six sigma 3 - analyze - optimized
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D M A I C
Analysis
Deliverables of the Analyze Phase:
1) Establish the capability of the current process (baseline)How good are we today at meeting customer CTQs?
What is the probability of making a defect for each CTQ? What sigma level does this translate into?
2) Define the performance objectives for measurable Ys (benchmark)
How good do we want to be at meeting customer CTQs?
3) Identify sources of variation
Based on analysis of historical (sample) data, which Xs might be affecting
the product (or process) quality?
AnalyzeAnalyze -- OverviewOverview
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D M A I C
Analysis
Analyze
Six Sigma RoadMap
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D M A I C
Analysis Tools of the Analyze Phase:AnalyzeAnalyze -- OverviewOverview
Basic graphical tools (run chart, histogram, pareto chart, boxplot,
scatter plot)
Fishbone diagram (cause-and-effect diagram)
Correlation & regression analysis
Capability indices
Confidence intervals
Process mapping (in more detail) value analysis
Variance component analysis
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D M A I C
Analysis Analyze - Baseline
1) Establish the capability of the current process (baseline)- What is the probability of making a defect for each CTQ?
If Y is a continuous r.v.,
P(defect) = P(Y>USL) + P(Yz) = P(defect)
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AnalysisAnalyze - B
Example 1: Viscosity of Aircraft Primer Paint
Batch Paint Viscosity
1 33.75
2 33.05
3 34.00
4 33.815 33.46
6 34.02
7 33.68
8 33.27
9 33.4910 33.20
11 33.62
12 33.00
13 33.54
14 33.1215 33.84
Data taken from:
Montgomery, D., (2001),
Introduction to Statistical Quality Control.John Wiley &Sons
P-Value: 0.704
A-Squared: 0.247
Anderson-Darling Normality Test
N: 15
StDev: 0.335552
Average: 33.5233
34.033.533.0
.999
.99
.95
.80
.50
.20
.05
.01
.001
Probabilit
y
Paint Viscosity
Normal Probability Plot
34.033.933.833.733.633.533.433.333.233.133.0
3
2
1
0
Paint Viscosity
Frequency
Histogram
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D M A I C
Analysis Analyze - Baseline
Minitab output:
Descriptive Statistics: Paint Viscosity
Variable N Mean Median TrMean StDev SE Mean
Paint Visc 15 33.523 33.540 33.525 0.336 0.087
Variable Minimum Maximum Q1 Q3
Paint Visc 33.000 34.020 33.200 33.810
Minitab input: Stat > Basic Statistics > Display Descriptive Statistics
Example 1 (contd)
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AnalysisAnalyze - B
Example 1 (contd)
LSL = 33.00, USL = 34.00
P(defect) = P(Y 34.00)
= P(Y
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D M A I C
AnalysisAnalyze - B
Example 1 (contd)
Find z s.t. P(Z>z) = .1375
Z = 1.09
Calculating sigma level:
P(defect) = .1375 137,500 DPMO
If the sample data only represents short-term variation in the process,
then this is the short term z. If long term variation is represented,
then the short term z = 1.09 + 1.50 = 2.59 (assuming a 1.5 shift).
