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MTCP ProgramSix Sigma Introduction
15th June 2009
Malaysia Productivity Corporation(Statutory Body under MITI)P.O Box 64, Jalan Sultan, 46904 Petaling JayaWebsite: www mpc gov my
Topic: Six Sigma Introduction
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Website: www.mpc.gov.my
Consultant: Mohd Azlan AbasTel: +6 012 308 7421Email: [email protected]
Why Does One Need a Quality Initiative?
Meet customer expectations for higher quality
Provide a competitive differentiator in the service market
Build greater pride and satisfaction in the team
Tangible Costs Intangible Costs- Inspection - Expediting- Scrap - Lost Customers- Rework - Longer Cycles- Warranty - Lower Morale
Drive other key goals: productivity and growth
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Enormous opportunityEnormous opportunity
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Vital Few CTQs that apply to all Customers:
– Responsiveness
– Marketplace Competitiveness
Six Sigma Provides focus on
Critical to Quality (CTQ) Metrics in businesses
p p
– On-time, Accurate and Complete Deliverables
– Product/Service Technical Performance
Key CTQs for a company:
– Post Sales Issue resolution
– Service Delivery Span
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– Contract Fulfillment
– Parts Fulfillment
– Pricing
– Customer Escalation Cycle Time
PracticalProblem Traditional
Approach
D fi & MD fi & M
Six Sigma Provides focus on
Critical to Quality (CTQ) Metrics in businesses
StatisticalProblem
StatisticalSolution
6Quality Methodology
Systematic Approach Focusing
Define & MeasureDefine & Measure
AnalyzeAnalyze
ImproveImprove
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Driving Customer & Shareholder BenefitsDriving Customer & Shareholder Benefits
PracticalSolution
Systematic Approach Focusing on Statistically Significant Root
Causes & Solutions
pp
ControlControl
3
What is Six Sigma?Process to reduce defects per million opportunities
• From current levels to “Six Sigma”
• “Sigma” is standard deviation from the ideal
• Can be applied to all business functions
2
3
308,537
66 807
B DPMO
• Can be applied to all business functions
» Manufacturing, Products, Transactions
» Service, Sales Support
Quantitative methodology
• Uses measurements and scientific process
3
4
56
66,807
6,210
233
3.4
3 to 620 000 times improvement
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... 20,000 times improvement ... ... A true quantum leap
Process = Hose
Four Important Properties:(1) Centering(2) Spread(3) Shape(3) Shape(4) Stability Over Time
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Y axis = Weight (lbs)
10.5 10 9.5
4
Every Human Activity Has Variability...
MeanUpper
C tLower
C t
Six Sigma Concept
1 p(defect)
Customer Specification
Customer Specification
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Reducing variability is the essence of six sigma
Target
1
Some Chance of
Failure
Mean
Th hi h th
Specification LimitWhat is Sigma?
1
3
Much Less Chance of
Failure
The higher the number (Z) in front
of the sigma symbol the lower the chance
of producing a defect
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Reducing variation is the key to reducing defects
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Reducing Variation is the Key
Starting Point After Project
Order by Order Delivery TimesWhat GE sees
28 29
Meanh
What Customers feel
13 17
2818
623
58
1619
296
1012
4101310
(Days)
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Big Change
VarianceNo Significant Change
30% improvement
193311
17
102013
13Average
Reference: Six Sigma Performance
Six Sigma99.99966% Good
• 20,000 lost articles of mail per hour
• Seven articles lost per hour
3.8 Sigma99% Good
• Unsafe drinking water for almost 15 minutes each day
• 5,000 incorrect surgical operations per week
• Two short or long landings at
• One unsafe minute every seven months
• 1.7 incorrect operations per week
• One short or long landing
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• Two short or long landings at most major airports each day
• 200,000 wrong drug prescriptions each year
• One short or long landing every five years
• 68 wrong prescriptions per year
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Key Terms: Process or Activity
OutputsProcess X’sor Factors
X1
XY1
For any given product, procedure or transaction, there are inputs, a process, and outputs. You will need to measure the outputs to quantify how well you satisfy a CTQ requirement; the output measures are Ys To
PROCESSX2
X3
X4
1
Y2
Y3
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Find and control the critical X’s
well you satisfy a CTQ requirement; the output measures are Ys. To change the process performance however, you must find and change the critical Xs.
Q
GM GlobalQuality
Master
The People
GreenbeltsApply Six Sigma toolsand methodology in
everyday work.
