
Module Objectives
By the end of this module, the participant will:• Receive a refresher on the 12 Steps of the Breakthrough
Strategy• Understand how the 12 Steps of the Breakthrough
Strategy provide the backbone for six sigma DMAIC projects
• Know the linkage of six sigma tools to the Breakthrough Strategy
• Understand the linkages of tools to each other
12© 2001 ConceptFlow
Goals Of Six Sigma
Center Process on TargetReduce Variation
Client target
Meet Client Target and Specifications
Client target
Eliminate DefectsReduce Variation
Client target
Defects Defects
GOAL
USLLSL
LSLLSL USL USL
13© 2001 ConceptFlow
The Breakthrough Strategy
Characterization
Optimization
Recognize PhaseDefine PhaseMeasure Phase Analyze Phase
Improve PhaseControl PhaseIntegrate PhaseSustain Phase
1 Select CTQ characteristic2 Define performance standards3 Validate measurement system
4 Establish product capability5 Define performance objectives6 Identify variation sources
7 Screen potential causes8 Discover variable relationship9 Establish operating tolerances
10 Validate measurement system11 Determine process capability12 Implement process controls
Purpose Phase Step
14© 2001 ConceptFlow
Benefits of Following the 12 Steps
• Logical and proven method for achieving success• “Would you want to give a baseline DPMO (step 4) if you did not
trust your data (step 3)?”
• “Would you put 6 months into fixing a client’s problem and then not
bother to control it to assure ongoing value (step 12)?”
• Provides a roadmap for BB activities
• Prevents “jumping to conclusions” and “firefighting”
• Forces data to be evaluated before used
• Provides a framework upon for analytical and statistical
tools
15© 2001 ConceptFlow
Practical Problem Statistical Problem
Statistical SolutionPractical Solution
Overall Problem Solving Approach
Measure Analyze
ImproveControl
y f x x x k ( , , . . . , )1 2
16© 2001 ConceptFlow
Optimized Process
10-15 Xs
8-10 KPIVs
4-8 Key KPIVs
Dynamics Of Execution Strategy - The Funnel Effect
3-6 Key KPIVs
30-50 Inputs (X)Define Phase
Measure Phase
Analyze Phase
Improve Phase
Control Phase
17© 2001 ConceptFlow
Road Maps
© 2001 ConceptFlow
Define the Project, the Customers and the ‘Big ‘Y’?
Breakthrough Strategy (DMAIC)
Focus
Vital Few x i
y
y
y
y
y
x1, x2, ... xn
x1, x2, ... xn
Vital Few x i
Vital Few x i
Vital Few x i
Vital Few x i
Ph
as
e
M easure
A nalyze
I mprove
C ontrol
Select Product or Process Key Characteristic(s); e.g..., ’Little’ y
Define Performance Standards For y
Validate Measurement System for y
Establish Process Capability of Creating y
Define Improvement Objectives For y
Identify Variation Sources In y
Screen Potential Causes For Change In y & Identify Vital Few xi
Discover Variable Relationships Between Vital Few xi
Establish Operating Tolerances On Vital Few xi
Validate Measurement System For xi
Determine Ability To Control Vital Few xi
Implement Process Control System On Vital Few xi
D efine Y
Step
0
1
2
3
4
5
6
7
8
9
10
11
12
Colors reflect training week
19© 2001 ConceptFlow
Define / Measure
Wk 11.
Select CTQ Characteristics
2.Define
Performance Standards
Phase Gate
Reviews
Customer(s)Customer Requirements (VOC)
Big Picture Big "Y"CT Trees - CTC - CTQ - CTDLittle "y"
Project Metrics for Little "y" or y'sPerformance StandardsGap Analysis
Availability of ResourcesBB/Team Training NeedsBarriersScheduleBudget
Metric DefinitionScopeCTSsHigh-Level Process Map (SIPOC)Process Knowledge
Process OwnerProject TeamChampion ApprovalBBMBB ApprovalEstablish Business Support (Viability)Project TrackingDocumentation
Create Project
Definition
3.Validate
Measurement System
KPOVs (y's)Validate Performance DataCapable Measurement System on y'sData Collection / Sampling Plan
Process MapOperational Definition(s)Measurement System EvaluationCalibration
Process Owner/ StakeholdersBusiness ObjectivesGap AnalysisScope (initial)Communication w/ BB, MBB, Champion
Identify the 'y' or 'y's' as the focus of your project (KPOV)Problem StatementGoals, ObjectivesCharterProject Schedule, Delivery Milestones, Resources (Project Plan)Team Members, Process OwnerBusiness Impact
20© 2001 ConceptFlow
Define/Measure Tool Linkage
S I P O C
Requirements Requirements
Suppliers Inputs Outputs ClientsInput Boundary Output Boundary
Process
Complete Travel
Authorization
Contact Agency
Traveler Information Verification
Gather Customer Billing Info
Auth. Code?
