6sigma handbook
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6 Sigma
Hand Book The Basics
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What is 6 Sigma ?
A structured and disciplined data-driven process for improvingbusiness performance in TRWs day-to-day activities
Focus on not making mistakes and reducing the variability inour processes
Six Sigma is all about improving the bottom line
*** It costs less to do it right the first time ***
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DEFINE
IMPROVE
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Green Belt Project Charter
Project Name Business / Location
Green Belt Telephone Number
Master Black Belt Telephone Number
Champion Telephone Number
Start Date: Target End Date:
Project Details
Project Description
Business Case
Problem Statement
Process & Owner
Scope Start:Stop:Excludes:
Project Goals Metric Baseline Current Goal Entitlement
Expected BusinessResults
Expected CustomerBenefits
Team members
Support Required
Risks/Constraints
Project CharterThis document is a Contract between the Project Team and the Project Champion.
Its purpose is :
1. To clarify what is expected of the team2. To keep the team focused
3. To keep the team aligned with organizational priorities
4. To transfer the project from the champion to the team
Main Elements of the Charter include :
Focussed Problem Statement $ Impact
Team Metrics
Scope > Start >Stop >Excludes Customer Benefits
Business Impact Risks & Constraints
DEFINE
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SIPOCA SIPOC is a high-level process map that includes Suppliers, Inputs, Process, Outputs, andCustomers.
Rolled Throughput Yield ( RTY )
The calculated value of all the Process Steps multiplied together. Ie Y1 x Y2 x ..Yn = RTY
The individual Yield Value can help you focus the project.
Significant differences in Yield suggest creating a new map for the sub-process with the lowestyield.
Inflator Assy
Customers
Ball weld
OutputsProcessInputsSuppliers
Design
EngineersComponent
manufacturer
Gas Fill
Heat
Pressure
Time
Operator
Inflator assembly
Heat
Good Part
Prod. operator
Heat age oven
Plant Quality
Start Stop
Load inflator
Press start to
perform weldRemove
welded inflatorPlace in tray
Ball
Load ball
Tip Design
Weld upset
Bad Part
Worn Tip
LaboratoryQualification
Inflator Assy
Customers
Ball weld
OutputsProcessInputsSuppliers
Design
EngineersComponent
manufacturer
Gas Fill
Heat
Pressure
Time
Operator
Inflator assembly
Heat
Good Part
Prod. operator
Heat age oven
Plant Quality
Start Stop
Load inflator
Press start to
perform weldRemove
welded inflatorPlace in tray
Ball
Load ball
Tip Design
Weld upset
Bad Part
Worn Tip
LaboratoryQualification
Y1
Y2
Y3
Y4
Y5
DEFINE
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Voice Of The CustomerVoice of the Customer (VOC) is used to describe customers needs and their perceptions of yourproduct or service.
The tree diagram format converts the Customers Need, from Broad to Specific requirements.
The Specific requirements are known as Critical To Quality (CTQs), which must be measurable andin the Customers language. Ie. What the Customer wants, not what you think the customer wants.
More available uptime
Tip Change Frequency Increase Tip Life from 300 to 1000 (1)
Reduce Tip Changeover time (2)
Less testing More time / parts for production
Reliable Weld QualityGuarantee in quality
Right first time
Reduction in approval time
Need Drivers CTQs
General Specific
Hard to measure Easy to measure
DEFINE
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DEFINE
Completion - Check ListBy the end of the DEFINE Phase, you should be able to answer the following :-
1. Why is the project important ?
2. What business goals the project must achieve to be considered successful ?3. Who are the key players in the project ( Champion, Team )
4. What limitations have been placed on the project ?
5. What is the process ( SIPOC ) ?
6. What is the current Yield ( RTY ) ?
7. What are the Key, Critical to Quality ( CTQs ) requirements ?
Only after answering the above questions, should you move onto the next Phase.
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DEFINE
Summary
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MEASURE
Data
Sampling
GageR&R
Patterns
Capability
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MEASURE
Data Collection PlanIt is extremely important to create a Data Collection Plan, so that every one involved in the project,knows :
What data you want collecting ?
What type of data is it ( Continuous or Discrete ) ?
How do you want the measurements to be taken ?
What sampling frequency to use ?
How you want the data recording ?
How you will ensure consistency ?
What is the plan for starting the data collection ?
Data Collection Plan. TitleUpdated by: Issue: 01 Last saved: 30-Oct-01
Project:What questions do you want to answer?
Data Operational DefinitionWhat Measure type / data type How measured 1 Related conditions to
record 2Sam pl ing notes How / w here rec orded
(attach form)
How wil l you ensure consistenc y & st abil ity? What is your pl an for starting data col lection? (Atta ch details if nec essary)
How will the data be displayed? (Sketch below)
1 Include the unit of measurement where appropriate. Be sure to test and monitor any measurement procedures / instruments.2 Related factors are stratificati on or potential causes you want to monitor as you collect data.
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MEASURE
Data TypesContinuous Data Discrete Data
Often obtained by use of a measuringsystem.
The usefulness of the data depends onthe quality of the measurement system.
Counts of non-rare occurrences are besttreated as continuous data.
Includes proportions, counts, attribute
Proportions = the proportion of itemswith a given characteristic; need to beable to count both occurrences andand non-occurrences.
For count data, it is impossible orimpractical to count a non-occurrence;the event must be rare.
Occurrences must be independent.
Continuous Data Discrete Data
Often obtained by use of a measuringsystem.
The usefulness of the data depends onthe quality of the measurement system.
Counts of non-rare occurrences are besttreated as continuous data.
