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Product & Process AssessmentProduct & Process AssessmentProduct & Process AssessmentProduct & Process Assessment
Six Sigma Foundations Continuous Improvement TrainingSix Sigma Foundations Continuous Improvement Training
Six Sigma Simplicity
Key Learning PointsKey Learning PointsKey Learning PointsKey Learning Points
Traditional Metrics vs. CI
DPU vs. DPMO
RTY vs. Hidden Factory
Traditional Metrics vs. CI
DPU vs. DPMO
RTY vs. Hidden Factory
AgendaAgendaAgendaAgendaObjectives of This Module
Introduction to defects First time yield (FTY) vs. rolled throughput yield (RTY)
COPQ vs. yield
The hidden factory
Defects per opportunity metric Complexity explained
Defects per unit metric
The basic Binomial model
The basic Poisson model
The application of defect data in process improvement efforts
Project metrics
Objectives of This Module
Introduction to defects First time yield (FTY) vs. rolled throughput yield (RTY)
COPQ vs. yield
The hidden factory
Defects per opportunity metric Complexity explained
Defects per unit metric
The basic Binomial model
The basic Poisson model
The application of defect data in process improvement efforts
Project metrics
Will the first time yield be correlated to other major business metrics?
What will the test yield be next week?
First Time (End of Line) Yield by Week
90
92
94
96
98
100
Wk
1
Wk
2
Wk
3
Wk
4
Wk
5
Wk
6
Wk
7
Wk
8
Wk
9
Wk
10
Wk
11
Wk
12
Wk
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Wk
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Wk
15
We
ek
ly Y
ield
(%
)
Where: FTY = First Time
Yield (test yield) P = Number of
units that pass test
U = Number of units tested
UFTY = P
* 100%
Traditional Method of Project Traditional Method of Project SelectionSelectionTraditional Method of Project Traditional Method of Project SelectionSelection
How does your organization identify poor quality products?How does your organization identify poor quality products?
Will traditional yield (end-of-line test yield) calculations correlate to business metrics?
End-of-line test yield has traditionally been considered a good predictor of profit margins and scrap rates. However, it rarely does a good job at either. Why not? What is missing? What’s the problem with classical yield calculations?
As managers and Black Belts, we shouldn’t select projects based on the FTY of a product.
Will traditional yield (end-of-line test yield) calculations correlate to business metrics?
End-of-line test yield has traditionally been considered a good predictor of profit margins and scrap rates. However, it rarely does a good job at either. Why not? What is missing? What’s the problem with classical yield calculations?
As managers and Black Belts, we shouldn’t select projects based on the FTY of a product.
Expected Relationships
1009080
25
20
15
10
5
0
Test Yield
Pro
fit
1009080
9
8
7
6
5
4
3
2
1
0
Test Yield
Scr
ap
The Traditional MethodThe Traditional Methodof Project Selectionof Project SelectionThe Traditional MethodThe Traditional Methodof Project Selectionof Project Selection
Defects vs. DefectivesDefects vs. DefectivesDefects vs. DefectivesDefects vs. Defectives
Defects: Countable failures that are associated with a
single unit. A single unit can be found to be defective, but it may have more than one defect.
Defectives: Completed units that are classified as bad.
The whole unit is said to be defective regardless of the number of defects it has. FTY = the number of non-defectives/the number of total units.
Defects: Countable failures that are associated with a
single unit. A single unit can be found to be defective, but it may have more than one defect.
Defectives: Completed units that are classified as bad.
The whole unit is said to be defective regardless of the number of defects it has. FTY = the number of non-defectives/the number of total units.
The Hidden FactoryThe Hidden FactoryThe Hidden FactoryThe Hidden Factory To analyze, re-work, and/or scrap potential product requires:
More manpower Extra floor space Longer cycle time More raw material More $$$$
How big is your “hidden factory”? What happens to cost as defects increase?
To analyze, re-work, and/or scrap potential product requires: More manpower Extra floor space Longer cycle time More raw material More $$$$
How big is your “hidden factory”? What happens to cost as defects increase? HiddenHidden
FactoryFactoryRe-WorkRe-Workor Scrapor Scrap
Re-WorkRe-Workor Scrapor Scrap
FailureFailureAnalysisAnalysis
FailureFailureAnalysisAnalysis
TestTestOperation 2Operation 2TestTestOperation 1Operation 1 ProductProduct
Hint: Go collect defect data!