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D M A I C
AnalysisAnalyze - Baseline
Other capability indices
stp
LSLUSL
C 6
=
st
pu
USLC
3
=
st
pl
LSLC
3
=
Based on short term variability: Based on long term variability:
ltp
LSLUSLP
6
=
lt
pu
USLP
3
=
),min( plpupk CCC = ),min( plpupk PPP =
lt
pl
LSLP
3
=
D M A I C
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D M A I C
Analysis Analyze - Baseline
Minitab input
Example 1 (contd)
D M A I C
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AnalysisAnalyze - B
34.534.033.533.032.5
USLLSL
Process Capability Analysis for Paint Viscos
PPM Total
PPM > USL
PPM < LSL
PPM Total
PPM > USL
PPM < LSL
PPM Total
PPM > USL
PPM < LSL
Ppk
PPL
PPU
Pp
Cpm
Cpk
CPL
CPU
Cp
StDev (Overall)
StDev (Within)
Sample N
Mean
LSL
Target
USL
144200.53
81444.07
62756.47
241398.67
131676.29
109722.38
66666.67
66666.67
0.00
0.47
0.51
0.47
0.49
*
0.37
0.41
0.37
0.39
0.341593
0.426165
15
33.5233
33.0000
*
34.0000
Exp. "Overall" PerformanceExp. "Within" PerformanceObserved PerformanceOverall Capability
Potential (Within) Capability
Process Data
Within
Overall
Minitab output:
Example 1 (contd)
D M A I C
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D M A I C
AnalysisAnalyze - B
Example 2 : Cycle time for Insurance Underwriting
CT = Date of UW decision Date that application data is submitted
USL (goal) = 14 days
100500
50
40
30
20
10
0
Submit to Approval CT
Freque
ncy
Histogram(Graph > Histogram > X=CT)
P-Value: 0.000A-Squared: 8.943
Anderson-Darling Normality Test
N: 353StDev: 21.3234
Average: 28.9717
9080706050403020100
.999.99
.95
.80
.50
.20
.05
.01
.001
Probability
Submit to Ap
Normal Probability Plot
(Stat > Basic Statistics > Normality Test)
D M A I C
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D M A I C
Analysis
100
90
80
70
60
50
40
30
20
10
0
6/25/20026/18/20026/10/2002
SubmittoApprovalCT
Date/Time
Analyze - B
Graphical analysis
of the data over time:
6/28
/200
2
6/27
/200
2
6/26
/200
2
6/25
/200
2
6/24
/200
2
6/22
/200
2
6/21
/200
2
6/20
/200
2
6/19/200
2
6/18/200
2
6/17/200
2
6/14/200
2
6/13/200
2
6/12/200
2
6/11/200
2
6/10/200
2
6/7/20
02
6/6/20
02
6/5/20
02
6/4/20
02
6/3/20
02
6/1/20
02
100
90
80
70
60
50
40
30
20
10
0
SUBMIT_DATE
Submitto
ApprovalCT
Run Chart
(Graph > Time series plot > Y=CT, Date/time stamp = submit date)
Dont use Time series plot if withinsubgroup order isnt known
(as in this case). Without a timestamp,
Minitab assumes the sample order
within each date is the same as theorder of the data set.
Boxplot of subgroups
(Graph > Boxplot > Y=CT, X=date)
Example 2 (contd)
D M A I C
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D M A I C
AnalysisAnalyze - B
Since CT is not normally distributed, we need to either transform
CT to normalize it, or find the appropriate probability distribution.
Box-Cox Power Transformation:Minitab input: Stat > Control Charts > Box-Cox Transformation
Example 1 (contd)
D M A I C
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D M A I C
AnalysisAnalyze - B
Minitab output:
3.02.52.01.51.00.50.0-0.5-1.0
70
60
50
40
30
20
95% Confidence Interval
StDev
Lambda
Last Iteration Info
17.858
17.873
17.932
0.282
0.225
0.169
StDevLambda
Up
Est
Low
Box-Cox Plot for CT
Example 1 (contd)
D M A I C l
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D M A I C
AnalysisAnalyze - B
Comparing the recommended transformation with the more common ln transform :
P-Value: 0.000
A-Squared: 2.041
Anderson-Darling Normality Test
N: 353
StDev: 0.456757
Average: 2.18922
321
.999
.99
.95
.80
.50
.20
.05
.01
.001
Probability
BoxCox CT (power of .25)
Normal Probability Plot
P-Value: 0.000
A-Squared: 3.231
Anderson-Darling Normality Test
N: 353
StDev: 0.877256
Average: 3.04177
43210
.999
.99
.95
.80
.50
.20
.05
.01
.001
Probability
LN CT
Normal Probability Plot
Example 1 (contd)
D M A I C A l B
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D M A I C
AnalysisAnalyze - B
Another approach find anappropriate distribution
In this case, we will
be better off with
the transformation
Example 1 (contd)
D M A I C A l B
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D M A I C
AnalysisAnalyze - B