Includes proportions, counts, attribute
Proportions = the proportion of itemswith a given characteristic; need to beable to count both occurrences andand non-occurrences.
For count data, it is impossible orimpractical to count a non-occurrence;the event must be rare.
Occurrences must be independent.
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MEASURE
Basic Statistical Concept
Mean / Average
Median :- Middle Value
Mode :- Most frequent value value with the highest number of occurrences.
Range :-
Variance:- Std Dev :-12 =i
i
Mean
ModeMedian
==
n
i i
xn
x1
1
minmax xx
1
)( 2
=
n
xx
s
n
1
)(1
2
=
=
n
xx
s
n
i
i
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MEASURE
The Normal CurveA probability distribution where the most frequently occurring value is
in the middle and other probabilities tail off symmetrically in both
directions. This shape is sometimes called a bell-shaped curve.
95.46%
99.73%
3S 0 +3S+2S+1S2S 1S
34.13% 34.13%
13.60% 13.60%2.14% 2.14%0.13% 0.13%
3S 0 +3S+2S+1S2S 1S
34.13% 34.13%
13.60% 13.60%2.14% 2.14%0.13% 0.13%
68.26%
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MEASURE
SamplingThis is collecting a portion of all the data, and using that portion to draw conclusions.
We sample because looking at all the data may be too expensive, too time-consuming, ordestructive.
Sampling Approaches Sample Size Calculations
Random
Sampling
Stratified
Random
Sampling
SamplePopulation
Each unit has
the same
chance of being
selected
Randomly
sample a
proportionate
number from
each group
AABBBB CDDD
Population Sample
C
AB
D
AA
A
C
D D
D
D D
BB
B
BB
BB
SamplePopulationor Process
Preserve time order
SamplePopulationor Process
Preserve time order
SampleProcess
9:00 9:30 10:3010:00
Preserve time order
SampleProcess
9:00 9:30 10:3010:00
Preserve time order
Systematic
Sampling
SubgroupSampling
Sample every nth one
(e.g., every 3rd)
Sample n units every
tth time (e.g., 3 units
every hour); calculate
the mean (proportion )
for each subgroup
Purpose of Sample Formula*/ Minitab Commands
Estimate average
(e.g., determine baselinecycle time)
(Where d = precision: __ units)
Estimate proportion
(e.g., determine baseline %defective)
(Where d = precision: proportion (fraction, not percent))
2
d
2sn
=
( )( )p1pd
2n
2
=
Must remain, and analysed in Time Order
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MEASURE
Gauge R&RA set of trials conducted to assess the Repeatability and Reproducibility of your measurementsystem.
Multiple operators measure multiple units a multiple number of times.
Repeatability:- is often substituted for precision.
Repeatability is the ability to repeat the same
measurement by the same operator at or near the
same time.
Reproducibility :- is customarily checked by
comparing the results of different operators taken
at different times.
%R&R
Describes the variation of the measurement system in comparison to the part variation
of the process
%P/T
Describes the variation of the measurement system in comparison to the part tolerances
total
systemtmeasuremen
S
SRR
_&% =
Tolerances
STP
systemtmeasuremen _*15.5/% =
Unacceptable
Desired Acceptable Borderline
0% 10% 20% 30% 100%
Unacceptable
Desired Acceptable Borderline
0% 10% 20% 30% 100%
General guidelines for interpreting Gage R&R results.
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0
1
2
3
4
5
6
7
8
9
10
4.004.054.104.154.204.254.304.354.404.454.504.554.604.65
Target
Weight
Fill weight for SKU 1234
1 July 7 July
Fill Weight
Numberofoccurren
ces
0
1
2
3
4
5
6
7
8
9
10
4.004.054.104.154.204.254.304.354.404.454.504.554.604.65
Target
Weight
Fill weight for SKU 1234
1 July 7 July
Fill Weight
Numberofoccurren
ces
MEASURE
Patterns in DataFrequency Plot :- shows the shape or distribution of thedata by showing how often different values occur.
Pareto Chart :- The Pareto principle is often described bythe 80/20 rule. This rule says that, in many situations,roughly 80% of the problems are caused by only 20% of thecontributors.
0
5000
10000
15000
20000
25000
AmountofSpoila
ge($$)
Produce
Meat
Dairy
Bakery
Other
Category
100%
80%
60%
40%
20%
Percentageoftotal
0
5000
10000
15000
20000
25000
AmountofSpoila
ge($$)
Produce
Meat
Dairy
Bakery
Other
Category
100%
80%
60%
40%
20%
Percentageoftotal
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Patterns in DataStratification :- Stratification means dividing datainto groups (strata) based on key characteristics.
A key characteristic is some aspect of the data
that you think could help explain when, where, andwhy a problem exists.
The purpose of dividing data into groups is to detecta pattern that localizes a problem or explains why
the frequency or impact varies between times,locations, or conditions.
Disaggregation :- Many figures we see are aggregated.
For example, if we look at total monthly production figures,each data value is really a combined figure representing allproducts, lines, shifts, weeks, etc.
If we take apartdisaggregatethese figures, we can
often see patterns that are masked in the roll up.
1
2
3
4
5
6
Count
8 9 10 11 1 2 1 3 14 15 16 1 7 18 19 20 21
Minutes
0
1
2
3
4
5
6
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
0
1
2
3
4
5
6
7 8 9 10 11 12 13 14 15 16 17 1 8 19 20 21
0
1
2
3
4
5
6
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Location A
Location B
Location C
Time to Complete Lubes
(all locations)
MEASURE
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MEASURE
Patterns in Data
Time Series Plot :- A time plot is a graph of data in timeorder.
Individuals Control Chart :-
Time ordered plot of results.