0
100
200
300
400
500
600
Defect-Based Cost ModelDefect-Based Cost ModelDefect-Based Cost ModelDefect-Based Cost Model
When we track individual defects rather than percent defective, we end up with a much better predictor of costs.
What constitutes a defect?
When we track individual defects rather than percent defective, we end up with a much better predictor of costs.
What constitutes a defect?
DPU vs. COPQ
0 1 2 3 4DPU
CO
PQ
($)
High
Low
DefectsDefects??
Proportion =Proportion =
Which metric do you need? DPU or DPMO?
In most cases, we end up converting defect data to a proportion as follows:
When we use defect data, we need to determine what number to put into the denominator of the equation above.
DefectsDefects
Total OpportunitiesTotal OpportunitiesDPMO =DPMO =
DefectsDefectsUnit ProducedUnit ProducedDPU =DPU =
Collect Defect DataCollect Defect Data
What do I What do I need to need to know? know?
Compare the quality Compare the quality level of non-identical level of non-identical parts, processes, or parts, processes, or
products.products.
Model process efficiency Model process efficiency or estimate the probability or estimate the probability of producing defect-free of producing defect-free
parts.parts.
? = A measure of complexity (i.e., opportunities)
? = The number of units produced (or processed through the operation)
DPMO DPU
ManagementMetric
Black Belt ProjectMetric
Project Selection MetricBenchmarking Metric
Black Belt Project Metric
x 1Mx 1M
DPU vs. DPMODPU vs. DPMODPU vs. DPMODPU vs. DPMO
A Metric to Expose the Hidden A Metric to Expose the Hidden FactoryFactoryA Metric to Expose the Hidden A Metric to Expose the Hidden FactoryFactory
Rolled Throughput Yield (RTY) The product of total throughput at each step in the process
Definition A measurement of yield which exposes the
extent and location of scrap and rework The proportion processed with no defects
Rolled Throughput Yield (RTY) The product of total throughput at each step in the process
Definition A measurement of yield which exposes the
extent and location of scrap and rework The proportion processed with no defects
Rolled Throughput Yield (RTY)Rolled Throughput Yield (RTY)Rolled Throughput Yield (RTY)Rolled Throughput Yield (RTY)
Y1=0.92Y1=0.92
First Pass Yield=804/1000=0.804First Pass Yield=804/1000=0.804
Y2=0.82Y2=0.82
Y3=0.84Y3=0.84
Scrap 4% - 40 units
Rework 4%
960 unitsScrap 9%
Rework 9%
- 86 units
874 unitsScrap 8%
Rework 8%
804 units
RTY=633/1000=0.633RTY=633/1000=0.633
920 units
754 units
633 units
RTY=0.92x0.82x0.84=0.633RTY=0.92x0.82x0.84=0.633
- 70 units
1000 units
HiddenHiddenFactorFactoryy
Cost of Hidden FactoryCost of Hidden FactoryCost of Hidden FactoryCost of Hidden Factory
To analyze, to rework, and to scrap requires:
More raw material (Scrap / re-order)
Manpower (Unproductive Hours)
Floor space (Capacity)
Longer cycle time (DSO)
To analyze, to rework, and to scrap requires:
More raw material (Scrap / re-order)
Manpower (Unproductive Hours)
Floor space (Capacity)
Longer cycle time (DSO)
YieldYieldYieldYield
Rolled Throughput Yield = 63%Rolled Throughput Yield = 63%
Test Yield = 84% Test Yield = 84%
First Pass Yield = 80% First Pass Yield = 80%
Identifies Result of
Final Inspection
Identifies Result of
Final InspectionIdentifies
Process Yield(Scrap)
IdentifiesProcess Yield
(Scrap)
Identifies Extent & Location
of COPQ
(Our Opportunity)
Identifies Extent & Location
of COPQ
(Our Opportunity)
Customer ViewCustomer ViewInternal ViewInternal ViewInternal PerformanceInternal Performance
The Greater Hidden FactoryThe Greater Hidden FactoryThe Greater Hidden FactoryThe Greater Hidden Factory Beyond the direct costs associated with finding and
fixing defects, “Cost of Poor Quality” also includes: The hidden cost of failing to meet customer
expectations the first time The hidden opportunity for increased efficiency The hidden potential for higher profits The hidden loss in market share The hidden increase in total cycle times
For an average company, the cost of poor quality can be as high as 25% of annual sales
COPQ can exceed the profit margin COPQ is our Opportunity!