Capability analysis for CT - Minitab input
Example 1 (contd)
Chooseoptions
D M A I C A l B
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D M A I C
AnalysisAnalyze - B
Example 1 (contd)
Capability analysis for CT - Minitab input (contd)
D M A I C Analyze B
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D M A I C
AnalysisAnalyze - B
Example 1 (contd)
Capability analysis for CT - Minitab output
3.02.52.01.51.0
USL*USL*
Process Capability Analysis for Submit to Ap
Box-Cox Transformation, With Lambda = 0.225
PPM Total
PPM > USL*
PPM < LSL*
PPM Total
PPM > USL*
PPM < LSL*
PPM Total
PPM > USL
PPM < LSL
Ppk
PPL
PPU
Pp
Cpm
Cpk
CPLCPU
Cp
StDev* (Overall)
StDev (Overall)StDev* (Within)
StDev (Within)
Sample NMean*
Mean
LSL*
LSL
Target*
Target
USL*
USL
708442.33
708442.33
*
708792.10
708792.10
*
657223.80
657223.80
*
-0.18
*
-0.18
*
*
-0.18
*-0.18
*
0.3814
21.33850.3807
21.1650
3532.0202
28.9717
*
*
*
*
1.8108
14.0000
Exp. "Overall" PerformanceExp. "Within" PerformanceObserved PerformanceOverall Capability
Potential (Within) Capability
Process Data
Within
Overall
D M A I C Analyze B
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AnalysisAnalyze - B
Example 1 (contd)
Capability analysis for CT - usingMinitab descriptive statistics todo a manual Z calculation:
Descriptive Statistics: BoxCox CT (power of .225)
Variable N Mean Median TrMean StDev SE Mean
BoxCox CT 353 2.0202 2.0248 2.0237 0.3812 0.0203
Variable Minimum Maximum Q1 Q3
BoxCox CT 1.0000 2.7727 1.7152 2.3248
P(defect) = P(CT.225 > 14.225)
= P( Z > (14.225 2.02)/.3812) )
= P(Z >-.2247) = .5899 589,900 DPMO
D M A I CAnalyzeAnalyze OverviewOverview
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Analysis
Deliverables of the Analyze Phase:
1) Establish the capability of the current process (baseline)How good are we today at meeting customer CTQs?
What is the probability of making a defect for each CTQ? What sigma level does this translate into?
2) Define the performance objectives for measurable Ys (benchmark)
How good do we want to be at meeting customer CTQs?
3) Identify sources of variation
Based on analysis of historical (sample) data, which Xs might be affecting
the product (or process) quality?
AnalyzeAnalyze -- OverviewOverview
D M A I CAnalyzeAnalyze - OverviewOverview
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Analysis
Generated a list of Statistically Significant Xs based on analysis
of historical data.
Process:1. Brainstorm Xs
2. Use historical data analysis to prioritize which Xs should
be investigated further in the Improve phase
Gained consensus with the project team on the list of Xs for
investigation
Identified value added & non-value added process steps
(this is especially important if your CTQ is a function of process
cycle time)
By the end of Analyze, you will have:
AnalyzeAnalyze -- OverviewOverview
D M A I CFishbone DiagramFishbone Diagram
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AnalysisFishbone DiagramFishbone Diagram
Begin by brainstorming a list of Xs which may affect the mean and/or
variance of the project CTQ(s). A useful tool for this is the Cause & EffectDiagram (Fishbone Diagram).
Purpose: To provide a visual display
of all possible causes of a specific
problem
When:
To expand your thinking toconsider all possible causes
To gain groups input
To determine if you have correctly
identified the true problem
CauseCause
EffectEffect
Categories
Causes
Problem
Statement
D M A I C
Fishbone DiagramFishbone Diagram
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Analysis
Problem
Statement
Measurements Materials Men & Women
MethodsEnvironment Machines
Draw a blank diagram on a flip chart.
Define your problem statement.
Label branches with categories appropriate to your problem.
Categories can also be Policies, Procedures, People, and Plant
or any other category that will help people think creatively.
The 4 Ps
Fishbone DiagramFishbone Diagram
D M A I CFishbone DiagramFishbone Diagram
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Analysis
Brainstorm possible causes and attach them to appropriate categories.
For each cause ask, Why does this happen?