Quality Leaders
Help choose projects, interview Black Belt candidates, tie projects to business needs. Remove barriers and
Master Black Belts
Develop tools and teaching materials. Conduct training and communication sessions. Mentor Six Sigma
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Remove barriers and drive Six Sigma into the culture of their functions.
Black Belts and their projects.
Project leaders, change agents, expert application of tools, mentor Green Belts and their projects.
gBlack Belts
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ObjectivesObjectives• DEFINE Phase Purpose
– Step A: Customer & Project CTQs
– Step B: Team Charter (4‐Blocker)
St C Th Hi h L l P M
DMAICStep A
– Step C: The High Level Process Map
• Change Acceleration Process (CAP)
– E = Q x A
– The Model
– Key CAP tools:
• ARMI
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ARMI
• GRPI
• Threat/Opportunity Matrix
• In/Out of the Frame
CTQ Definition and CTQ Elements
DMAICStep A
Cycle Time to Deliver Drawings
Product/Process
Characteristic
Customer & Project CTQsCustomer & Project CTQs
From Notice To Proceed To Delivery Time of Drawings
(Weeks)
On Time Delivery
Measure
Specification/Tolerance
Target13 Weeks
CustomerNeed
CTQ
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ToleranceLimit(s)
A performance standard translates customer needs intoA performance standard translates customer needs intoquantified requirements for our product or processquantified requirements for our product or process
15 Weeks
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A Project Team CharterA Project Team Charter DMAICStep B
Business Case (Problem statement) Potential Issues/ Speed Inhibitors
Project Team
•Multilin has a small market share in Indonesia
compared to the more established European relays
manufacturer. Need to improve our service to
customer and increase sales in Indonesia
• Data collection
Milestones
Goal Statement
Name Org. Role % Ded.
Owner Date
Vince Tullo Manager ChampionStuward Thompson Manager ChampionW.N. Yew Sales Leader 70%Daniel Sutando Sales leader Member 10%W.Y. Tan Sr App Engr Member 10%Steven Tao BB Member 5%
customer and increase sales in Indonesia.
•To increase sales figures in Indonesia in 2004 to
$1.8M.
• To ensure relevant projects are pursued and to
improve the market coverage for distributors, EPCs,
and end users.
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esto es
Scope Included:
Deliverables
Date
Project Charter Approved YWN /Tao Apr 30
Measure /Baseline YWN/Tan July 30
Analyze WN/Tao Aug 30
Improve YWN/Tao Sept 30
Control YWN/Tao Oct 30
Close YWN/Tao Nov 30
•Multilin relays, Indonesia Market
Order growth for 2004
11 9 8 5 4 3
1
6 7 10 2 12
correct size
out of round
wire on pulley
damaged pulley
measurement accuracy
cold weld stand
change reel
wire speed# feet per spool
correct size
out of round
wire on pulley
damaged pulley
measurement accuracy
wire build on reel
proper die l b i ti
Input Legend
WIRE MILL PROJECT
Xs
DMAICStep C
14 15 16 17 18 19 20 21 22 23 13
1) Start of shift2) Change final capstan felt3) Check for excessive slivers/fines4) Check size5) Check surface quality6) Check stand supply
13) Wire size change14) Stop machine15) Replace dies (as required)16) Restring new setup17) Check wire size18) Attach wire to spool
correct size
out of round
accurate tension setting
lubrication
direction of lubricant flowpH level
fat level
pressuretemperature
A) DiameterB) Out-of-round
Legend
CTQ’s
critical
controllablenoise
Ys
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6) Check stand supply7) Is reel spooled 8) Connect wire to new reel9) Check size10) Check surface quality11) Check for acceptable spool build12) Store in enamel room
) p19) Set dancer air pressure20) Crack valve21) Check lubricant flow22) Start spooler23) Start capstan
)C) LoopsD) TanglesE) PinchoutsF) Surface quality
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Objectives• Introduction to Measure
- Measure Phase Deliverables
- Using Statistics to Solve Problems
• Measure Step 1: Select CTQs
- Quality Function Deployment (QFD) Process
DMAIC
- Quality Function Deployment (QFD) Process
- Process Mapping
- Failure Modes & Effect Analysis (FMEA)
- Pareto Chart
- Cause & Effect Diagram
• Measure Step 2: Define Performance Standards
- Performance Standard / Defect
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/
- Basic Nature of Data
• Measure Step 3: Measurement System
• Introduction to Measurement Systems Analysis (MSA)
The Statistical ProblemThe Statistical ProblemGoal: Find the Relationship
Y = f(X1, …, Xn) Process - BProcess - A