Beyond the direct costs associated with finding and fixing defects, “Cost of Poor Quality” also includes: The hidden cost of failing to meet customer
expectations the first time The hidden opportunity for increased efficiency The hidden potential for higher profits The hidden loss in market share The hidden increase in total cycle times
For an average company, the cost of poor quality can be as high as 25% of annual sales
COPQ can exceed the profit margin COPQ is our Opportunity!
Measure
Analyze
ImproveControl
Management
Man
agem
ent
Management
Management
Managem
ent
Measure
Analyze
ImproveControl
Select a new project Goal: Goal:
YY == ff(x)(x)
Review progress and modify
Use DPMOHere
Use DPUHere
Remember: Strategic Black Belt Remember: Strategic Black Belt OverviewOverviewRemember: Strategic Black Belt Remember: Strategic Black Belt OverviewOverview
Black Belts should use the DPU (or PPM) metric to track their project performance.
Management should use the DPMO metric to select projects and conduct benchmark studies for dissimilar goods and services.
Black Belts should use the DPU (or PPM) metric to track their project performance.
Management should use the DPMO metric to select projects and conduct benchmark studies for dissimilar goods and services.
Defects per unit Defects per unit ====unitsunits
defectsdefectsDPUDPU
1,000,0001,000,000 **
//1,000,0001,000,000**
OppsOpps TotalTotal // DefectsDefects
(Opps/unit)(Opps/unit)DPUDPUDPMODPMO
==
==
DPU and DPMO CalculationsDPU and DPMO CalculationsDPU and DPMO CalculationsDPU and DPMO Calculations
DPMO, Measures of ComplexityDPMO, Measures of ComplexityDPMO, Measures of ComplexityDPMO, Measures of Complexity Product complexity
Number of parts
Number of functions
Process complexity Number of attachments
Number of welds
Transactional complexity Number of entries
Software complexity Lines of code
Product complexity Number of parts
Number of functions
Process complexity Number of attachments
Number of welds
Transactional complexity Number of entries
Software complexity Lines of code
DPMO, Measures of ComplexityDPMO, Measures of Complexity- continued- continuedDPMO, Measures of ComplexityDPMO, Measures of Complexity- continued- continued
“Complexity” is a measure of how complicated a particular good or service is. Theoretically, it’s doubtful that we will ever be able to quantify complexity in an exacting manner.
If we assume that all characteristics are independent and mutually exclusive, we may say that “complexity” can be reasonably estimated by a simple count. This count is referred to as an “Opportunity Count”.
In terms of quality, each product and/or process characteristic represents a unique “opportunity” to either add or subtract value.
Remember, we only need to count opportunities if we want to estimate a sigma level for comparisons of goods and services that are not necessarily similar.
“Complexity” is a measure of how complicated a particular good or service is. Theoretically, it’s doubtful that we will ever be able to quantify complexity in an exacting manner.
If we assume that all characteristics are independent and mutually exclusive, we may say that “complexity” can be reasonably estimated by a simple count. This count is referred to as an “Opportunity Count”.
In terms of quality, each product and/or process characteristic represents a unique “opportunity” to either add or subtract value.
Remember, we only need to count opportunities if we want to estimate a sigma level for comparisons of goods and services that are not necessarily similar.
Def
ects
Def
ects
Op
po
rtu
nit
yO
pp
ort
un
ity
DP
MO
=D
PM
O =
x 1
Mx
1MDPMO, Counting OpportunitiesDPMO, Counting OpportunitiesDPMO, Counting OpportunitiesDPMO, Counting Opportunities
Non-value-added rules: No opportunity count should be applied to any operation that does not add value. Transportation and storage of materials provide no
opportunities. Deburring operations can also be considered.
Testing, inspection, gauging, etc., do not count. The product, in most cases, remains unchanged. An exception: An electrical tester where the tester is also used to program an EPROM. The product was altered and value was added.
Supplied components rules: Each supplied part provides one opportunity. Supplied materials such as solder, machine oil,
coolants, etc., do not count as supplied components.
Non-value-added rules: No opportunity count should be applied to any operation that does not add value. Transportation and storage of materials provide no
opportunities. Deburring operations can also be considered.
Testing, inspection, gauging, etc., do not count. The product, in most cases, remains unchanged. An exception: An electrical tester where the tester is also used to program an EPROM. The product was altered and value was added.
Supplied components rules: Each supplied part provides one opportunity. Supplied materials such as solder, machine oil,
coolants, etc., do not count as supplied components.
DPMO, Counting Opportunities DPMO, Counting Opportunities -cont.-cont.DPMO, Counting Opportunities DPMO, Counting Opportunities -cont.-cont.
