1 2002 North Haven Group Lean Six Sigma DMAIC: Measure Phase.
Cairo 01 Six Sigma Measure
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SIX SIGMA MEASUREMENTS
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METRICS ASSOCIATED WITH SIX SIGMA
DON’T HAVE TO USE ALL THESE METRIC
KNOWLEDGE IS NECESSARY TO INSURE GOOD COMMUNICATION
DON’T HAVE TO USE ALL THESE METRIC
KNOWLEDGE IS NECESSARY TO INSURE GOOD COMMUNICATION
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SIX SIGMA RELATIONSHIPS
SIX SIGMA RELATIONSHIPS
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DEFININITIONS
Number Of Operation Steps = m Defects = DUnit = UOpportunities For A Defect = OYield = Y
Nomenclature
Total Opportunities (TOP) = U X O
Defects Per Unit (DPU) = D/U
Defects Per Unit Opportunity (DPO) = DPU/O = D/(U X O)
Defects Per Million Opportunities (DPMO) = DPO X 106
Basic Relationships
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DISTRIBUTION OF DEFECTS IN MANUFACTURED PRODUCT
Non-Randomly Occurring Defect
Randomly Occurring Defect
Example
Result
Conclusion
Wrong part in manualinsertion parts bin
Every board contains same wrong part insame location.
Defects are easier todetect/diagnose & are less likely to be sent tonext operation
Mixed parts in manualinsertion parts bin.
Probability of a boardcontaining wrong part isequal to proportion of wrong parts in bin
Defects are harder todetect/diagnose and are more likely to be sent to next operation
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PROBABILITY OF DEFECTS IN MANUFACTURED PRODUCT
GIVEN: (1) Average DPU For This Product Is One (DPU=1)(2) Defects are randomly distributed
What Is The Probability of Zero Defects In This Unit?
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GENERAL CHARACTERISTICS OF DPU
Directly Proportional To:• Parts Count • Lines of code• Die Area
Product Built In Plant Having Best Process Controls Will Have The Lowest Defects Per Unit Level
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DEFECTS PER UNIT
Defect Prevents Product From Fulfilling Physical And Functional Requirements Of The Customer
A Unit• A Measure Of Volume Of Output• Observable & Countable• Is An Individual Measurement - Not An Average
Number of Defects Found at Any Review Point
Number of Units Processed Through That Review PointDefects Per Unit =
A Count of All Defects - Not a Measure of the Consequences of The Defect
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PREDICTING THE QUALITY OF PRODUCTS
FTY = e-DPU DPU = -ln FTY
Estimation of units containing “q’ defects (where “q” is not limited to zero)
If we use the Poisson distribution
Becomes
(DPU)q e -DPU
q!
x e-
x!P{x} =
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YIELD RELATIONSHIPS
Throughput Yield : YTP = e-DPU
Defects Per Unit: DPU = -ln(Y)
Rolled Throughput Yield: YRT = YTPi
Total Defects Per Unit: TDPU = -ln(YRT)
Normalized Yield: Ynorm =
Defects per Normalized Unit: DPUnorm = -ln(Ynorm)
i=1
mYRT
m
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YIELDProbability with zero defects
Y = P(x = 0) =e-x
x! e-= = e-D/U = e-DPU
Specification Limit
Probability of Defect= 1 - e-DPU
Yield = e-DPU
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THE HIDDEN FACTORYTHE HIDDEN FACTORY
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THE HIDDEN FACTORY
Customer Quality
Operation
NotOK
Scrap
Verify
Rework
Operation
NotOK
Scrap
Verify
Rework
Ytp
Throughput Yield
Ytp
Throughput Yield
Non-Value Added(The Hidden Factory)
Value Added(The Visible Factory)
ProducersQuality
Supplier Quality
Yrt = Ytpi
m
i=10
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IMPLICATIONS OF THE HIDDEN FACTORY
Y e eTP
DPU 3679
1 0 . = 1.6321
.
1.63 Equivalent Units Must Be Produced To Get Out 1 Good Unit
Every Occurrence Of A Defect Within The Manufacturing Process Requires Time To Verify, Analyze, Repair And Re-verify
Average Cycle Time Per Unit Is Directly Proportional To The Total Number Of Defects Per Unit
Cycle Time = Work In ProcessThroughput
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#1
#6
#2
#7
#5
#9
#4
#8
#3
#10Final Insp..
Process Yield is 93.17% - Right??????
A FACTORY WITH 10 PROCESSES
NOT QUITE!!!
1200 Good & 88 BadItems [93.2%Found OK]
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COMPARISON OF YIELDS
Y = SU
= 12001288
= .931677
S = Number of Units That PassU = Number of Units Tested
Throughput Yield Analysis Tells UsYTPI = .47774
.4774 .932Why Not???