DMAIC
Shape of the Curves CHARACTERIZES the ProcessShape of the Curves CHARACTERIZES the Process
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ppProcess B is Better than Process A*Process B is Better than Process A*
* Assumes same scale
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Select CTQ CharacteristicsSelect CTQ Characteristics
Functional Requirements(HOW’s)
DMAICStep 1
Quality Function Deployment (QFD)Quality Function Deployment (QFD) Process Mapping (Flow Chart)Process Mapping (Flow Chart)
Map Customer Needs to Potential Hows
Cu
sto
mer
Req
uir
emen
ts
(WH
AT
’s)
Identify Critical Few Identify Critical Few -- Resource PlanningResource Planning Map “Information” FlowMap “Information” FlowIdentify All Touch PointsIdentify All Touch Points
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Select CTQ CharacteristicsSelect CTQ Characteristics DMAICStep 1
Anticipate Potential Failures in Process / Products & Develop Proactive Mitigation PlansAnticipate Potential Failures in Process / Products & Develop Proactive Mitigation Plans
Process Step
OR
Part Number
Potential Failure Mode
Potential Failure Effects
SEV
Potential Causes
OCC
Current Controls
DET
RPN
Action Recommended
Owner
Failure Modes & Effects Analysis (FMEA)Failure Modes & Effects Analysis (FMEA)
20% of causes account for 80% of the problem
Anticipate Potential Failures in Process / Products & Develop Proactive Mitigation PlansAnticipate Potential Failures in Process / Products & Develop Proactive Mitigation Plans
PE FLOWP FLOW
0
500000
1000000
0
20
40
60
80
100
Pe
rce
nt
Co
unt
Defects by Operation
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MA CH. SHA PE
FINA L STA GE FLO
COA THOL E 1
X-RA Y INSP
HOLE 2INSP
BENCHHOLE 3
FINAL W A TER FLO
276144130844127204102599101491 93353 82861 54110 49643 3670726 .2 12.4 12 .1 9 .7 9 .6 8.8 7 .9 5 .1 4.7 3.5
26 .2 38.6 50 .6 60 .4 70 .0 78.8 86 .7 91 .8 96.5 100.0
Defect
C ountP ercentC um %
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Performance Standards Objectives
• Determine the Performance Standard
• Define a Defect- What are the customer’s acceptance criteria for the part/product or process?
DMAICStep 2
• Established How to Measure the Quality of the Part / Product or Process
- Where are the data coming from?
- How do you measure the process?
- What are the units of measure?
- Is it a discrete or continuous measure?
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• Gained Consensus On the Performance Standard
• Are Requirement(s) or Specification(s)Requirement(s) or Specification(s) Imposed by the
Customer on a Specific CTQ
• Translate Customer Needs into Measurable Measurable
What’s Performance StandardsDMAICStep 2
CharacteristicCharacteristic– Have Clear Operational Definition, i.e. Specifies What to Measure, How to
Measure & Collect the Data
– Specifies Target or Mean
– Impose Specification Limits
– Have Clear Defect Definition
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CTQs Quantified CTQs Quantified –– Everybody on Same PageEverybody on Same Page
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More Performance Standards . . .DMAICStep 2
Good Product
Target
LSLLower Spec Limit
USLUpper Spec Limit
Tolerance
= USL - LSL
Defective ProductDefective Product
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Specification limitsSpecification limits are set in order to divide customer satisfaction from customer disappointment. While the exact limits may not be explicitly stated by the customer (and captured in Step 1), their specific values come from what the customer defines as a defect.
Lower Spec Limit Upper Spec Limit
The Basic Nature of Data•• Continuous DataContinuous Data
- Characterizes a product or process feature in terms of its size, weight, volts, time, or currency
- The measurement scale can be meaningfully divided into finer and finer increments of precision
DMAICStep 2
-- Distributions: Distributions: To apply the normal distribution, one must necessarily use continuous data
•• Discrete DataDiscrete Data- Counts the frequency of occurrence: e.g., the number of times something
happens or fails to happen - Is not capable of being meaningfully subdivided into more precise
increments The validity of inferences made from discrete data are highly dependent
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- The validity of inferences made from discrete data are highly dependent upon the number of observations. The sample size required to characterize a discrete product or process feature is much larger than that required when continuous data is used.