Authorized TravelAuth. Code
ŸŸ
Authorization Form, S
DomesticInternationalTravelerApprover
Website, STravel Budget CCost Estimate SComputer Systems,NLocation Variation,N
Ÿ
ŸŸŸŸ
ŸŸŸŸ
Ÿ
Contact Service, SPhone/Web
Travel Information,STraveler/Designee, N Agency Resources
day time, SNafter hours, SN
Computer Systems, NMeasurement Systems, STime In Queue
Time in VRUCall VolumePeak Hours
ŸŸ
ŸŸŸ
ŸŸ
ŸŸ
ŸŸŸŸ
Agency Request Entered
Ÿ Correct Traveler Information
Ÿ
Traveler Info, SCompany Info, SRestrictions if applicable, SPreferences, S (seat, class)
Agent NTraveler NComputer Systems, NMeasurement Systems, S
ŸŸŸŸŸŸŸŸ
Client name, SLocation, SAuth. Code, SOperator, SAgent NTraveler NComputer Systems, N
Measurement Systems, N
ŸŸŸŸŸŸŸŸ
Correct Traveler Billing
Info Into System
Ÿ
Y
NNeed For
Travel
Rationale, NViable Alternatives, N
Traveler NDestination Customer,N
ŸŸŸŸ
Complete Travel Request
Form
Request Form, SCharge No., STraveler NLocation Variation, NComputer Systems, NOther Personnel?Form Procedure
STravel Information N
ŸŸŸŸ
Ÿ
ŸŸ
Ÿ
InformationCorrect
Updated ProfileŸTravel RequestŸ
X Y
Detailed Process Map
Critical to Satisfaction
CostCTC
QualityCTQ Delivery
CTD
CTQCTQ CTQ CTD
CTD CTDCTC
CTC CTC
CT TreeVoice Of the Client
21© 2001 ConceptFlow
Measurement Systems Analysis
Resolution?
Accuracy/Bias?
Linearity?
Stability?
Precision ?
OK
OK
OK
OK
Bob Sue Tom
60
70
80
90
100
Appraiser
Perce
nt
Appraiser vs Standard
[ , ] 95. % CIP rcent
AttributeMSA
ObservationalMSA
Data type?
Gage name:Date of study:Reported by:Tolerance:Misc:
00.30.40.50.60.70.80.91.01.1 1 2 3
Xbar Chart by Operator
Sam
ple
Mea
n
Mean=0.8075UCL=0.8796
LCL=0.7354
0
0.00
0.05
0.10
0.15 1 2 3
R Chart by Operator
Sam
ple
Ran
ge
R=0.03833
UCL=0.1252
LCL=0
1 2 3 4 5 6 7 8 9 10
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Part
OperatorOperator*Part Interaction
Ave
rage
1 2
3
1 2 3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Operator
By Operator
1 2 3 4 5 6 7 8 9 10
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Part
By Part
%Contribution
%Study Var %Tolerance
Gage R&R Repeat Reprod Part-to-Part
0
100
200
Components of Variation
Per
cent
Gage R&R (ANOVA) for Response
Variable MSA
All Measurement
Systems
22© 2001 ConceptFlow
Analyze
4.Establish Process
Capability
5.Define
Performance Objectives
(final)
Phase Gate
Review
Define Rational SubgroupsActive data collectionValid DataVOC (specs)
Histogram on yBaseline Control Chart or Metric Graph over timeBaseline CapabilityVoice of ProcessZst, Cpk, DPMO, COPQ, RTYPareto types of defects
Revised Project DefinitionProcess MetricsQuantified Project ObjectivesDefect definitionValidated Financial Goals
Baseline PerformanceBenchmarking / Competitive Analysis
BBMBBProcess OwnerChampionFin. AnalystValidate Business SupportProject TrackingMaj. StakeholderDocumentation
Availability of ResourcesBB/Team Training NeedsBarriersScheduleBudget
6.Identify
Variation Sources
(Subjective)
6.Identify
Variation Sources
(Statistical)
"Low hanging Fruit"Identify Major Sources of VariationPotential KPIVsData collection on KPIV's
Active and/or Passive Data Collection / Sampling PlansGraphical TechniquesMulti-VarANOVAVariance ComponentsHypothesis TestingCorrelationRegression
Identify Potential Critical Xs and Improvement OpportunitiesRanked importance of KPIV's
Wk 2
Current Control Plan Detail Process Map BrainstormingFishbone/CE FMEAMistakeProofingSPC (Ys & Xs) SOP's Laws of Nature Process Knowledge
23© 2001 ConceptFlow
What Is a Control Chart?
Statistical control limits at +/- 3 standard deviations from mean
Region ofnon random
variation
Region ofrandom variation
10050Subgroup 0
70
60
50
40
30
Ind
ivid
ual
Val
ue
Mean=50.06
UCL=66.49
LCL=33.63
20
10
0
Mov
ing
Ran
ge
1
R=6.179
UCL=20.19
LCL=0
R = 13.
LCL= 0
I and MR Chart
Patterns within the “Region of random variation” can also indicate non-randomness
24© 2001 ConceptFlow
Control Chart Selection Process
Characteristic Selected
Variable Data?