Statistically determined control limits are drawn on the plot.
3020100
70
80
90
100
110
120
130
140
Cycle Time for T420 Orders
June 130
Numberofdays
3020100
70
80
90
100
110
120
130
140
Cycle Time for T420 Orders
June 130
Numberofdays
3130292827262524232221201918171615141312111098765432Subgroup 1
250000
200000
150000
100000
50000
0
IndividualValue
July
June
May
April
M
arch
February
January
December
November
October
September
August
July
June
M
ay
April
M
arch
February
January
December
November
October
September
August
July
June
M
ay
April
M
arch
February
JanuaryMonth
I Chart for Volume by Year
Mean=69481
UCL=117036
LCL=21926
2001 2002 2003
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MEASURE
Patterns in DataCommon Cause & Special Cause Variation
Common Cause :- always present to somedegree in the process.
Special Cause :- something different
happening at a certain time or place
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MEASURE
Signals in Data
7 or more points in a row on the same
side of the median indicates a process shift.
(If the data are symmetric, its OK to use theaverage as the centerline instead of the median.)
7 or more points in a row continuously
increasing or decreasing indicates a trend.(Start counting at the point where the directionchanges.)
Too few runs indicates a shift in the process
average, a cycle, or a trend.
Too many runs indicates sampling from twosources, overcompensation, or a bias.
MEASU
REMENT
Median
MEASUREMENT
Upward Trend Downward Trend
MEASUREMENT
Median
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MEASURE
Signals in Data
14 or more points in a row alternating up
and down indicates bias or sampling problems.
One or more points outside the control
limits indicates that something is different aboutthose points.
MEASUREMENT
MEASURE
MENT
MEASUREMENT
MEASURE
MENT
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Process CapabilityProcess capability measures are statistical measures that summarize how much variation there is ina process relative to customer specifications.
To increase the Process Capability, you have to decrease the process variability.
When continuous data are normally distributed, calculating a process capability index is reallyequivalent to finding the area under the normal (or bell-shaped) curve that is outside the spec limits,as depicted in the diagram below.
Defects
Defects
Too early Too late
Delivery Time
Reduce
variation
Delivery Time
Too early Too late
Lower specification Upper specification
LSL USLLSL USL
MEASURE
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MEASURE
Process CapabilityChecking for Normality ( Normal Distribution )
If the data is Normal, the points will fall on a straight line.
Straight means within the 95% confidence bands.
You can say the data is Normal if approximately 95% of the data points fall within the confidencebands.
25 35 45 55
1
5
10
2030
40
50
60
70
80
90
95
99
Data
Percent
ML Estimates
Mean:
StDev:
40.1271
4.86721
95% confidence ba nds
25 35 45 55
1
5
10
2030
40
50
60
70
80
90
95
99
Data
Percent
ML Estimates
Mean:
StDev:
40.1271
4.86721
95% confidence ba nds
Conclusion
Not a serious departure
from Normality
Conclusion
There is a serious
departure from Normality
25 35 45 55
1
5
10
20
30
40
50
60
70
80
90
95
99
Data
Percent
ML Estimates
Mean:
StDev:
40.1271
4.86721
-2 -1 0 1 2 3 4
1
5
10
20
30
40
50
60
70
80
90
95
99
Data
Percent
ML Estimates
Mean:
StDev:
1.13627
1.07363
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MEASURE
Process CapabilityBaseline Sigma ValueProcess Sigma builds on the basic foundation of process data and specification limits.
Increase in ProcessSigma requiresexponential defect
reduction
DPMO
Process
Sigma
308,537 266,807 3
6,210 4233 53.4 6
ProcessCapability
Defects perMillion
Opportunities
(distribution shifted 1.5s)
Process
Sigma Scale
Increase in ProcessSigma requiresexponential defect
reduction
Increase in ProcessSigma requiresexponential defect
reduction
DPMO
Process
Sigma
308,537 266,807 3
6,210 4233 53.4 6
ProcessCapability
Defects perMillion
Opportunities
(distribution shifted 1.5s)
Process
Sigma Scale
DPMO
Process
Sigma
308,537 266,807 3
6,210 4233 53.4 6
ProcessCapability
Defects perMillion
Opportunities
(distribution shifted 1.5s)
Process
Sigma ScaleLSL USLLSL USL
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MEASURE
Process CapabilityBaseline Sigma ValueThere are two methods commonly used to determine Process Sigma.
Method 1 :-Look-up Actual Yield in a process sigma conversionTable.
Method 2 :-Look up a Normal Approximation of yield in theprocess sigma table.
LSL USL
Actual Yield:
60% Yield = 1.8 Process Sigma
LSL USL
Actual Yield:
60% Yield = 1.8 Process Sigma
LSL USL
Area under Normal Curve
60% Yield = 1.8 Process Sigma
LSL USL
Area under Normal Curve
60% Yield = 1.8 Process Sigma
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MEASURE
Process CapabilityMethod 1 :-Look-up Actual Yield in a process sigma conversion table.
1. Determine number of defect opportunities O = ______ per unit
2. Determine number of units processed N = ______
3. Determine total number of defects D = ______ made (include defects made and later fixed)
4. Calculate Defects Per Opportunity DPO= = ______
5. Calculate Yield Yield = (1-DPO) x 100 = ______
6. Look up Process sigma in the Process Sigma TableProcess Sigma = ______
D
N x O
D
N x O
5
100
7
.014
98.6
3.7
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MEASURE
Process CapabilityMethod 2 :-
Look up a Normal Approximation of yield inthe process sigma table.