-- Distributions:Distributions: The Poisson and binomial models are used in connection with this type of data
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Making Data Driven Decisions• Six Sigma is all about reducing defects for the customer. Fewer defect result in a more satisfied customer.
• The project team must decide what needs to be done to improve quality for the customer based on actual data – measurements of the product or process.
• The measurement system (gauge) used to collect the project data has to be
DMAICStep 3
• The measurement system (gauge) used to collect the project data has to be sufficiently good to allow the project team to make the correct decisions.
• A measurement system must deliver data that accurately represents the project or product. It is defective if it does not.
• The Six Sigma project team becomes the customer for the measurement process. There are many CTQs a project team must consider when evaluating the quality of a gauge…
If th i ’t d h f th d f th j tIf th i ’t d h f th d f th j t
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If the gauge isn’t good enough for the needs of the project, If the gauge isn’t good enough for the needs of the project, you have to fix it (using DMAIC) before you can move on!you have to fix it (using DMAIC) before you can move on!
In order to improve a product or process, we must measure it. We have submit the output from that process to a second measurement process.
ProcessInputs Outputs
Parts(Example)
DMAICStep 3
As a result, all of our observations of the original process are distorted by
The Measurement Process
MeasurementProcess
Outputs
• Observations• Measurements• Data
ocess
Inp
uts
p yerrors in our measurement system. We need to make sure these error don’t dominate our view of the process!
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DMAICStep 3
+ =
ProcessInputs Outputs Inputs MeasurementProcess
Outputs
Accuracy (Bias) ‐ Shift in the Average
True Avg Bias Obs. Avg
Actual(Part) + Meas. System = Observed(Total)
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Measurement System Bias Measurement System Bias ––Determined through “Calibration Study”Determined through “Calibration Study”
Product Variability Total Variability
DMAICStep 3
Measurement
Measurement System Precision
ProcessInputs Outputs Inputs MeasurementProcess
Outputs
Product Variability (part)
Total Variability (Observed total)
actual(part) +
meas. system = observed(total)
Measurement Variability
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Measurement System Variability Measurement System Variability ––Investigated through “R&R Study”Investigated through “R&R Study”
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Accuracy vs. PrecisionDMAICStep 3
xxxxxxxxxx
xxx xxxxxx
No
Accurate?
Precise?
Yes
Yes
No
No
Accurate?
Precise?
Yes
Yes
No
No
Accurate?
Precise?
Yes
Yes
No xx x
xxx
xx
x
x
x
xx
x
x
xx
x x
Measured Value
The True Value
No
Accurate?
Precise?
Yes
Yes
No
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xx
xx
Accuracy: the difference between the observed average and the truth.Precision: the amount of inconsistency between measurements.
Characteristics of a Measurement System
•• AccuracyAccuracy : Differences between observed average measurement and a standard.
•• ResolutionResolution : The smallest scale of the measurement.
•• StabilityStability : Do measurements change with time?
•• LinearityLinearity : Is the measurement proportional to the magnitude (size,
DMAICStep 3
yy p p g ( ,weight, etc) of the sample.
•• PrecisionPrecision : Noise of the measurements.
– Repeatability: variation when one person repeatedly measures the same unit with the same measuring equipment. Also called Equipment Variation (EV).
– Reproducibility: variation when two or more people measure the same unit with the same measuring equipment. Also called Appraiser Variation (AV)
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Variation (AV).
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WHAT IS MINITAB?• Statistical software package• Has many of the tools needed to successfully analyze data with
rigor- Graphs- Statistical tools for data analysis- Six Sigma Reports
• Descriptive Statistics
• Gage R & R
• Capability Analysis (ZST/ZLT)
• Graphing - Many Types! (Try them all!)
• Pareto, Fish bone
• Hypothesis Testing
• Product & Process Six Sigma Reports
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• Generation of Test Plans for Designed Experiments
• Analysis of DOE results
• Statistical Process Control
A Great Toolbox for Six Sigma Projects!A Great Toolbox for Six Sigma Projects!
What does Minitab Look Like?What does Minitab Look Like?Menu Bars: For quick access to common commands.
Session Window:Shows Minitab text output (One only is present)
Worksheet Window: Kind of like an Excel worksheet (at least one is always present). A tool is available to
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tool is available to manage multiple worksheets.