Connections rules: Each “attachment” or “connection” counts as one. If a device requires four bolts, there is an
opportunity of fourone for each bolt connected. A 60-pin integrated circuit, surface mount device,
soldered to a printed circuit board counts as 60 connections.
A 16-pin dual in-line package with through-hole mounting counts as 16 joints. There is no double counting of joints one for the top side and one for the bottom side is not correct.
Once you define an “opportunity,” you must institutionalize that definition to maintain consistency.
Connections rules: Each “attachment” or “connection” counts as one. If a device requires four bolts, there is an
opportunity of fourone for each bolt connected. A 60-pin integrated circuit, surface mount device,
soldered to a printed circuit board counts as 60 connections.
A 16-pin dual in-line package with through-hole mounting counts as 16 joints. There is no double counting of joints one for the top side and one for the bottom side is not correct.
Once you define an “opportunity,” you must institutionalize that definition to maintain consistency.
Def
ects
Def
ects
Op
po
rtu
nit
yO
pp
ort
un
ity
DP
MO
=D
PM
O =
x 1
Mx
1M
DPMO, Counting Opportunities DPMO, Counting Opportunities -cont.-cont.DPMO, Counting Opportunities DPMO, Counting Opportunities -cont.-cont.
Machine shop equipment rules: There is one opportunity count for
each machined surface. If one tool makes five separate cuts,
the count is five opportunities. When a hole is drilled and counter-
bored, the count is two because there are two separate operations.
A hole that is drilled and honed because the drilling operation is not trusted to hit the dimension is only a count of one. The honing operation is re-work of the drilling operation.
Machine shop equipment rules: There is one opportunity count for
each machined surface. If one tool makes five separate cuts,
the count is five opportunities. When a hole is drilled and counter-
bored, the count is two because there are two separate operations.
A hole that is drilled and honed because the drilling operation is not trusted to hit the dimension is only a count of one. The honing operation is re-work of the drilling operation.
Def
ects
Def
ects
Op
po
rtu
nit
yO
pp
ort
un
ity
DP
MO
=D
PM
O =
x 1
Mx
1M
DPMO, Counting Opportunities DPMO, Counting Opportunities -cont.-cont.DPMO, Counting Opportunities DPMO, Counting Opportunities -cont.-cont.
Transactional process rules: Filling out a form provides one opportunity per data-
entry field, not one opportunity for each character. One line of assembly equivalent code counts as one
opportunity for software programs. Sanity check rule:
“Will applying counts in these operations take my business in the direction it is intended to go?”
If counting each dimension adds no value, and increases cycle time then this type of count would be contrary to the company objective and would not provide an opportunity.
Once you define an “opportunity”, you must institutionalize that definition to maintain consistency.
Transactional process rules: Filling out a form provides one opportunity per data-
entry field, not one opportunity for each character. One line of assembly equivalent code counts as one
opportunity for software programs. Sanity check rule:
“Will applying counts in these operations take my business in the direction it is intended to go?”
If counting each dimension adds no value, and increases cycle time then this type of count would be contrary to the company objective and would not provide an opportunity.
Once you define an “opportunity”, you must institutionalize that definition to maintain consistency.
Def
ects
Def
ects
Op
po
rtu
nit
yO
pp
ort
un
ity
DP
MO
=D
PM
O =
x 1
Mx
1M
Application to a Measured Quantitative Parameter
If This Part Were A Supplied Part, It Would Count As One Opportunity. As Supplied Parts, At Least 2.275% Of Them Had Defects. Therefore, The DPMO = 0.02275*1,000,000 = 22750.
Spec Limit
Measurement of a Product Characteristic
Probability of producing a “bad” part =
0.02275
Probability of producing a
“good” part = 0.97725
Part Specification: 1.240 ± .003
Xbar = 1.241 S = 0.001
DPMO ExamplesDPMO ExamplesDPMO ExamplesDPMO Examples
DPMO = dpu/opportunities/unit * 1,000,000
= (8/1)/(1,000/1) * 1,000,000 = 8,000
Application to an Inspected Parameter
A circuit board has 800 solder joints and 200 components.
How many opportunities do we have?
Six defective joints and two defective components were found in this unit.
What is the DPMO?
DPMO Examples DPMO Examples -cont.-cont.DPMO Examples DPMO Examples -cont.-cont.
Fundamental Question:What Is the Likelihood Of Producing
A Unit With Zero Defects?