1. ENTER AVERAGE, STANDAR D DEVIATION, AND SPEC LIMITS
2. LABEL A NORMAL CU RVE
Average Standard dev iation USL (and s hade to LEFT for A rea 1) LSL (and shade to LEFT for Area 2)
3. DETERMINE AREA BELOW USL ( AREA 1)
5. CALCULATE YIELD
6. LOOK UP YIELD IN PROCESS SIGMA TA BLE
s
X + sX X + sX + sXX
Find Z1
Look up Z1 in Normal Table NormDist (Z1) = Value from Normal Tab le =
4. DETERMINE AREA BELOW LSL, IF ANY (AREA 2)
Find Z2
Look up Z2 in Normal Table
Z 2 = =( ) ( )
( )
( ) ( )
( )=
NormDist (Z2) = Value from Normal Tab le =
LSL - X
s
LSL - X
s
LSL - X
s
Yield = Area 1 Area 2= ______ ______ =
Yield (percentage)= Yield x 100 % =
Process S igma = Look-Up from Sigma Table =
Z1 = =( ) ( )
( )
( ) ( )
( )=
USL - X
s
USL - X
s
USL - X
s
X = ______ s = ______ USL = ______ LSL = _______X = ______ s = ______ USL = ______ LSL = _______17 3 N/A25
3
17 20
USL = 25
25 17
32.67
.996533
N/A
.996533
99.6%
4.2
.996533 0
X = 17 s = 3 USL = 25 LSL = none
0
2
4
6
8
10
12
8-1
0
10-1
2
12-1
4
14-1
6
16-1
8
18-2
0
20-2
2
22-2
4
24-2
6
26-28
USL
Frequency
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MEASURE
Process Capability IndicesCp & PpThis is the performance index which is defined as the tolerance width divided by the performance,irrespective of process centering.
s
LSLUSLp
p 6
=
Where: USL = upper specification limit
LSL = lower specification limit
6s = 6 times the sample standard deviation
LSL USL
CAPABILITY INDICESPp = (USL-LSL)/6s
cap2.mgf
(USL-LSL)
6s 6s
The Pp
is determined by the tolerance and spread of the
process, location is not considered. The red (left) and blue
(right) distributions have the same Pp. Virtually all of the
parts produced on the red (left) process will be in
specification, while virtually all of the parts from the blue
(right) process will be out of specification.
EASU E
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MEASURE
Process Capability IndicesCpk & PpkThe process performance index, Ppk,, which accounts for process centering and is defined as :
( ) ( )
=
s
LSLxor
s
xUSLMinp
pk 33
LSL USL
cap4.mgf
CAPABILITY INDICESPpk = min{(USL - Xbar)/3s or (Xbar - LSL)/3s}
(Xbar - LSL)
(Xbar - LSL) Red 3s = Blue 3s
To estimate the Ppk perform both calculation above andreport the smaller value. A quicker way is to determinewhich specification limit (USL or LSL) is closest to theaverage and only do that calculation, it will be the smallest.
Here we can see the impact of the specification in thedefinition of Ppk. Both processes above will have the samePp, same spread and tolerance. The Ppk for the blue (left)
process will be lower because (Xbar-LSL) is smaller.
MEASURE
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MEASURE
Completion ChecklistBy the end of the Measure Phase, you should be able to answer the following :-
1. What specifically is the main problem or problems.
2. What you have done to validate the measurement system.
3. What patterns are exhibited in the data.
4. What the current / baseline capability is.
Only after answering the above questions, should you move onto the next Phase.
MEASURE
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MEASURE
Summary
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ANALYSE
DoE
IMPROVE
ANALYSE
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ANALYSE
Process Door vs Data Door
Process
Door
Process
Door
Data DoorData Door
Detailed Process Map
Value Added Analysis
Cycle Time Analysis
Stratification
Scatter Diagrams
Multi-Vari Analysis
ANALYSE
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ANALYSE
Process DoorActivity Flow Chart :- Specific about what happens in aprocess.
Deployment Flow Chart :- These show detailed steps
in a process and which people or departments are involvedin each step.
Value Stream Map :- Value Stream Mapping is agraphic representation of the flow from the customer andsupplier through the plant. The map is a visualrepresentation of both the material and information flows.This is a key difference between process mapping and
value stream mapping.
Sales Technical Shipping Coordinator Sales Technical Shipping Coordinator
ANALYSE
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Data Door
Scatter Plot :- a graph that helps you visualise therelationship between two variables. It can be used to checkwhether one variable is related to another variable and is
an effective way to communicate the relationship you find.
T i m e(mi ns )
M on ths on job
c a e r o o
T i me N e e de d to A s s e m bl e the Produc t v s .
W ork e rs T i me on the J ob
Produc t B
Produc t A
1
2
3
4
5
6
7
8
9
1 0
1 2 3 4 5 6 7 8 9 10 1 1 1 2 >12
222
2
Possible Positive
Correlation
Possible Negative
Correlation
Strong PositiveCorrelation
Strong NegativeCorrelation
Other PatternNo Correlation
AD-079
ANALYSE
ANALYSE
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ANALYSE
Transforming to Normal DataTransforming non normal data into normal data is necessaryas incorrect inferences will be made with tests, requiringnormal data.
Non-Normal Data can be transformed using a (Lambda)value calculated through a Box-Cox transformation.