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ObjectivesObjectives
• Calculate baseline capability of the process using either continuous or discrete data
• Statistically define the improvement goals
DMAIC
y p g
• Generated a list of Statistically Significant Xs based on analysis of historical data
• Identified which Xs to further investigate in the Improve phase
• Gained consensus with the project team on the list of Xs for
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Gained consensus with the project team on the list of Xs for investigation
Step 4: Establish Process CapabilityStep 4: Establish Process Capability
USLUSL
Y = f (X 1 . . . X )n
DMAICStep 4
The variation inherent to any dependent variable (Y) is determined bythe variations inherent to each of the independent variables. (X)
Very Low Probability of
Defects
Very Low Probability of
Defects
ExcellentProcess Capability
Very High Probability of
Defects
Very High Probability of
Defects
PoorProcess Capability
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Low Z High Z
LSL USLLSL USL
Z is a Measure of Process CapabilityZ is a Measure of Process Capability
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p(x) BenchmarkEntitlement
Baseline
Step 5: Define Performance ObjectiveStep 5: Define Performance Objective
Benchmark: World-Class performance
Entitlement: The level of performance a business should be able to achieve given the investments already made
Defects
Baseline: The current level of performance
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Benchmarking Sets the Ultimate Goal, while Baselining Benchmarking Sets the Ultimate Goal, while Baselining
Takes Current Measurements to Monitor a ProcessTakes Current Measurements to Monitor a Process
Step 6: Identify Sources of VariationStep 6: Identify Sources of Variation
To get results, should we focus our behavior on the Y or X ?
Y= f (X)
DMAICStep 6
n Y
n Dependent
n Output
n Effect
n Symptom
n X1 . . . Xn
n Independent
n Input-Process
n Cause
n Problem
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Historically the Y, … with Six Sigma the XsHistorically the Y, … with Six Sigma the Xs
n Monitor n Control
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1.1. Identify Requirements on the Customer or Internal YIdentify Requirements on the Customer or Internal Y
These are often expressed quantitatively as target values plusspecification limits. - Anything “outside of the specification limits” is a defect.
Determining Process Capability (Steps 1 Determining Process Capability (Steps 1 –– 4)4)
Target ValueUSLLSL
Process CapabilityProcess Capability DMAICStep 4
2.2. Determine Process DistributionDetermine Process DistributionWe expect variation in our process.The Y’s measured on a large number
110Defects
gUSL (upper specification limit)(lower specification limit) LSL
Tolerance
10090Defects
Mean = 102 = 5.0
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The Y s measured on a large numberof parts will form a distribution. Forsimplicity, we’ll assume that they forma normal distribution with a knownmean and standard deviation.
85 90 95 100 105 110 115
3.3. Superimpose your process distribution on to the targetSuperimpose your process distribution on to the targetand specification limits.and specification limits.
USLLSL
Target Mean = 102 = 5.0
Process CapabilityProcess Capability DMAICStep 4
4.4. Apply some Basic Statistics.Apply some Basic Statistics.1. We can relate our distribution to the standardized normal distribution.
• The total area under the standard curve = 1 (or 100%)2 If d i h Z l di ifi i li i
85 90 95 100 105 110 115
USLLSL
Probability of a Defect
Probability of a Defect
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2. If we can determine the Z-value corresponding to a specification limit,then we can calculate the area beyond that limit (out of specification)• The area beyond a given specification limit is the fraction of the
population that is defective wrt that limit.