Proportions Counts
Individuals Chart (I-MR)
Subgroup size > 9
Ability to calculate s for each subgroup
Average Chart (Xbar-R)
Average Chart (Xbar-s)
No
Yes
No
Yes
YesNo
Constant sample size
np or p Chart
p Chart
No
Yes
No
Yes
Constant sample size
c or u Chart
Yes
u ChartNo
Yes NoVariable Data Discrete or Attribute Data
RationalSubgroup
25© 2001 ConceptFlow
Process Capability
Eliminate out of
control situation
Yes
No
Variable Data Discrete or Attribute Data
Data normal?
Transform data
No
ProcessStable?
Descriptive StatisticsHistogramNormality Plot
Control Chart
DataType?
CapabilityAnalysis(Normal)
Box-Cox Transformation
SummaryStatistics
Cp, CpkDPMO/ppmZ
Attribute Type?
SummaryStatistics
Convert to ppm
CalculateSigma
CapabilityAnalysis
(Binomial)
CapabilityAnalysis(Poisson)
Alternate
StartCharacteristic
Selected
Binomial Poisson
Process Z DPU
Z Table
26© 2001 ConceptFlow
95.44%
68.26%
99.73%
43210-1-2-3-4
…………………….60-75%
…………………….90-98%
…………………….99-100%
The Standard Normal Curve
The standard normal curve is a special case of the normal distribution where the mean = 0 and the standard deviation = 1
Theoretical Empirical
95% of the population is within approximately ± 2 standard deviations or Z-scores of the mean
27© 2001 ConceptFlow
Z Transformations
X
Z
Point of Interest
Mean
Z = 3
1 2 3
28© 2001 ConceptFlow
Transforming a Data Distribution to a Standard Normal Curve
Area under curve can be used to estimate the probability of an “event” occurring
60 70 80 9 100 110 120
Days
Z-Scale
-3 -2 -1 0 2 3
1
-7 -6 -5 -4 4 5 6 7
95% of the observations will fall within ± 2 standard deviations
0
29© 2001 ConceptFlow
Z-Score Relationship to Six Sigma® Philosophy
A six sigma process would have six standard deviations between the mean and both spec limits for a short term capability study
60 70 80 90 100 110 120
Days
Z-Scale
-3 -2 -1 0 2 3
1
1st
-7 -6 -5 -4 4 5 6 7
What is the minimum number
of Z’s between the spec limits and the mean?
6st
LSL USL
30© 2001 ConceptFlow
Long-Term Versus Short-Term Sigma
Acceptable
USL
ZLT
ZST
ZLT = ZST – 1.5
1.5
ZLT estimates PPM or
DPMO over the long-term
ZST is used to rate
performance over the short-
term
31© 2001 ConceptFlow
DPMO = =
Total Defects x 1,000,000
Total Units x Total Opportunities Per UnitDPMO =
Defects Per Million Opportunities (DPMO)
Defects x 1,000,000 D x 1,000,000
Total Opportunities TOP
DPMO = DPO x 1,000,000
Number of Defects
Total Units= DPU =
D
U
32© 2001 ConceptFlow
Hidden Factory
Final Yield, FY = U/S = Units Passed/Units Submitted
Verify
Rework
Scrap
ProductS U
Operation
Hidden Factory:
Defects and Rework
Classic Yield Ignores Role of “Hidden Factory”
33© 2001 ConceptFlow
Throughput Yield Exercise
• Calculate the TPY for Process Steps 2 and 3• Calculate the FY for each step and compare
Step 3100
Units70 Units
10 units lost as scrap
Step 1
10 Rework 10 Rework 10 Rework
10 units lost as scrap
10 units lost as scrap
Step 2
34© 2001 ConceptFlow
Rating of Importance to
Client
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Process Inputs Total
1
2
3
45
6
7
Cause and Effect Matrix
Process Outputs
Complete Travel
Authorization
Contact Agency
Traveler Information Verification
Gather Customer Billing Info
Auth. Code?