Method Consequence ofNon-Normality
Process Sigma calculation Incorrect Process Sigma value
Individuals contr ol chart False detection of some specialcauses, missed signals of others
Hypothesis testing Incorrect conclusions aboutdifferences between groups
Regression Misidentification of importantfactors; poor predictive abi lities
Design of experiments Incorrect conclusions aboutimportant factors; poor predictionabilities
5 7 9 11 13 15 17 19 21 23
0
10
20
CycleTime
Freque
ncy
-5 -4 -3 -2 -1 0 1 2 3 4 5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.595% Confidence Interval
StDe
v
Lambda
Last Iteration Info
Lambda StDev
-0.393
-0.337
-0.281
2.285
2.285
2.284
Low
Est
Up
Box-Cox Plot for CycleTime
0.8 0.9 1.0 1.1 1.2 1.3 1.4
0
10
20
LogCycletime
Freque
ncy
ANALYSE
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ANALYSE
Hypothesis Testing
A hypothesis test is a procedure that summarizes data so you can detect differences amonggroups.
Tests the null hypothesis -H0: no difference between groups
Against the alternative hypothesis -Ha: groups are different
Obtain a P-value for the null hypothesis -Use the data and the appropriate hypothesis test statistic to obtain a P-value
If P < .05, reject the H0 and conclude the Ha
If P .05, cannot reject the H0
IF P IS LOW
REJECT Ho
ANALYSE
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ANALYSE
Hypothesis Testing
Compare two or moregroup averages.
Compare two or more
group proportions.
Chi-square test
Compare two or moregroup variances.
Test for equal variances(F-test, Bartletts test,
Levenes test)
ANOVA
(Analysis Of Variance)
Compare two groupaverages when data is
matched.
paired t-test
Compare two groupaverages.
t-test
PurposeHypothesis Test
Discrete
Data Type
Continuous
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ANALYSE
Hypothesis Testing
F-Test Output
( Minitab ) Bartletts Test:assumes normal
distributed data.
Levenes Test:
No normalitynecessary.
Conclusion: BothP-values are < .05, soconclude the variances
in production volumesare significantlydifferent before andafter the improvement.
25001500500
95% Confidence Intervals for Sigmas
new
std
52000510005000049000480004700046000
Boxplots of Raw Data
Prod Vol
P-Value : 0.017
Test Statistic: 6.282
Levene's Test
P-Value : 0.029
Test Statistic: 0.355
F-Test
Factor Levels
std
new
Test for Equal Variances for Prod VolBartletts Test:
assumes normal
distributed data.
Levenes Test:
No normalitynecessary.
Conclusion: BothP-values are < .05, soconclude the variances
in production volumesare significantlydifferent before andafter the improvement.
25001500500
95% Confidence Intervals for Sigmas
new
std
52000510005000049000480004700046000
Boxplots of Raw Data
Prod Vol
P-Value : 0.017
Test Statistic: 6.282
Levene's Test
P-Value : 0.029
Test Statistic: 0.355
F-Test
Factor Levels
std
new
Test for Equal Variances for Prod Vol
25001500500
95% Confidence Intervals for Sigmas
new
std
52000510005000049000480004700046000
Boxplots of Raw Data
Prod Vol
P-Value : 0.017
Test Statistic: 6.282
Levene's Test
P-Value : 0.029
Test Statistic: 0.355
F-Test
Factor Levels
std
new
Test for Equal Variances for Prod Vol
ANALYSE
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ANALYSE
Hypothesis Testing
T-Test Output ( Minitab )
= n= n
Draw conclusions by
looking at theP-value. Is it < .05?
Standard error of the
mean = st. dev. of the
average
Session Window Output Confidence interval for the avg. dif f.Std - New
Interval does not contain zero, so asignificant difference does exist with
95% Confidence
The value of t
ANALYSE
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ANALYSE
Hypothesis Testing
ANOVA Test Output ( Minitab )
Sum of Squares
One-way Analysis of Variance
Analysis of Variance for FaceAmt
Source DF SS MS F P
Form 6 539413 89902 11.56 0.000
Error 98 762240 7778
Total 104 1301653Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev -------+---------+---------+---------
A 15 446.00 100.56 (----*---)
B 15 277.33 105.46 (----*---)
C 15 376.67 102.72 (----*---)
D 15 384.00 82.27 (---*----)
E 15 476.00 65.01 (----*---)
F 15 514.67 71.70 (---*----)
G 15 414.00 80.78 (---*----)
-------+---------+---------+---------
Pooled StDev = 88.19 300 400 500
The variance between
groups is 11.5 timesbigger than thevariance within groups
The parenthesesrepresent confidenceintervals forgroup
averages (notindividual values)
Draw conclusion
from P-value
We assume the variancesfor all groups are the same
Mean Squaresanother name for
varianceBetween
Within
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Hypothesis Testing
Chi-Squared Test Output ( Minitab )
P value of
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Regression AnalysisRegression analysis generates a line that quantifies the relationship between X and Y.
The line, or regression equation is represented as Y=b0+b1X
Where :-
b0 = intercept ( where the line crosses X=0 )
b1 = slope ( change in Y per unit increase in X )
The regression line / equation is determined by aprocedure that minimises the total squareddistance of all the points to the line.
This is known as The Least Squares Method
Height (m)
ShoeS
ize
(Eur)
1.951.901.851.801.751.70
49
48
47
46
45
44
43
42
41
S 0.485759
R-Sq 89.7%
R-Sq( ad j) 88. 9%
Regression
95% CI
95% PI
Fitted Line PlotShoe Size (Eur) = 3.445 + 22.83 Height (m)
Read Model / Equation
y = 3.445 + 22.83x
ANALYSE
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Regression Analysis
R-Squared = R-sqMeasures the percent of variation in the Y-values that is explained by the linear relationship with X.