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Putting it all together (Steps 1 Putting it all together (Steps 1 –– 4)4)
Total Area Outside of Specification Limits = (0.055 + 0.008) = 0.063Total Area Outside of Specification Limits = (0.055 + 0.008) = 0.0636.3% of what we produce is defective6.3% of what we produce is defective
Process CapabilityProcess Capability DMAICStep 4
USLLSL
Target Mean = 102 = 5.0
0.055y Probabilit
1.65
102110
(USL)Z
0.008y Probabilit
2510290
4.(LSL)Z Notice also that ourNotice also that ourprocess is not centeredprocess is not centered
on the targeton the target
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85 90 95 100 105 110 115
Z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.42470.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.38590.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.34830.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.31210.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.27760.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.24510.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.21480.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.18670.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.16111 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379
SingleSingle--Tail Z Table (values from 0.00 to 3.99)Tail Z Table (values from 0.00 to 3.99)
z
1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.11701.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.09851.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.08231.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.06811.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.05591.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.04551.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.03671.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.02941.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.02332 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183
2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.01432.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.01102.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.00842.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.00642.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.00482.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.00362.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.00262.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.00192 9 0 0019 0 0018 0 0018 0 0017 0 0016 0 0016 0 0015 0 0015 0 0014 0 0014
Calculates the probability of a USL defect above the given value of z
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2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.00143 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010
3.1 9.68E-04 9.36E-04 9.04E-04 8.74E-04 8.45E-04 8.16E-04 7.89E-04 7.62E-04 7.36E-04 7.11E-043.2 6.87E-04 6.64E-04 6.41E-04 6.19E-04 5.98E-04 5.77E-04 5.57E-04 5.38E-04 5.19E-04 5.01E-043.3 4.83E-04 4.67E-04 4.50E-04 4.34E-04 4.19E-04 4.04E-04 3.90E-04 3.76E-04 3.62E-04 3.50E-043.4 3.37E-04 3.25E-04 3.13E-04 3.02E-04 2.91E-04 2.80E-04 2.70E-04 2.60E-04 2.51E-04 2.42E-043.5 2.33E-04 2.24E-04 2.16E-04 2.08E-04 2.00E-04 1.93E-04 1.85E-04 1.79E-04 1.72E-04 1.65E-043.6 1.59E-04 1.53E-04 1.47E-04 1.42E-04 1.36E-04 1.31E-04 1.26E-04 1.21E-04 1.17E-04 1.12E-043.7 1.08E-04 1.04E-04 9.96E-05 9.58E-05 9.20E-05 8.84E-05 8.50E-05 8.16E-05 7.84E-05 7.53E-053.8 7.24E-05 6.95E-05 6.67E-05 6.41E-05 6.15E-05 5.91E-05 5.67E-05 5.44E-05 5.22E-05 5.01E-053.9 4.81E-05 4.62E-05 4.43E-05 4.25E-05 4.08E-05 3.91E-05 3.75E-05 3.60E-05 3.45E-05 3.31E-05
21
Problem with SpreadDesiredCurrent
SituationAccurate but not Precise
Goal: Process on Target with Minimum SpreadGoal: Process on Target with Minimum Spread
DMAICStep 6
Identify Variation SourcesIdentify Variation Sources
Situation
LSL USLT
not Precise
DesiredCurrent
SituationPrecise but not
Accurate
Problem with Centering – Not on Target
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LSL USLT
Accurate
Is the Problem Centering, Spread, or Both?Is the Problem Centering, Spread, or Both?
One Sample Two Samples Multiple Samples
Study Stability(Run Chart)
Study Shape
Continuous Data Analysis Road MapContinuous Data Analysis Road Map DMAICStep 6
Study Shape(Histogram, Dot Plot, Normality)
Study Spread(Chi Square-Test)
Data paired?
Study Spread(F-test)
Study Centering(Paired t test)
Study Spread(Homogeneity of Variance)
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(F test)
Study Centering(2 sample t-test)
Study Centering(1 sample t-test)
(Paired t-test)
Study Centering(ANOVA)
22
Descriptive StatisticsDescriptive StatisticsStat > Basic Statistics > Display Descriptive Statistics
Provides summary reportof basic statistical
DMAICStep 6
p-value > .05 Cannot Reject H0
No evidence that data is non-normal
Basic Statistical Information
Dot Plot
Histogram
Minitab Output
of basic statisticalinformation
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Confidence Intervals
X and Y Data CorrelationX and Y Data Correlation
5
10
15
20
25
Y
Strong Positive Correlation
DMAICStep 6
00 5 10 15 20 25
X
10
15
20
25
Y
5
No Correlation
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5 10 15 20 25
X
0
5
0
23
Improve Phase ObjectivesImprove Phase Objectives• The benefits of Design of Experiments (DOE’s)
• Key concepts and terms associated with DOE’s
• Performing a simple full factorial and fractional DOE’s and interpreting the results
• Awareness of screening designs and higher level response surface designs
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What’s Improve Phase About. . .What’s Improve Phase About. . .• Develop an Improvement Strategy
• Determine which candidate x’s identified in the Analyze Phaseare truly “critical X’s”.
• If possible, determine a quantitative transfer function thatrelates your Y to these critical X’s
DMAIC
• Identify Improvement Actions• Determine optimal settings for the X’s• Show the impact of the changes on meeting
project or business objectives.