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ROLLED THROUGHPUT YIELD
Operation Defects UnitsDPU(D/U)
Throughput Yield(YTPI = e-D/U = e-DPU)
12345678910
57518726
2882703588
523851334
1202252243943894234
1200
0.009560.088130.053890.059900.023810.115230.086960.078300.149570.07333
0.990490.915640.947530.941860.976470.891160.916720.924690.861080.92929
Sum of
Operation Steps = 479 6676 0.73868 0.47774 (YRT)
47.9 667.6 0.07387 0.73868 =TDPU TDPU = -ln(YRT)
Avg.. ofOperation Steps
=
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HOW MANY UNITS PRODUCED?
UNITS PRODUCED = 1 + (1 - e-DPU)
= 1 + (1 - e-73868)= 1 + (1 - .477744)= 1 + .5222558= 1.52
To Achieve 100 Conforming Units, 152 ( 1.52 X 100) Would Need To Be Produced
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INSPECTIONS AND
TESTS
INSPECTIONS AND
TESTS
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Inspection E = 0.8 Escaping
DPU Level
Observed DPU Level
Submitted DPU Level
QUANTIFICATION OF DEFECTS
Given: Observed Defects = DPU of 0.25Then: Submitted Defects = (0.25/0.8) = DPU of 0.31
Escaping Defects = (0.31-0.25) = DPU of 0.06
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A TYPICAL PROCESS
Operation1
INSP TESTPrior Operation
do
d1d2 di dt
dn
Operation2
do = Defects Escaping Prior Processd1 = Defects Added in Operation 1d2 = Defects Added in Operation 2di = Defects Found by Inspection & Correcteddt = Defects Found by Test and Correcteddn = Defects Escaping to Next Operation
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Op.1 INSP TESTOp
2
DPU = 0.349 DPU = 0.907 DPU = 0.420 DPU = 0.075DPU = 0.07
FromPriorProcess
DPU = 0.279 DPU = 0.558 DPU = 0.487 DPU = 0.345
PD = Part Defective = 800 PPMSC = Solder Defective = 300 PPMPA = Part Assembly Error = 1000 PPM
EFF: PA = .8 PD = .0 SC = .8
EFF: PA = .9 PD = .95 SC = .05
ToNextProcess
DEFECT-BASED PLANNINGFOR A TYPICAL PROCESS
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Operation 1 Operation 2 Inspection Test
# Parts
PD
PA
SC
TDU
FTY
Submitted Created Submitted Created Submitted Observed Submitted Observed
100
330
0.080
0.100
0.099
0.279
210
600
0.05
0.02
0.00
0.07
0.13
0.120
0.099
0.349
0.168
0.210
0.180
0.558
0.298
0.330
0.279
0.907
0.000
0.264
0.223
0.487
61.44%
0.298
0.066
0.056
0.420
0.283
0.059
0.003
0.345
70.82%
Escaping
0.015
0.007
0.053
0.075
DEFECT-BASED PLANNINGFOR A TYPICAL PROCESS
Total Observed Defects Per Unit = 0.832
Rolled Yield = 43.52%
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REVIEW THE THREE PHASES OF PRODUCT LIFE
Early Life Useful Life Wear Out
PROB. OF FAILURE
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EARLY LIFE FAILURE RATE & LATENT DEFECTS
•The Degree Of Abnormality
•The Magnitude Of Applied Stress
•The Duration Of Applied Stress
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PROBABLE TIME TO FAILURE & DEGREE OF ABNORMALITY
Gross
ModerateSlightD
egre
e of
Ab
nor
mal
ity
Probable Time to Cause Failure
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MAJOR CAUSE OF LATENT DEFECTS
The Design And Execution Of Processes Is The Major Cause of Latent Defects
Cpk - Major Cause of the Degree of Abnormality
The Average Number of Latent Defects Per Unit - Determines the Shape of Early Life Failure Rate Curve
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WHAT CAN BE DONE TO MINIMIZE LATENT DEFECTS?
•Design & Document Detailed Product Flow
•Use Simplest Operations Possible
•Use Operations Of Known Capability
•Provide Documented Information - Each Operation
•Perform Each Operation Identically
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MINIMIZATION OFOTHER FAILURE TYPES?
• Use The Fewest Number Of Parts
• Use Parts Of Known Capability
• Use Lowest Possible Stress Levels
• Avoid Marginal Overstress
• Provide Maximum Possible Operating Margins And Mechanical Tolerances
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TOTAL DEFECTS PER UNIT (TDU)
TDU = DPU For All Key Characteristics
+ DPU For All Component Part Defects
+ DPU For All Process Defects
WHERE:Key Characteristics Are Measured By Cp & Cpk
Component Part Defects Are Defects Found In Material From Suppliers.