Authorized TravelAuth. Code
ŸŸ
Authorization Form, S
DomesticInternationalTravelerApprover
Website, STravel Budget CCost Estimate SComputer Systems,NLocation Variation,N
Ÿ
ŸŸŸŸ
ŸŸŸŸ
Ÿ
Contact Service, SPhone/Web
Travel Information,STraveler/Designee, N Agency Resources
day time, SNafter hours, SN
Computer Systems, NMeasurement Systems, STime In Queue
Time in VRUCall VolumePeak Hours
ŸŸ
ŸŸŸ
ŸŸ
ŸŸ
ŸŸŸŸ
Agency Request Entered
Ÿ Correct Traveler Information
Ÿ
Traveler Info, SCompany Info, SRestrictions if applicable, SPreferences, S (seat, class)
Agent NTraveler NComputer Systems, NMeasurement Systems, S
ŸŸŸŸŸŸŸŸ
Client name, SLocation, SAuth. Code, SOperator, SAgent NTraveler NComputer Systems, N
Measurement Systems, N
ŸŸŸŸŸŸŸŸ
Correct Traveler Billing
Info Into System
Ÿ
Y
NNeed For
Travel
Rationale, NViable Alternatives, N
Traveler NDestination Customer,N
ŸŸŸŸ
Complete Travel Request
Form
Request Form, SCharge No., STraveler NLocation Variation, NComputer Systems, NOther Personnel?Form Procedure
STravel Information N
ŸŸŸŸ
Ÿ
ŸŸ
Ÿ
InformationCorrect
Updated ProfileŸTravel RequestŸ
X Y
Detailed Process Map
Scoping
KPIV Identification
Voice Of the Client
Delivery Defects
PEOPLE
ENVIRONMENT
MATERIALS
METHODS
MEASUREMENTS
MACHINES
Maintenance
Servers
Resources/Shift
Ticket Types
Times
Training
Freq of Updates
Experience Level
Postal Service
Co. Profiles
Traveler Profiles
Terminals
Call Volume
S
elf
systems
internet
Zabar Volume
Process
Queue
Hol
ida
yTim
e of
D
ay
Phone Service
T-1
Line
s
Credit card
addressem
ail
Computer Prog
PO Damage
PO DamageCall Routings
Carrier Updates
Time Zones
Comp Downtime
Team Ratings
C&E Matrix Construction
35© 2001 ConceptFlow
C&E Matrix Scoring
Rating of Importance to
Client
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Process Inputs Total
1
2
3
45
6
7
Cause and Effect Matrix
Process Outputs
0
1000
2000
3000
4000
5000
6000
7000
Defect
Cou
nt
C&E Matrix, Pareto of Customer Requirements As They Relate To The Process
Rank and display on Pareto Chart
36© 2001 ConceptFlow
0
1000
2000
3000
4000
5000
6000
7000
Defect
Cou
nt
C&E Matrix, Pareto of Customer Requirements As They Relate To The Process
FMEA Construction
Complete Travel
Authorization
Contact Agency
Traveler Information Verification
Gather Customer Billing Info
Auth. Code?
Authorized TravelAuth. Code
ŸŸ
Authorization Form, S
DomesticInternationalTravelerApprover
Website, STravel Budget CCost Estimate SComputer Systems,NLocation Variation,N
Ÿ
ŸŸŸŸ
ŸŸŸŸ
Ÿ
Contact Service, SPhone/Web
Travel Information,STraveler/Designee, N Agency Resources
day time, SNafter hours, SN
Computer Systems, NMeasurement Systems, STime In Queue
Time in VRUCall VolumePeak Hours
ŸŸ
ŸŸŸ
ŸŸ
ŸŸ
ŸŸŸŸ
Agency Request Entered
Ÿ Correct Traveler Information
Ÿ
Traveler Info, SCompany Info, SRestrictions if applicable, SPreferences, S (seat, class)
Agent NTraveler NComputer Systems, NMeasurement Systems, S
ŸŸŸŸŸŸŸŸ
Client name, SLocation, SAuth. Code, SOperator, SAgent NTraveler NComputer Systems, N
Measurement Systems, N
ŸŸŸŸŸŸŸŸ
Correct Traveler Billing
Info Into System
Ÿ
Y
NNeed For
Travel
Rationale, NViable Alternatives, N
Traveler NDestination Customer,N
ŸŸŸŸ
Complete Travel Request
Form
Request Form, SCharge No., STraveler NLocation Variation, NComputer Systems, NOther Personnel?Form Procedure
STravel Information N
ŸŸŸŸ
Ÿ
ŸŸ
Ÿ
InformationCorrect
Updated ProfileŸTravel RequestŸ
X Y
Detailed Process Map
37© 2001 ConceptFlow
FMEA Construction (continued)
Delivery Defects
PEOPLE
ENVIRONMENT
MATERIALS
METHODS
MEASUREMENTS
MACHINES
Maintenance
Servers
Resources/Shift
Ticket Types
Times
Training
Freq of Updates
Experience Level
Postal Service
Co. Profiles
Traveler Profiles
Terminals
Call Volume
Self
systems
internet
Zabar Volume
Process
Queue
Hol
ida
yTim
e of
D
ay
Phone Service
T-1
Line
s
Credit card
addressem
ail
Computer Prog
PO Damage
PO DamageCall Routings
Carrier Updates
Time Zones
Comp Downtime
38© 2001 ConceptFlow
RPN on Pareto Chart
39© 2001 ConceptFlow
Core Team: Date (Orig):
Date (Rev):
Process Step
Input Output
Process Spec (LSL, USL,
Target)
Cpk / Date
(Sample Size)
Measurement
System
%R&R or P/T
Current Control Method (from FMEA)
Who Where WhenReaction
Plan
8 9 10 11 12
LSL USL
Process Capability Analysis for Distance
USL
Target
LSL
Mean
Sample N
StDev (Within)
StDev (Overall)
Cp
CPU
CPL
Cpk
Cpm
Pp
PPU
PPL
Ppk
PPM < LSL
PPM > USL
PPM Total
PPM < LSL
PPM > USL
PPM Total
PPM < LSL
PPM > USL
PPM Total
12.0000