• Validate the Improvement• Demonstrate the validity of your identified improvement
actions via additional experiments or a pilot study
Y = f(x)
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• Develop a Plan to Implement the Change
It’s More than Just Designed ExperimentsIt’s More than Just Designed Experiments
24
Common “Improve” ToolsCommon “Improve” Tools
BasicBasic Process Map
Fishbone
Box Plot
IntermediateIntermediate DOE
Full Factorial
Fractional
AdvancedAdvancedDOEResponse Surface
Taguchi (Inner /
DMAIC
Box Plot
Time Order Plots
Hypothesis Tests
Linear Regression
Mistake Proofing
Fractional Factorial
Intro to Response Surface
Multivariate Regression
Taguchi (Inner / Outer Array)
Simulation Models
Problem SophisticationProblem Sophistication
Already Covered Covered in Improve Covered in DFSS Adv. Level III e.g. ProModel
LOWLOWLOWLOW
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Problem SophisticationProblem Sophistication
• Complexity
• Business Impact
• Risk
• Data AvailabilityMatch the Tool to the Match the Tool to the
ProblemProblem
LOWLOWLOWLOW
HIGHHIGHHIGHHIGH
Y = f (x1, x2, x3,……xn)
Response (Y)Response (Y) Factors (x’s)Factors (x’s)
DMAICSteps 7-8DOE DOE –– Design of ExperimentsDesign of Experiments
Response (Y)Response (Y)
• The measured outcome of an experiment
• The value observed for the CTQ being explored
Factors (x s)Factors (x s)
• The critical X’s which determine the response,Y
•• They can be categorical or They can be categorical or numericalnumerical
LevelsLevelsRangesRanges
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LevelsLevels
• In DOE’s we investigate the effect of each factor at more than one setting or value
RangesRanges
• The extreme values for each factor determines the range for that factor - the region of interest/investigation
25
Classical ApproachClassical ApproachOFAT OFAT -- One Factor at a TimeOne Factor at a Time
• Change one variable, X2,while holding all others
Benefits of DOEsBenefits of DOEs
90100
DMAICSteps 7-8
constant.
• Find a maximum
• Hold X2 at the“maximum effect” level andrepeat the process for the other variables.
60
7080
Factor X1
OFATOFAT
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OFATOFAT• Requires more experiments than a DOE• Becomes unmanageable as the number of factors increases• Can be very expensive and time consuming – and may not work very well
DOE ApproachDOE Approach
• Select factors and levels
• Select mathematical modeldesigned to obtain maximuminformation for the number
Benefits of Design of ExperimentsBenefits of Design of Experiments
90100
DMAICSteps 7-8
information for the numberof factors/levels selected.
• In your experiments changethe factor levels in a systematicmanner so that all coefficients inthe model can be uniquely computed.(Orthogonality)
• Solve the resulting set of simultaneous equations to obtain the coefficients
60
7080
90
Factor X1
00
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• Solve the resulting set of simultaneous equations to obtain the coefficients.
• Use statistical tests to determine if the coefficients are statistically significant, and if the resulting model (transfer function) is adequate.
• Use the results of your DOE to plan the next DOE (if needed).
26
DMAICSteps 7-8
Screening DesignsScreening Designs
The Team’s understanding atThe Team’s understanding atthe beginning of the projectthe beginning of the project What Mother Nature KnowsWhat Mother Nature Knows
The following 7 Factors The following 7 Factors may bemay be critical X'scritical X's Yield = 64.25Yield = 64.25
A. Temperature (160C A. Temperature (160C -- 180C)180C)B. Monomer Concentration (20% B. Monomer Concentration (20% -- 40%)40%)C. Catalyst Vendor (Sally C. Catalyst Vendor (Sally -- Ed)Ed)D. Stirring Speed ( 50 RPM D. Stirring Speed ( 50 RPM -- 100 RPM)100 RPM)E. Monomer Purity ( 90% E. Monomer Purity ( 90% -- 98%)98%)F. Pressure ( 100 PSI F. Pressure ( 100 PSI -- 500 PSI)500 PSI)G. Acetone/Methanol Ratio G. Acetone/Methanol Ratio -- ( 0.25 ( 0.25 -- 0.50)0.50)
++11.50*A11.50*A
--2.50*B2.50*B
++0.75*C0.75*C
++5.00*A*C 5.00*A*C
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We need an efficient method for screening these"candidate critical X's"
so that we can identify the 'Vital Few"
ObjectivesObjectives
• In the physical world, the law of Entropy explains the gradual loss of order in a system. The same law applies to business processes.