Problem
Statement
Measurements Materials Men & Women
MethodsEnvironment Machines
CauseWhy
Analyze results, any causes repeat? As a team, determine the three to five most likely causes.
Determine which likely causes you will need to verify with data.
Fishbone DiagramFishbone Diagram
D M A I C
A lFishbone DiagramFishbone Diagram
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Analysis
Stamp
paperCut Fold
Variation
of CTQApply tail clip
Process Fishbone Example (Helicopter Example)
Fishbone Diagramb ag a
Package
D M A I C
A l iTools for prioritizing XTools for prioritizing Xss
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Analysisp gp g
Once the team has a list of potential Xs, use historical dataanalysis to prioritize their importance.
Simple statistical tools/analytical methods will be very usefulhere, for example:
Pareto charts
Other graphical tools, such as side-by-side boxplots,scatterplots, etc.
ANOVA, variance component analysis
Correlation matrix
D M A I C
A l i
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Analysis
Pareto Chart
Purpose: To separate the vital few from the trivial many in a process. Tocompare how frequently different causes occur or how much each cause costs
your organization.
When: To sort data for determining where to focus improvement efforts.
To choose which causes to eliminate first
To display information objectively to others
Pareto Principle:
20% of causes
account for 80% of
the effect
Pareto Principle:
20% of causes
account for 80% of
the effect
D M A I C
A l iValueValue--Add AnalysisAdd Analysis
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Analysisy
Steps That Are
EssentialBecause They
Physically
Change The
Product/Service,
The Customer IsWilling To Pay For
Them And Are
Done Right The
First Time.
Steps That Are
EssentialBecause They
Physically
Change The
Product/Service,
The Customer IsWilling To Pay For
Them And Are
Done Right The
First Time.
Steps That Are
Considered Non-Essential To
Produce and
Deliver The
Product Or
ServiceTo Meet The
Customers Needs
And
Requirements.
Customer Is Not
Willing To Pay For
Step.
Steps That Are
Considered Non-Essential To
Produce and
Deliver The
Product Or
ServiceTo Meet The
Customers Needs
And
Requirements.
Customer Is Not
Willing To Pay For
Step.
Value-Enabling Work
Steps That Are
Not Essential To
The Customer,
But That Allow
the Value-
Adding Tasks
To Be DoneBetter/Faster.
Steps That Are
Not Essential To
The Customer,But That Al low
the Value-
Adding Tasks
To Be DoneBetter/Faster.
Value-
AddedWork
Non
Value-
Added
Work
D M A I C
Analysis
ValueValue--Add AnalysisAdd Analysis
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Analysis
Types Of Nonvalue-added Work
Internal Failure Delay
External Failure Preparation/Set-Up
Control/Inspection Move
What Does the Customer Value?What Does the Customer Value?
D M A I C
AnalysisValueValue--Add AnalysisAdd Analysis
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Analysis
Cycle TimeCycle Time
Process TimeProcess Time
Delay TimeDelay Time+
D M A I C
AnalysisValueValue--Add AnalysisAdd Analysis
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Analysis
Gaps
Redundancies
Implicit or unclear requirements
Tricky hand-offs
Conflicting objectives
Common problem areas
Process Disconnects (will increase process cycle time):
D M A I C
AnalysisProcess Flow AnalysisProcess Flow Analysis
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Analysis
5. Retrieve
application
and review for
completeness
10. Review
for
completenes
s and make
decision
1. Receive
applicationin mail and
open
envelope
2. Place
application
in mail slot
3. Move
application
to Entry
Dept.
4. Place
application
in
in-box
Isapplication
complete?
7. Enter
application
to computer
system
6. Call to
obtainnecessary
information
8. Score
application
9. Queue
application
for credit
review
Are weextending
loan?
19. Generate
turndownletter
12. Generate
loan packet
13. Place in
out-box
14. Move to
mail room
15. Wait forpostage
16. Postpackage or
letter
17. Place in
outbound
mail basket
18. Post
man picks
up outbound
mail
No
Yes
Yes
No
UnclearUnclearrequirementsrequirements
TrickyTrickyhandhand--offoff
RedundancyRedundancy
UnclearUnclearrequirementsrequirements
TrickyTrickyHandHand--offoff
11. Makeloan
decision
xample loan evaluation process
D M A I C
Analysis
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Analysis
Cake Example Analyze phase
1) Establish the capability of the current process (baseline)
2) Define the performance objectives for measurable Ys (benchmark)
How good do we want to be at meeting customer CTQs?