D
Defect Defect Missing PartMissing Part
Opportunity for Opportunity for a Defecta Defect
The DPU MetricThe DPU MetricThe DPU MetricThe DPU Metric
Suppose we have a unit with 10 components. Each component within the unit is a chance (or opportunity) for a defect to occur. Thus, each unit can contain up to 10 defects.
Note: This means you need to be able to track more than one defect per unit through your data-collection system.
Suppose we have a unit with 10 components. Each component within the unit is a chance (or opportunity) for a defect to occur. Thus, each unit can contain up to 10 defects.
Note: This means you need to be able to track more than one defect per unit through your data-collection system.
Fundamental QuestionFundamental Question::Given these facts, what is the likelihood of Given these facts, what is the likelihood of producing a unit with zero defects?producing a unit with zero defects?
How many units had:_____ Zero defects
_____ One defect
_____ Two defects
_____ Three defects
_____ Four defects
_____ Five or more defects
Question 1: How many total defects are observed?
Question 2: What is the number of DPUs?
Production Run
DPUs from the ProcessDPUs from the ProcessDPUs from the ProcessDPUs from the Process
Tally the number of defects within each unit. Based on this sample, calculate the probability of producing a zero-defect unit.
Tally the number of defects within each unit. Based on this sample, calculate the probability of producing a zero-defect unit.
Given: 60 defects observed 60 units processed 10 opps per unit
The probability that any given opportunity will be a defect is:
The probability that any given opportunity will NOT be a defect is:
The probability that all 10 opportunities on a single unit will be defect free is:
Given: 60 defects observed 60 units processed 10 opps per unit
The probability that any given opportunity will be a defect is:
The probability that any given opportunity will NOT be a defect is:
The probability that all 10 opportunities on a single unit will be defect free is:
If we extend the concept to an infinite number of opportunities, all at a DPU of 1.0, we will approach the value of 0.368.
Fundamental Question: Given these facts, what is the likelihood of producing a unit with zero defects?
6060*10 = 0.1 or 10%
6060*10 = 0.9 or 90%1 -
0.90 (10) = 0.3487 => 34.87%
RTY for DPU = 1
0.348
0.352
0.356
0.36
0.364
0.368
10 100 1,000 10,000 100,000 1,000,000
Chances per Unit
Yie
ld
DPU ModelingDPU ModelingDPU ModelingDPU Modeling
ChancesProb (Chance Is
a Defect)Prob (Chance
Is Not a Defect)RTY (Prob the Unit
Is Defect Free)10.00 0.1 0.9 0.34867844100.00 0.01 0.99 0.366032341
1,000.00 0.001 0.999 0.36769542510,000.00 0.0001 0.9999 0.367861046
100,000.00 0.00001 0.99999 0.3678776021,000,000.00 0.000001 0.999999 0.367879257
Two Major Uses of Defect DataTwo Major Uses of Defect DataTwo Major Uses of Defect DataTwo Major Uses of Defect Data
Prediction of true factory yield (RTY) Defect data can be used in an analysis to predict factory
(or line) yield, as shown below.
Data analysis for project scoping Defect data is most commonly used to perform Pareto
analysis on information to determine priorities for action items within the project planning cycle. The following slides demonstrate this idea.
Prediction of true factory yield (RTY) Defect data can be used in an analysis to predict factory
(or line) yield, as shown below.
Data analysis for project scoping Defect data is most commonly used to perform Pareto
analysis on information to determine priorities for action items within the project planning cycle. The following slides demonstrate this idea.
Operation 2Operation 2RTY = 96%RTY = 96%DPU = 0.04DPU = 0.04
Final RTY = (0.99)*(0.96)*(0.98) = 0.93*100% = 93%
Operation 1Operation 1RTY = 99%RTY = 99%DPU = 0.01DPU = 0.01
Operation 3Operation 3RTY = 98%RTY = 98%DPU = 0.02DPU = 0.02
OtherSupplier
Process
0
3000
6000
9000
12000
Operator Dropped Material Cuts Other
PP
M
Scratch DefectsScratch Defects
The Three-LevelPareto Principle
Analysis of Defect DataAnalysis of Defect DataAnalysis of Defect DataAnalysis of Defect Data
02000
40006000
8000
Part Sticks to Rack Packaging Other
PP
M
Operator DroppedOperator Dropped
0300060009000
12000
Scratches Cracked Light Other
PP
M
Ecoat DefectsEcoat Defects
Product & Process AssessmentProduct & Process AssessmentProduct & Process AssessmentProduct & Process Assessment
Six Sigma Foundations Continuous Improvement TrainingSix Sigma Foundations Continuous Improvement Training