*
10.0000
9.8614
125
0.328760
0.490139
1.01
2.17
-0.14
-0.14
*
0.68
1.45
-0.09
-0.09
576000.00
0.00
576000.00
663368.77
0.00
663368.77
611349.22
6.41
611355.63
Process Data
Potential (Within) Capability
Overall Capability Observed Performance Exp. "Within" Performance Exp. "Overall" Performance
Within
Overall
Initial Control Plans
Contact Agency
Traveler Information Verification
Gather Customer Billing Info
Contact Service, SPhone/Web
Travel Information,STraveler/Designee, N Agency Resources
day time, SNafter hours, SN
Computer Systems, NMeasurement Systems, STime In Queue
Time in VRUCall VolumePeak Hours
Agency Request Entered
Correct Traveler Information
Ÿ
Traveler Info, SCompany Info, S
Restrictions if applicable, SPreferences, S (seat, class)
Agent NTraveler N
Computer Systems, NMeasurement Systems, S
ŸŸŸŸŸŸŸŸ
Client name, SLocation, SAuth. Code, SOperator, SAgent NTraveler N
Computer Systems, NMeasurement Systems, N
ŸŸŸŸŸŸŸŸ
Correct Traveler Billing
Info Into System
Ÿ
InformationCorrect
Updated ProfileŸ
Detailed Process Map
Gage name:Date of study:Reported by:Tolerance:Misc:
00.30.40.50.60.70.80.91.01.1 1 2 3
Xbar Chart by Operator
Sam
ple
Mea
n
Mean=0.8075UCL=0.8796
LCL=0.7354
0
0.00
0.05
0.10
0.15 1 2 3
R Chart by Operator
Sam
ple
Ran
ge
R=0.03833
UCL=0.1252
LCL=0
1 2 3 4 5 6 7 8 9 10
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Part
OperatorOperator*Part Interaction
Ave
rage
1 2
3
1 2 3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Operator
By Operator
1 2 3 4 5 6 7 8 9 10
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Part
By Part
%Contribution
%Study Var %Tolerance
Gage R&R Repeat Reprod Part-to-Part
0
100
200
Components of Variation
Per
cent
Gage R&R (ANOVA) for Response
MSA
FMEA
40© 2001 ConceptFlow
Data Collection Plan
What to Measure
Defect Definition
Type of Measure
Type of Data
Operation Definition
Data Collection
form
Sampling Plan
Service Quality Professionalism, Courteous Output/Process Discrete Continuous Ordinal scale 1-5 where 1 = did not meet expectation,
5 = exceeded expectation
Survey form tracked by job number
Internal audit by trained personnel; corporate accounts, 3 branches, 2 shifts, 10 operators within branch, 10 trials per operator at random
Service Delivery Time in queue, Time to process
Time to deliver itinerary/ticket
Delivery error:
• Agent error
• Profile error
• Mail error
Output/Process Continuous for times collected; discrete counts for defects
Queue = answering service to agent pick up
Process time = agent pick up to end call
E-ticket Itinerary: end call to message sent
Ticket mailed: end call to FedEx pickup
Time study form for auditors; time in queue and time to process
Internal time stamps on collection form by job number; time stamped for pick up
Time in queue and time to process collected by auditors above; estimated collection is One Week to determine baseline
• Build Data Collection Plan based on:• SIPOC• Process Maps• C&E Matrix• FMEA• Sampling strategy
41© 2001 ConceptFlow
Basic Descriptive Statistics
42© 2001 ConceptFlow
Graphical Analysis
18 10 19 43 59274 4.3 2.4 4.510.213.964.8
100.0 95.7 93.4 88.9 78.7 64.8
400
300
200
100
0
100
80
60
40
20
0
Defect
CountPercentCum %
Per
cen
t
Cou
nt
Pareto Chart for DefectsPareto Chart Box Plots
Run Chart Scatter Plot Histogram
43© 2001 ConceptFlow
More Graphical Analysis
Main Effects Plot
Interaction Plot
Normal Probability
Multi-Vari Chart
44© 2001 ConceptFlow
Hypothesis Testing Roadmap
i
j
1 or 2 Factors?
1 or >1 Levels?
Contingency Table
HO : FA Independent FBHA: FA Dependent FB
Stat > Tables > Chi2 Test
Attribute
1 Factor
2-Proportion Test
Stat > Basic Stat >2-Proportion
2 Samples2 levels to test
1-Proportion Test
Stat > Basic Stat >1-Proportion
1 Sample1 levelto test
Is data normal?
Stat > Basic Stat >1-Sample t
Chi2 Test
Stat > BasicStat > Display Desc >Graphical Summary(if target sigma falls
between CI, then fail toreject H O )
Stat > ANOVA >Test for Equal
Variance
2-Sample t Test
Stat > Basic Stat >2-Sample t
(if sigmas are equal, usepooled std dev to compare.
If sigmas are unequalcompare means using
unpooled std dev)
1 level
2 levels
Bartlett's Test
Stat > ANOVA > Test for Equal Variance
If sigmas are NOT equal, reduce data to determine which is different
1-Way ANOVA(assumes equality of
variances)
Stat > ANOVA > 1-Way(select stacked or
unstacked data)
Test for means
*Data is Normal
HO: 1 = t
HA : 1 tt = target
Data Not Normal
1, 2 or morelevels?