3) Identify sources of variation
Based on analysis of historical (sample) data, which Xs might be affecting
the product (or process) quality?
D M A I C
Analysis
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Analysis
Cake % Flour % Sugar % Water % Oil Oven Temp Mixing Time Bake Time Mix Spd Num Eggs FPS height (mm)
1 47.0 20.0 5.0 27.0 373 5 54 low 2 0.40 42.0464
2 47.0 27.0 5.0 20.0 381 3 50 low 2 0.26 44.6038
3 47.0 20.0 5.0 27.0 377 3 52 med 3 0.33 59.1240
4 40.0 27.0 5.0 27.0 383 5 51 high 3 0.42 38.0634
5 40.0 20.0 19.0 20.0 368 4 50 med 3 0.30 35.7231
6 54.0 20.0 5.0 20.0 373 5 49 low 2 0.30 43.0212
7 47.0 27.0 5.0 20.0 361 3 50 high 2 0.37 46.5552
8 40.0 20.0 5.0 34.0 368 5 54 low 2 0.45 11.9006
9 47.0 20.0 5.0 27.0 382 5 50 med 3 0.37 45.6810
110
10 cakes sampled randomly per day for 11 days, measurements made
CTQ
Height LSL = 40
D M A I C
Analysis
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Analysis
Height appears normally distributed.
Sample avg = 43.54, s = 11.7
85756555453525155
99
9590
80706050403020
105
1
Data
Percent 0.453AD*
Goodness of Fit
Normal Probability Plot for height (mm)ML Estimates - 95% CI
Mean
StDev
43.5393
11.6997
ML Estimates
D M A I C
Analysis
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y
Calculating short term capability for Height:
P(height
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y
706050403020100
20
10
0
height (mm)
Frequency
LSL
Need to increase
the mean heightand also possibly
reduce variability
D M A I C
Analysis
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y
1) Establish the capability of the current process (baseline)
2) Define the performance objectives for measurable Ys (benchmark)
How good do we want to be at meeting customer CTQs?
3) Identify sources of variation
Based on analysis of historical (sample) data, which Xs might be affecting
the product (or process) quality?
D M A I C
Analysis
Fishbone
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Measurements Machines Man/Mother Nature
Material:
Quality
Methods:
Formulation
Methods:
Processing
height
bulk density
viscosity
particle size
sugar
baking powder
salt
eggs
flour
oil
%flour
%sugar
%baking powder
%salt
#eggs
%oil
%water
dry mix time
dry mix speed
wet mix time
wet mix speed
Dry mix vessel
Dry mix blade
Wet Mix Blender
Oven Rack
humidity
Baking time
Baking temp
elevation
Mean
Heighttoo low
D M A I C
Analysis
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Next step: figure out which variables on fishbone are controllable and whichones are uncontrollable
Uncontrollable variables are the noise variables
Controllable variables can either be varied in the experiment or held constant
We need to categorize the xs on the fishbone as follows: (Schmidt andLaunsby, 1994)
control xs (label as a X) noise xs (label as a N)
constant xs (label as a C)
D M A I C
Analysis
Use impact scores from QFD to help decide if a x should be labeled X or C
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industrial engineering ui - where the science of engineering and management blends 43TEKNIK INDUSTRIUNIVERSITAS INDONESIA
Measurements Machines Man/Mother Nature
Material:
Quality
Methods:
Formulation
Methods:Processing
height
bulk density
viscosity
particle size
sugar
baking powder
salt
eggs
flour
oil
%flour
%sugar
%baking powder
%salt
#eggs
%oil
%water
dry mix time
dry mix speed
wet mix time
wet mix speed
dry mix vessel
dry mix blade
wet mix blender
oven rack
humidity
baking time
baking temp
N
N
N
NN
N
N
N
N
N
N
C
C
C
C
C
CC
C
X
XX
X
X
XXX
X
elevation N
Mean
Height
too low
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