• Unless we add “energy” (in the form of documentation and ongoing process controls), processes will tend to degrade over time, losing the
DMAIC
gains achieved by design and improvement activities.
• The quality plan is the structure through which we add this “energy” to business processes. This is Control and the main objectives:
– To make sure that our process stays in control after the solution has been implemented.
– To quickly detect the out of control state and determine the associated special causes so that actions can be taken to correct the problem before
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special causes so that actions can be taken to correct the problem before nonconformance are produced.
27
DefineMeasureAnalyze
• Focus on the Right CTQ• Quantify the Problem• Determine the Drivers
Y = f(X)• Identify Needed Change
Control Control –– Keep It On TargetKeep It On Target DMAIC
• Validate Measurement System (Xs)• Determine Process Capability
AnalyzeImprove
Control
• Identify Needed Change• Implement the Change
• Develop/Modify Quality Plan> Process Documentation
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• Implement Process Controls• Audit Plan Established• Transition to Operating Owners
> Process Controls
On the Lookout for Special CauseOn the Lookout for Special Cause• Common cause variation
– Natural variability
– Random
– Inherent in the process
DMAIC
• Special cause variation– May be caused by operator errors, adjusted machines, or
defective raw materials
– Generally large when compared to the common cause variation
– Considered an unacceptable level of process performance
• Special causes tend to cause a process to shift out of
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control where. The output does not meet the desired specifications.
28
What is a Process Control System?What is a Process Control System?•• A Process Control System (PCS)A Process Control System (PCS)
– strategy for maintaining the improved process performance over time
– identifies the specific actions and tools required for sustaining the process improvements or gains
•• A control system may incorporateA control system may incorporate
DMAIC
y y py y p
– Risk Management
– Mistake‐proofing devices
– Statistical process control (SPC)
– Data collection plans
– Ongoing measurements
– Audit plans
– Response plans*
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Response plans
– Product drawings
– Process documentation
– Process ownership
Statistical Process ControlStatistical Process Control
StatisticalStatistical -- Probability based decision rules.
ProcessProcess -- Any repetitive task or steps.
ControlControl -- Monitoring of process performance.
DMAICStep 12
SPC will signal when the process is “out-of- control”.
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Your Mission is to find out why and take Your Mission is to find out why and take corrective action!corrective action!
29
Control Chart ComponentsControl Chart Components
0.065
0.060
Average ChartAverage Chartst
ic (
me
an
/de
fect
s)
me
asu
red Upper Control Limit
Lower Control Limit
Grand AverageCentral Line
DMAICStep 12
2520151050
0.055
0.010
0 005
Variation ChartVariation ChartMonitors ShiftMonitors Shift
Sample / Subgroup (time ordered)
Sta
tis Lower Control Limit
Upper Control Limit
e/S
igm
a)
red
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0.005
0.000
Monitors DriftMonitors Drift
Average Range/SigmaCentral Line
Lower Control Limit
Sample / Subgroup (time ordered)Sta
tistic
(R
an
gem
ea
sur
Significance of 3s limitSignificance of 3s limitA Control Chart is a graphic display of a
continuing two tailed test with HO and HAdefined as:
Ho: iHa: i
/2
DMAICStep 12
LCLx
UCLx
/2
/2
X
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• For 3 limits, = 0.00135. approximate confidence level is 99.7%.• 3 limits provide good sensitivity to change with low potential for over-
reacting when the process is stable.
30
Types of Control ChartTypes of Control ChartVariable Chart (Continuous)
• Uses Measured Values
–Cycle Time, Lengths, Diameters, Drops, etc.
• Generally One Characteristic Per
Attribute Chart (Discrete)• Defects: Number of non
conformance in a part• Defective: Pass/Fail,
Good/Bad, Go/No-Go Information
DMAICStep 12
yChart
• More Expensive, But More Information
Information • Can Be Many Characteristics
Per Chart• Less Expensive, But Less
Information
High or Low Volume?
L High
ConstantLot / Unit Size
VariableLot / Unit Size
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Individuals &MovingRange
Low High
X-Bar &Range
cDefects Poisson
BinomialDefective
u
np p
THANK YOU
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