Ranges from 0 to 1 (= 0% to 100%)
The correlation, r:Ranges from -1 to 1
r = -1= perfect negative or inverse relationship
r = 0 = no linear relationshipr = +1 = perfect positive relationship
Measures the strength of the relationship
R2 is equal to square of r
Known as Pearsons correlation coefficient
Explained%100xvariationTotal
variationExplainedsq-R ==
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
Strong Positive Correlation
r = .95
R2 = 90%
Moderate Positive Correlation
r = .70
R2 = 49%
No Correlation
r = .006
R2 = .0036%
Other Pattern -
No Linear Correlationr = -.29
R2 = 8%
Moderate Negative Correlation
r = -.73R2 = 53%
Strong Negative Correlation
r = -.90R2 = 81%
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
Strong Positive Correlation
r = .95
R2 = 90%
Moderate Positive Correlation
r = .70
R2 = 49%
No Correlation
r = .006
R2 = .0036%
Other Pattern -
No Linear Correlationr = -.29
R2 = 8%
Moderate Negative Correlation
r = -.73R2 = 53%
Strong Negative Correlation
r = -.90R2 = 81%
ANALYSE
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Regression AnalysisOther Types of Regression
Using indicator variables(for discrete Xs)
x
x
x
xx
x
x
x
x x
xx
x
xx
Xi
Y
Xa
Xb
Xc
Using indicator variables(for discrete Xs)
x
x
x
xx
x
x
x
x x
xx
x
xx
Xi
Y
Xa
Xb
Xc
Curvilinear (One X)
X
Y
Curvilinear (One X)
X
Y
X
Y
Simple linear (One X)
X
Y
Simple linear (One X)
X
Y
X
Y
Multiple (Two or more Xs)
Y
X2
X 1
Multiple (Two or more Xs)
Y
X2
X 1
Y
X2
X 1
Logistic (for discrete Ys)
1
0
%yes
X
Logistic (for discrete Ys)
1
0
%yes
X
Curvilinear (Two or more Xs)
Y
X1
X2
Curvilinear (Two or more Xs)
Y
X1
X2
ANALYSE
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Design of Experiments ( DOE )Design of Experiments is an approach for effectively and efficiently exploring the cause-and-effect
relationship between numerous process variables (Xs) and the output or process performancevariable (Y).
1. Identifies the vital few sources of variation (Xs)
2. Those that have the biggest impact on results
3. Quantifies the effects of the important Xs, including their interactions
4. Produces an equation that quantifies the relationship between the Xs and Y
5. You can predict how much gain or loss will result from changes in process conditions
Types of Experimental Design
Full Factorial ( 2 or more Levels ) Fractional Factorial
Screening Designs Plackett-Burman Design
Central Composite Response Surface Methodology
ANALYSE
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Design of Experiments ( DOE )The Approach :-
Experiment
Design
Experiment
Analysis
1. Identify responses
2. Identify factors
3. Select design
4. Choose factor levels
5. Randomize runs
6. Conduct experiment and collect data
7. Analyze data
8. Draw conclusions
9. Verify results
Experiment
Design
Experiment
Analysis
1. Identify responses
2. Identify factors
3. Select design
4. Choose factor levels
5. Randomize runs
6. Conduct experiment and collect data
7. Analyze data
8. Draw conclusions
9. Verify results
ANALYSE
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Design of Experiments ( DOE )2 Level Full Factorial ( Example ) :- Fractional Factorial Fit: Bends versus Vendor, Size, Heat
Estimated Effects and Coefficients for Bends (coded units)
Term Effect Coef SE Coef T P
Constant 15.688 0.9902 15.84 0.000
Vendor -0.875 -0.437 0.9902 -0.44 0.670
Size 1.125 0.562 0.9902 0.57 0.586
Heat 8.125 4.062 0.9902 4.10 0.003
Vendor*Size -5.125 -2.563 0.9902 -2.59 0.032
Vendor*Heat -1.625 -0.813 0.9902 -0.82 0.436
Size*Heat 1.375 0.688 0.9902 0.69 0.507
Vendor*Size*Heat 1.625 0.812 0.9902 0.82 0.436
Analysis of Variance for Bends (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 3 272.188 272.188 90.73 5.78 0.021
2-Way Interactions 3 123.188 123.188 41.06 2.62 0.123
3-Way Interactions 1 10.562 10.562 10.56 0.67 0.436
Residual Error 8 125.500 125.500 15.69
Pure Error 8 125.500 125.500 15.69
Total 15 531.438
Estimated Coefficients for Bends using data in uncoded units
Recommendations
In general, request or buy heat-treated clips
If you want to use both sizes and can have two vendors:
Purchase heat-treated No. 1 clips from Abel
Purchase heat-treated Jumbo clips from Noesting
If you want both sizes but only one vendor, choose heat-
treated Noestings
StdOrder RunOrder CenterPt Blocks Vendor Size Heat Bends
16 1 1 1 Abel Jumbo Yes 18
12 2 1 1 Abel Jumbo No 5
1 3 1 1 Noesting No.1 No 9
14 4 1 1 Abel No.1 Yes 21
9 5 1 1 Noesting No.1 No 7
2 6 1 1 Abel No.1 No 21
8 7 1 1 Abel Jumbo Yes 18
15 8 1 1 Noesting Jumbo Yes 26
13 9 1 1 Noesting No.1 Yes 15
7 10 1 1 Noesting Jumbo Yes 22
6 11 1 1 Abel No.1 Yes 173 12 1 1 Noesting Jumbo No 16
10 13 1 1 Abel No.1 No 10
4 14 1 1 Abel Jumbo No 12
5 15 1 1 Noesting No.1 Yes 21
11 16 1 1 Noesting Jumbo No 13
43210
C
AB
AC
ABC
BC
B
A
Pareto Chart of the Standardized Effects
(response is Bends, Alpha = .05)
A: Vendo rB : S iz eC: Heat
Vendor Size Heat
Noestin
g
Abel
No.1
Jumb
oNo Ye
s
12
14
16
18
20
Bends
Main Effects Plot (data means) for Bends
ANALYSE
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Completion Checklist
By the end of the Analyse Phase, you should be able to answer the following :-
1. What potential causes you have identified.
2. Which potential causes you decided to investigate and why ?
3. What data you collected to verify those causes.
4. How you interpreted the data.
Only after answering the above questions, should you move onto the next Phase.