1 level
Stat > BasicStat > Display Desc >Graphical Summary(if target sigma falls
between CI, then fail toreject HO )
HO : 1 = tHA : 1 t
t = target
1-Sample Wilcoxon or
1-Sample Sign
Stat > Non-parametric >and either 1-Sample
Sign or 1-SampleWilcoxon
TestMedians
2 ormorelevels
Mood’s Median Test(used with outliers)
Stat > Non-parametric >Mood's test
Kruskal-Wallis Test(assumes no outliers)
Stat > Non-parametric >Kruskal-Wallis
2 ormorelevels
H O : M 1 = M 2 = M 3 ...HA : M M j
for i j(or at least one is different)
H O : M 1 = M 2
= M 3 ...
HA : M i M for i j(or at least one is different)
HO: M 1 = M tHA: M 1
M tt = target
Mann-Whitney Test
Stat > Non-parametric >Mann-Whitney
H O: M 1 = M 2H A: M 1 M 2
HO : 1 = t
HA : 1 tt = target
HO : 1 = 2 = 3 ...HA : i j for i j
(or at least one is different)
H O: 1 = 2HA : 1 2
HO : 1 = 2
= 3 ...
HA: i j for i j
(or at least one is different)
HO: P1 = Pt
HA: P1 Ptt = target
HO: P1 = P2
HA: P1 P2
2 levels only
If P > 0.05, then fail to reject HO If P < 0.05, then reject HO
Ensure the correct sample size is taken
1, 2 or moreFactors?
Variable
2 levels or> 2 levels?
Fail to reject HO
START
2 or more Factors
1 Factor
OH : Data is normal
AH : Data is not normal
orStat > Basic Stat > Normality Test Stat > Basic Stat > Descriptive Statistics
(graphical summary)Assumption that sample size is sufficient
HO : 1 = 2HA : 1 2
Design of Experiment
Paired t Test
Stat > Basic Stat >Paired t
HO: 1 = 2
HA : 1 2
Test for Std.Dev.
Levene’s Test
Test for Equal Variance
H O : 1 = 2 = 3 ...H A : i j for i j(or at least one is different)
(If the Null Hyp is rejected,use 2 sample T test)
Test for mean or
Std.Dev.?
1, 2 or >2 levels?
More than 2 levels
Test for mean or
Std.Dev.?
Test for means
Test for Std.Dev.
F Test
Test for mean or
Std.Dev.?
Test for means
Test for Std.Dev.
Is Data Dependent?
Yes, Data is Paired
No, Data is drawn independently from 2 populations
1-Sample t Test
2 Factors
Stat > ANOVA >
Variable or
Attribute
Data?
Test for median or Std.Dev.?
Test for Std.Dev.
Chi2 Test
In general:
* basic hypothesis tests are robust to reasonable departures from normality
45© 2001 ConceptFlow
Process Flow Of A Hypothesis Test
DECIDE:What does the evidence suggest?Reject Ho? or Fail to reject Ho?
Calculate test statistic and/or p-value
Collect sample data
Establish significance level ()
State the “Alternate Hypothesis” (Ha)
State a “Null Hypothesis” (Ho)
Define the problem and state objectives
46© 2001 ConceptFlow
Goal is to Collect Variable Data
More powerful statistical techniques can be performed using variable input and response data
Inputs (X)
Outputs (Y)
Attribute Variable
Variable
AttributeProportion tests,
Chi-SquareT-tests, ANOVA, DOE, Regression
Correlation, Multiple Regression
Discriminant Analysis, Logistic
Regression
47© 2001 ConceptFlow
Improve
Wk 3
8.Discover Variable
Relationshipy=f(x)s=g(x)
9.Establish Operating
Tolerances
Phase Gate
Review
KPIVsIdentif y RelationshipsOptim. Input Levels - y=f (x) - s=g(x)Conf irmation Runs / PilotTo-be processAlternative Solutions
Active data collection on KPIV's & KPOV'sMultiple RegressionRSMSimulationModelingDOE (optimizing)
Identif ied RelationshipsOptimum Input LevelsConf idence IntervalsCost/Benef it Analysis
Optimal Robust Settings f or Xs with Tolerances
BBMBBProcess OwnerChampionFinancial AnalystProject TrackingDocumentation
Implementation Buy-inAvailability of ResourcesBB/Team Training NeedsBarriersScheduleBudget
7.Screen
Potential Causes
Identif y Potential Critical Xs and Improvement OpportunitiesRanked importance of KPIV's
Passive and/or active data collection on KPIV's & KPOV'sMSA on XsCorrelationRegressionDOE (screening)
48© 2001 ConceptFlow
IMPROVE PHASE Identifies and validates the optimum operating conditions
Improve Phase Roadmap
DESIGN OF EXPERIMENTS (DOE)
• Simulation or physical
MODELING• Discover variable relationships• What’s the best combination of the X’s (inputs) for
producing the best Y (output) to meet or exceed the CTQ• Diagnose PIV performance and establish performance
objectives
REGRESSION• Historical or active data• Multiple or simple
VALIDATE IMPROVEMENT• Pilot test improvements• Ensure that optimum inputs truly result in
desired output• Update FMEA and process map
SELECT IMPROVEMENTS• Identity alternative solutions• Determine the optimum solution• Cost benefit analysis
49© 2001 ConceptFlow
Correlation Coefficient
302010
100
90
80
70
60
50
40
X
Y
r = -1.0302010
90
80
70
60
50
40
30
20
X
Y
r = +1.0
302010
76
75
74
73
72
71
X
Y
r = 0.0
No correlation
50© 2001 ConceptFlow
Regression Plot