Process Defects - Created As Product Goes Through Manufacturing Process
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DPU AS A DEFECT BUDGETING TOOL
Defect Budgeting Is A Method To Ensure Robust Product Design
A Robust Design Will Be Insensitive To Long-term Process & Material Variations & Product Misuse
Goal Of Defect Budgeting For A New Product/process Is A Lower TDU
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OVERVIEW OF THE DEFECT BUDGETING PROCESSStructured Process Flow Diagram
- All Inspection /Test Points- Flow Of Non-conforming Product
Determine Capability/Error Rate Of Existing Process
Establish Maximum DPU Level For Delivered Product
Work Backwards & Establish Maximum DPUs
Revise Process Flow - Add Inspection/test Points- Redesign Operations
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BENCHMARKING AGAINST BEST IN CLASS
Determine Factors Critical To Long-term Success
Compare Performance With Toughest Competitors Or Others
Use Info to Develop Strategies And Functional Standards
The Goal Of Benchmarking Is:- Exceed The Competition- Make Your Business The Very Best
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EQUIVALENT COMPARISONSIN BENCHMARKING
DPU Must Be Normalized - Provide An Equivalent Comparison
Opportunities For Error - Accounts For Varying Complexity
Examples Of Opportunities For Error• Part Count• Process Step Count• Total Part Count And Process Step Count• Lines Of Solder Per Square Inch Of Printed Circuit Board
Defects Per Million Opportunities (DPMO) Provides An Equivalent Comparison
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DEFECTS PER MILLION OPPORTUNITIES (DPMO)
DPMO = DPU x 1,000,000
Parts CountDPMO =
DPU x 1,000,000Average Opportunities For Error in One Unit
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BENCHMARKING THE PROCESS1. Define The Purpose Of The Project
2. Define A Unit
3. Determine The Number Of Opportunities For Error In A Unit
- For Manufactured Product- Other Than Manufactured Product
4. Measure The Total Defects Per Unit (DPU)
5. Calculate Defects Per Million Opportunities (DPMO)
6. Estimate Specification Width
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0.001
0.01
0.1
1
10
100
1K
10K
100K
2 3 4 5 6 7.67 1.0 1.33 1.67 2.0
SigmaCpk
DP
MO
Specification Width
BENCHMARKING AGAINST BEST IN CLASS
1.5 Sigma Shift
Centered
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PROCESS CYCLE TIMEPROCESS CYCLE TIME
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PROCESS CYCLE TIME
Time To Do An Entire Process
Could Be Time From Material ArrivingTo Final Product In Customer’s Hands
Real Process Time Includes Waiting,Storage & In-between Operations Times.
Theoretical Process Time - No Waiting
Compare Real And Theoretical Process Time
Reducing Real Process Cycle Time Can Reduce The Number Of Defective Units And Improve Process Performance
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THEORETICAL PROCESS CYCLE TIME
Theoretical Process Cycle Time
Real Daily Operating Time
Number of Units Required Daily
=
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TEST/INSPECTION WORK LOAD NONREPARIABLE PRODUCT
Failure Of Test Or Inspection - Item Must Be Scrapped. To Yield One Acceptable Unit, We Must Test/inspect A Larger Number Of Units
1YIELD
Starts =
= e DPU
The Number of Parts Required to Start (T)
= e -DPU
1
Test/Inspection Cycle Time = T x Time Per Test= (e DPU) x time Per Test
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TEST WORK LOAD REPARIABLE PRODUCT
One Test Required To Catch Each Defect
Another Test Required To Pass Repaired Unit
T = Number Of Tests Per Accepted UnitT = (1+DPU)
Test Cycle Time = T x Time Per Test= (1 + DPU) x Time Per Test
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EXAMPLE OF TEST WORK LOADFOR REPAIRABLE PRODUCT
NumberOf Tests
Number Of Units
NumberOf Defects
Total NumberOf Tests
1
2
3
4
187
35
9
3
234
0
35
18
9
62
187
70
27
12
296Totals
FTY = 187/234 = 80%TDU = 62/234 = 0.265
FTY = e-0.265 = 77%TDU = -ln(0.80) = 0.233
Observed Results: Estimated From Observations
Results Close Enough - Defects Randomly Distributed & Poisson Ok
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INSPECTION WORK LOAD REPARIABLE PRODUCT
• Inspection Is Capable Of Finding All Defects In An Assembly On One Pass
• Each Assembly Must Be Inspected The First Time
• All Assemblies Containing One Or More Defects Must Be Inspected A Second Time
I = Number Of Inspections Per Accepted Unit
I = 1 + (1 - Yield) = 1 + ( 1- e -DPU) = 2 - e -DPU
Inspection cycle time = I x Time Per Inspection= (2 - e -DPU) x Time Per Inspection
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ANALYZE WORK LOADEvery Unit Must Be Worked On
Work Load Is Directly Proportional To Defects Per Unit
Failures Analyzed One At A Time:Work Load = A = Analysis Per Unit = DPU
Analysis Cycle Time = A x Time Per Analysis
= DPU X Time Per Analysis
Failures Analyzed All At One Time:Work Load = A = 1 - e -DPU
Analysis cycle Time = A x Time Per Analysis
= 1 - e -DPU x time Per Analysis
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REPAIR WORK LOAD
For Failures Repaired One At a Time:Work Load = R = Repair Per Unit = DPURepair Cycle time = R x Time Per Repair = DPU x Time Per Repair
For Failure Repaired All At One Time:Work Load = R = 1 - e -DPU
Repair Cycle time = R x Time Per Repair = 1 - e -DPU x Time Per Repair
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CYCLE TIME
Test
Analysis
Repair
Test Cycle Time = (1+ DPU ) x Time Per Test
Analysis Cycle Time= DPU x Time Per Analysis
or = 1- e-DPU x Time Per Analysis
Repair Time= DPU x Time Per Repairor= 1- e-DPU x Time Per Repair
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StoresandBank Time Total Mfg..