ANALYSE
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Summary
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IMPROVE
Solutions
FMEA
Pilot
Impl
emen
-
tatio
n
IMPROVE
Solutions
FMEA
Pilot
Impl
emen
-
tatio
n
IMPROVE
IMPROVE
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Generating, Evaluating and Selecting Solutions
Creativity Techniques :-
Quick and Dirty Short Time Investment More Involved
Think like a kid Candid Comments SCAMPER
Challenge the rules Musical Chairs Slice & Dice
Set a deadline Edison Ideas box
Get rid of excuses Brutethink
IMPROVE
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Generating, Evaluating and Selecting SolutionsCost Benefit Analysis
Express the financial benefits in terms that make sense for your business :-
Return on Capital Return on Equity Return on Investment
Economic Value Added Cash Flow Payback PeriodNet Present Value
Express non-financial improvements in terms that make both sense for the customer and your
business :-Reduced cycle time Improved on-time delivery Increased flexibility
Faster response Reduced effort Increased availability
Fewer defects
Selecting Solutions
If there is an obvious winner from the evaluation step, go with that choice.
If there is no clear choice, use decision making :- Consensus,
Majority vote, One person
IMPROVE
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Assessing Risks
FMEA :-
Is a structured approach to identify, estimate, prioritize and evaluate risk.
Aims at failure prevention.Is primarily used to limit the risk involved in changing the process.
FMEA AnalysisProject: _____________________ Team: _____________________
Date ___________ (original)___________ (revised)
Item orProcess
Step
PotentialFailure
Mode
PotentialEff ect (s)
of Failure
Potential
Cause(s)
Current
Controls RPN Recommended
Action
Responsibilityand
Tar get Date Ac tion Taken Severity
Oc
currence
De
tection
RP
N
After
Se
verity
Oc
currence
De
tection
Total Risk Priority Number = After Risk Priority Number =
IMPROVE
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Piloting Solutions
Pilot when :-
You need to confirm the expected results andpracticality of the solution.
You want to reduce the risk of failure.
The scope of the change is large, and reversing the
change would be difficult.Implementing the change will be costly.
Changes would have far-reaching, unforeseenconsequences.
Steps of a Pilot Program
1. Select pilot steering team
2. Brief participants
3. Plan pilot
4. Inform associates
5. Train employees6. Conduct pilot
7. Evaluate results
8. Increase scope
IMPROVE
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Implementing SolutionsPlanning :- Elements of a Plan
Understand the why.
Plan the work.
Plan the tasks and the subtasks.
Plan the time.
Plan the people and resources.
Understand if it worked. Potential Problems
Tasks & Timeline
Aug. Sept. Oct. Nov. Dec. Jan. Feb.Step
How to Check
PLAN ACTUALS
Change made
Stakeholders
PERSONor GROUP
Communication& Participation
Finance
Sales
IS
Step Pot.
Failure
Pot.
Cause
Counter-
measures
Budget & Resources
Expenses
Staff time
xxxxx 00.00xxxxx 00.00xxxxx 00.00
Ted 5 hrs
IMPROVE
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Completion Check ListBy the end of the Improve Phase, you should be able to answer the following :-
1. What factors you considered to decide about the strategy.
2. What solutions you identified.
3. What criteria you used to select a solution.
4. The results of any small scale tests of the solutions.
5. Plans for detailed implementation.
6. How the planned changes align with management systems, policies, and procedures.
Only after answering the above questions, should you move onto the next Phase.
IMPROVE
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Summary
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CONTROL
Control
Standardize
Document
Monito
r
Evaluate
Closure
IMPROVE
Control
Standardize
Document
Monito
r
Evaluate
Closure
IMPROVE
CONTROL
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Quality Control & Process Change ManagementReacting to Problems :-
Howto
Produc
eit
Process
Inputs
Measurements Machines
Methods People Environment
Produce it
Policies
FixProduct
StoreProduct
Customer
Output
LEVEL 1: FIX THE OUTPUT- Containment
LEVEL 2: FIX T HE PROCESS- Defect Root Cause
LEVEL 3: FIX THE SYSTEM-Systemic Root Cause
What toProduce
Fix or control?
Where we
sometimes
stop
Example: Toaster Manufacturing Corrosion Problem
Level 1
Containment
Level 2
Defect Root Cause
Level 3
Systemic Root Cause
Fix the process forhandling corrodiblematerial:
a) in house
b) at suppliers
How??
Use no touchhandling
Fix the system thatproduced changesin designs that haveproblems like these.
How??
Incorporate as apart of all designreviews a checkfor possiblecorrosionproblems.
Fix the toasters thathave corrosionproblems:
a) units in the field
b) units still in house
How??
Replacedamaged parts
CONTROL
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Quality Control & Process Change ManagementQC Process Chart :-
The plan is
typicallycaptured as a
flowchart.
The middle column
describes what you willcheck in the process tomonitor its quality.
The thirdcolumn
describes howthe processoperators
should reactdepending on
what they findin the
measures.
Flowchart IndicatorsCorrective
Actions
PLAN/DO CHECK ACT
Count errors If more than 1 per order,stop process, contactSam
Alert Sam immediately;organize investigation
Plot time on each order;should be < 2 hours;check for special causes
The plan is
typicallycaptured as a
flowchart.