550 600 650
1000
1500
2000
X
Y
Sales = -4710.51 + 10.0720 Shelf Space
S = 87.2641 R-Sq = 95.7 % R-Sq(adj) = 95.3 %
Regression Plot
Xbar
Ybar
51© 2001 ConceptFlow
Correlation and Regression
• Correlation tells how much linear association exists between two variables
• Regression provides an equation describing the nature of relationship
Correlations: Shelf Space, Sales
Pearson correlation of Shelf Space and Sales = 0.978
p-value = 0.000
Regression Analysis: Sales versus Shelf Space
The regression equation is Sales = - 4711 + 10.1 Shelf Space
52© 2001 ConceptFlow
FULL FACTORIAL SIMPLE 2K• Testing many variables at 2 levels (high/low)• Screening, characterization, optimization
GENERAL FULL FACTORIAL• Tests multiple variables, at various levels• Characterization, optimization
FRACTIONAL FACTORIAL• Tests multiple variables but not all
interactions; Not all levels, less experimentation require
• Screening
IMPROVE PHASETests multiple variables at different levels to screen, characterize and optimize process output
DESIGN OF EXPERIMENTS (DOE)
• Simulation or physical
Improve Phase Roadmap
53© 2001 ConceptFlow
Strategy of Experimentation
Planning Phase
1.Define the problem
2.Set the objective
3.Select the response(s), Y’s
4.Select the factors(s), X’s
5.Select the factor levels
6.Select the DOE design
7.Determine sample size
8.Run the experiment
Execution Phase
9.Collect data
10.Analyze data
11.Validate results
12.Evaluate conclusions
13.Revise SOP’s
14.Train affected workforce
15.Document results
16.Consider next experiment
Manage resources; have a contingency plan; use statistical common sense
54© 2001 ConceptFlow
The ANOVA Results
The ANOVA Table shows which factors are significant. Regression coefficients are listed.
55© 2001 ConceptFlow
The Pareto of Standardized Effects
The Pareto Chart of effects shows the ranking of the variation identified by each source. Note the “line of significance”
56© 2001 ConceptFlow
By factor, low level to high level
Main Effects, Interactions and Cube Plots
Parallel lines indicate NO interaction
The response is plotted on the orthogonal factor axis
57© 2001 ConceptFlow
The Graph Results
The residual vs. fits show slight widening, but the widening here is not a concern. Looking for strong outliers and patterns
that could indicate special cause.
Looking for random distributions without a pattern.
Normality Plot and Histogram of the residuals show the residuals
to be “normal”
58© 2001 ConceptFlow
Reducing Risk
Define the population or process aboutwhich inferences are to be drawn
Y
Y
N
PROCEED
N
N
Define the goal of the study
Define the characteristicor property of interest
Define the environment or type of data that you have access to
Evaluate relevance of planned data for desired inferences,
i.e., evaluate whether there is a “gap”
Can werestrict population
of interest?
Can wechange accessible
data?
Risk OK?
59© 2001 ConceptFlow
Cost / Benefit Studies
• Verify and validate benefits outweigh costs• Consider ALL costs of implementation• Determine ALL benefits
• expense• time• customer/employee satisfaction• Safety• Others
60© 2001 ConceptFlow
Pilot
Pilot Purpose• Revise improvement before
implementation• Determine best
implementation method• Lower failure risks• Identify all implementation
costs/benefits• Confirm expected results• Obtain user feedback• Obtain buy-in
Pilot Execution• Involve management –
especially Process Owner• Carefully and thoroughly plan
pilot activities• Use affected personnel – get
buy-in• Use same measurement
system from “Measure” phase• Monitor results• Debrief • Adjust full scale
implementation accordingly
Don’t shortcut – always do a pilot!
61© 2001 ConceptFlow
Control
Wk 4
11.Determine Process
Capability(Ys and Xs)
12.Implement Process Control
Final Project Presentation/ Phase Gate
Certification &
Celebration
Pilot Plan ResultsControl Charts (x's & y 's)Improved Capability (LT)Improved Benchmark (Zst, Cpk, DPMO)Signif icance of Improvement (hypothsis test)Re-Calculate FMEA-RPN
Active data collectionCurrent Control PlanSPC on Xs + YsSOP, TrainVOCCapability Analysis
ISO Document.Ident'd KPIVSOPs, TrainMistake Proof ing / Error Proof ingAccountabilityResponsibilityFinalize Transition to Process Owner
Control Plan (x's & y 's)Validate Controlled ProcessSustained Perf ormanceMonitor Plan BB Audit PlanLink to Customer CTsTransition to Process Owner
Lessons Learned / Best Practices (Translate)Communicate SuccessCelebrate TeamDocument Results
DocumentProcess OwnerChampion BB MBB Fin. ValidationProj. Tracking EntryReplication ?