Cycle Time
Queue, Run, and Changeover Time
Output(capacity)
Input
CYCLE TIME / INVENTORY RELATIONSHIPS
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INVENTORY AND THROUGHPUT RATE
How Are Inventory and Cycle Time Related?
Cycle Time = Inventory
Throughput Rate
Number of Days = Total # of Pieces in Stock
Pieces Processed Per day
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UNIVERSAL CYCLE TIME/INVENTORY RELATIONSHIP
Work -In-processInventory
= Throughput Rate x Cycle Time
Number Of Work Orders
Number Of Pieces
Dollars
Orders Per Day
Pieces Per Day
Dollars Per Day
# Of Days
# Of Days
# Of Days
Inventory Throughput Rate Cycle Time
Examples
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CYCLE TIME CONTROLS WIP INVENTORY
The Longer A Unit Of Product Remains In A Production Area, The Higher The Work In Process (WIP) Inventory Is In That Area
Time Unit Is Expected To Remain In Area = Average Total Time
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RawMaterial
StoresFabrication
FabricationStores
Sub-Assembly
Sub-Assembly
Stores
FinalAssembly
FinishedGoods
Inventory
Work-In-ProcessManufacturing Cycle Time
InventoryCarryingCost
TotalValue of Product
RawMaterials Acquisition
Finished GoodsShipment
TRUE COST OF INVENTORY$
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CYCLE TIME AND INVENTORY TURNS
An Inventory Turn Is An Index Or Indicator Of HowOften A Company’s Entire Inventory Stock Is Replaced
Cost Of Goods Sold
Average Annual InventoryTurns =
1.25
1.44
5.00
10.00
20.00
40.00
288
250
72
36
18
9
Turns Turn Days
Note:Dell Has been Able toAchieve 1440 Turns
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INVENTORY COST AT MOTOROLA
Inventory Carrying Cost Equals At Least 25% of the Value of Average Annual Inventory Levels
Year Sales Average AnnualInventory Levels
InventoryCarrying Costs
1987198919911995
$6,700,000,000$9,620,000,000$11,340,000,000$27,037,000,000
$909,000,000$1,158,000,000$1,242,000,000$3,528,000,000
$227,000,000$289,000,000$310,500,000$882,000,000
In 1991, This cost can becompared to taking $310 million and burning it , since it adds no value to the company
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THE BOTTOM LINE IMPACTIn 1987, Motorola Discovered That
Poor Quality Accounted For Approximately
25% Of Their Annual Inventory Carrying Costs.
This Expense Added No Value, It Was Just Like Taking
$250,000,000 and pouring it down a drain
….Annually!
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OVERALL MANUFACTURING COST AND DPU
Defects Cost Money as Result Of:
Diagnostic Time
Repair Time / Re-Inspection
Extra Labor
Extra Materials
Extra Capacity
Extra Support
Extra Management
Extra Inventory
Cost of Failure (Internal) =
DPU x Volume x Average Cost
Defect
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REDUCING CYCLE TIME & INVENTORY SUMMARY
Cycle Time & Inventory Are Key Competitive Factors
Cycle Time Is The Inverse Of Inventory Turns (Shorter Cycle Times = Lower Inventories)
Defects Have A Major Controlling Effect
Defect Must Be Analyzed And Repaired
Two Important Work Load Measures - Test & Inspection, And Analyze & Repair
Capacity Of Test / Inspection Equipment Is Inversely Proportional To Work Load