The middle column
describes what you willcheck in the process tomonitor its quality.
The thirdcolumn
describes howthe processoperators
should reactdepending on
what they findin the
measures.
Flowchart IndicatorsCorrective
Actions
PLAN/DO CHECK ACT
Count errors If more than 1 per order,stop process, contactSam
Alert Sam immediately;organize investigation
Plot time on each order;should be < 2 hours;check for special causes
CONTROL
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StandardizationNothing happens on a reliable, sustained basis unless we build a system to cause it to happen ona reliable, sustained basis.
Standardization is what allows high quality to happen on a reliable, sustained basis.
Standardization helps us compete more successfully in the marketplace by providing :-
Increased reliability Reduced costs Improved employee performance
Increased safety Continuous improvement Flexible practices
Processes that remain in control
CONTROL
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MonitoringOn-going monitoring is typically managed with a control chart.
Start
Type
of data
?
Counting
items with an
attribute or counting
occurrences?
Equal
sample
sizes
?
Equal
opportunity?
p chartp chart
np chartnp chart
Individuals
chart
Individuals
chart
EWMA
chart
EWMA
chart
Continuous
Yes
No
Yes
Rational
Subgroups
Discrete
Yes
No
No
u chartu chart
c chartc chart
Do limits
look right?
Try individuals chartTry individuals chart
Need to
detect small shifts
quickly?
Individual
measurements
or subgroups
?
Try transformation to make data normalTry transformation to make data normal
Do limits
look right?
YesNo
Either/Or
No
Yes
Individual
measurements
Occurrences
X, R chartX, R chart
Items withattribute
StartStart
Type
of data
?
Type
of data
?
Counting
items with an
attribute or counting
occurrences?
Counting
items with an
attribute or counting
occurrences?
Equal
sample
sizes
?
Equal
sample
sizes
?
Equal
opportunity?
Equal
opportunity?
p chartp chart
np chartnp chart
Individuals
chart
Individuals
chart
EWMA
chart
EWMA
chart
Continuous
Yes
No
Yes
Rational
Subgroups
Discrete
Yes
No
No
u chartu chart
c chartc chart
Do limits
look right?
Try individuals chartTry individuals chart
Need to
detect small shifts
quickly?
Need to
detect small shifts
quickly?
Individual
measurements
or subgroups
?
Individual
measurements
or subgroups
?
Try transformation to make data normalTry transformation to make data normal
Do limits
look right?
Do limits
look right?
YesNo
Either/Or
No
Yes
Individual
measurements
Occurrences
X, R chartX, R chartX, R chartX, R chart
Items withattribute
X = averageR = Range
p = proportion
c = count
Control Chart Type Data Type
Individuals chart Continuous or Discrete
p chart ornp chart Discrete-attribute
cchart oru chart Discrete-count
R,X R,X Continuous
CONTROL
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Before After
}Improvement
Target}Remaining Gap
Good
Step 4 changesimplemented
} ImprovementBefore After
A1 A2 A3 A4 A2 A1 A3 A4
Before After
Before After
}Improvement
Target}Remaining Gap
Good
Step 4 changesimplemented
} ImprovementBefore After
A1 A2 A3 A4 A2 A1 A3 A4
Before After
Evaluating ResultsIn advance of improvement implementation, it is help toconsider how you will present before and afterevaluation -
1. Allocate some time in project plan to step back andbuild the before / after graphics
2. Maintain a set of good illustrations of before versusafter as the project progresses
3. Consider from the perspective of selling thebenefits of the project to your key customers withsimple, clear graphics
4. Where possible, declare $ value of savingsattributable to a given aspect of the improvementproject
CONTROL
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Evaluating ResultsRe-Calculate Process Sigma
Step BEFOREOpportunitiesUnits
1
2
3
4
5
6
7
8
9
10
11
12
4040
2 x 40 = 80 6137
113
34
142
38
69
143
37
64
72
35
1 x 40 = 40
3 x 40 = 120
1 x 40 = 40
4 x 40 = 160
1 x 40 = 40
2 x 40 = 80
4 x 40 = 160
1 x 40 = 40
2 x 40 = 80
2 x 40 = 80
1 x 40 = 40
40
40
40
40
40
40
40
40
40
40
960 846
AFTER
171
12
0
8
0
3
37
0
5
2
1
86
Yield = 1
= 1 .88
= 12%
Sigma = 0.3
960846960846
Yield = 1
= 1 .09
= 91%
Sigma = 2.8
960
86
960
86
BEFORE
AFTER
CONTROL
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Closure1. Improvement must be continuous, but individual initiatives and project teams come to an end.
2. Learn when its time to say goodbye.
3. Effective project closure weaves together the themes of: Project purpose.
Improvement methods.
Team skills and structures.
4. Develop managerial systems to capture learnings and enable the organization to addresssystem issues.
5. Documentation and recognition are two critical aspects of project team closure.
6. Celebrate!
CONTROL
Completion Check List
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Completion Check ListBy the end of the Control Phase, you should be able to answer the following :-
1. What the data showed about the effectiveness of the solution, and how the actual resultscompare to the plan.
2. Why you are now confident that the current solution should be standardise.
3. How the new methods have been documented and how this is used in the day-to-daybusiness.
4. What you do to monitor the process to sustain the gains.
5. What the key learnings are, and what recommendations the team developed for furtherimprovements.
Only after answering the above questions, you can bring your project to an end.
CONTROL
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8/2/2019 6SIGMA Handbook
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Information & Graphics Source :- TRW / Rath & Strong
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