Document-Ev idenceProcess OwnerChampionBBMBBFinal Financial Validation (2 projects)Leadership coursesProj. Tracking Entry
10.Validate
Measurement System &
Improvements
Update Process Maps, CE, FMEA, MetricsPilot Plan / RunValidated Measurement System Af ter Improve (Xs & Ys)Conf irmation of Changes (stat)
Active data collectionNew Process MapMeasurement System EvaluationCalibration StudyControl ChartsValidation or Pilot Run Planning
62© 2001 ConceptFlow
Verb
al In
stru
ctio
ns –
Not
cons
ider
ed a
ccep
tabl
e
cont
rol f
or S
ix S
igm
a
Proj
ects
Stan
dard
Ope
ratin
g
Proc
edur
es (S
OP’
s)
Stat
istic
al P
roce
ss
Con
trol
(SPC
)Po
ka -
Yoke
(Mis
take
Pro
ofin
g)
Des
ign
For S
ix S
igm
a
Employ the Control Method that ensures the Greatest Control with the Least Amount of On-Going Effort from the Process. Typically, a combination of several are required
Proc
ess
or P
rodu
ct
Re-
desi
gn
Least Control Effectiveness Most
Least Effort to Implement Most
SOP’
s w
/Tra
inin
g &
Eval
uatio
n
63© 2001 ConceptFlow
CONTROL PLAN AND REACTION PLAN
LONG TERM MSA PLAN
CHANGE CONTROL
TRAINING PLAN; STANDARDIZED WORK; VISUAL WORK PLACE
STATISTICAL PROCESS CONTROL
Control Phase Roadmap
5S AND MISTAKE PROOFING
INTEGRATE WITH QUALITY SYSTEM
SUSTAIN EXPECTATIONS
64© 2001 ConceptFlow
Major Control Tools
Prepared by: Page: of
Approved by: Document No:
Location: Approved by: Revision Date:
Area: Approved by: Supercedes:
KPOV KPIV
Measurement Method
Who Measures
Sub ProcessSub Process
StepSpecification
Characteristic
Specification/ Requirement
USL LSL
CTQSample Size Frequency
Where Recorded
SOP Reference Decision Rule/
Corrective Action
Six Sigma Process Control Plan
Customer
Process Name:
Int/Ext
1S
2S
3S4S
5S05
10
1520
65© 2001 ConceptFlow
Module Objectives
By the end of this module, the participant will:• Receive a refresher on the 12 Steps of the Breakthrough
Strategy• Understand how the 12 Steps of the Breakthrough
Strategy provide the backbone for six sigma DMAIC projects
• Know the linkage of six sigma tools to the Breakthrough Strategy
• Understand the linkages of tools to each other
66© 2001 ConceptFlow
Exercise
67© 2001 ConceptFlow
Exercise: Rapid Fire Catapult Launch
OBJECTIVE:
To fire the catapult and record the distance in inches for each of the launches. The measured distance will be from the front of the launcher base to the point where the ball hits the floor. Use a data sheet to record the distances in the order in which they were obtained and who fired the catapult
Target is 60 inches; Spec limit is: LSL= 50, USL = 70
RULES
1.Every shot will be launched with the same catapult settings:a Let it set as isb. Stop angle = 130 degrees
2. Each member of the team will perform an equal number of launches (as near as possible). A “launch” consists of loading, pulling back, and releasing. Do 5 each
3.There will be a time limit of 15 seconds between successive launches. Each group is to be self policed with a penalty associated to late firings.
4. You must get plan approval before any launches
5. 5 practice shots MAXIMUM.
68© 2001 ConceptFlow
Deliverables CTS Statement
Process Flow Map
Cause and effect for problem “missed target”
Measurement System Analysis
Run Chart, control chart
Histogram, normal probability plot
Tally Sheet for “missed target”
Pareto, box plots
Descriptive Statistics – Mean, Median, Std. Dev., Variance
Confidence Interval for Mean and Std. Dev.
Hypothesis test for means comparing operators, tables
Capability Study
Vary one factor, hold all other constant, take 10 shots and plot correlation
Trademarks and Service Marks
Six Sigma is a federally registered trademark of Motorola, Inc.
Breakthrough Strategy is a federally registered trademark of Six Sigma Academy.
ESSENTEQ is a trademark of Six Sigma Academy.
INTELLEQ is a trademark of Six Sigma Academy.
METREQ is a trademark of Six Sigma Academy.
Weaving excellence into the fabric of business is a trademark of Six Sigma Academy.
FASTART is a trademark of Six Sigma Academy.
Breakthrough Value Services is a trademark of Six Sigma Academy.
Breakthrough Design is a trademark of Six Sigma Academy.
Breakthrough Lean is a trademark of Six Sigma Academy.
Breakthrough Six Sigma is a trademark of Six Sigma Academy.
Design with the Power of Six Sigma is a trademark of Six Sigma Academy.
Design for Six Sigma Software is a trademark of Six Sigma Academy.
Design Six Sigma for Software is a trademark of Six Sigma Academy.
Legal Lean is a trademark of Six Sigma Academy.
SSA Navigator is a trademark of Six Sigma Academy.
SigmaCALC is a trademark of Six Sigma Academy.
SigmaFlow is a trademark of Compass Partners, Inc.
SigmaTRAC is a trademark of DuPont.
MINITAB is a trademark of Minitab, Inc.
VarTran is a trademark of Taylor Enterprises.