Chapter 9 Capability and Rolled Throughput Yield

Chapter 9

Capability and

Rolled Throughput Yield

What is capability analysis? And what can it tell us?

Provides a measure of how well a process satisfies customer requirements.

Will provide various ways to calculate defects per unit

Allow us to calculate the rolled throughput yield

Therefore uncovering the hidden factory (often consuming 30% of an org’s resources).

Measuring Capability

• Measure the true quality levels of products and services. • Report the relationship between what is acceptable to the

customer and what the process can naturally deliver. • Process Capability – is defined as the spread within which

almost all of the values of a data distribution will fall. (Generally described as 6s or 3s)– The main objective of 6 s is to have no more than 3.4

defects per million opportunities (DPMO).– The process must be brought into statistical control so

that performance becomes predictable and capable of consistently meeting customer expectations.

What is a normal distribution?

www.barringer1.com/jan98f1.gif

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

So what is Capability?• The proportion of output that will be within product specification tolerances.

Specification RangeUsually set by customer

LSLLower Specification Limit

USLUpper Specification Limit

Process Range

How is capability measured?

Cp>=1 process capableCp<1 process not capableCp= 1.33 minimum value for process to be

considered capable*.*Most organizations use 1.33 as the minimum due to the shift that occurs over time We have a lower sigma for long-term than short-term since long-term process capability is expected to shift over time by 1.5 .s

6 -1.5 = 4.5 s s s 3.4 DPMO answer to HW #1

ST6 or capability Process

tolerance ionSpecificatC index Capability p

Indices of Capability - Cp

LSLLower Specification Limit

USLUpper Specification Limit

Cp<1

Cp= 1

Cp= 1.5

Cp= 2.0

Impr

ovem

ent

Capability Example Example 9.1

• CALCULATE the Cp

– Process has a mean = .738– =.0725s– LSL=.500, USL=.900

Is this process capable? Why?

92.0435.

400.

)0725(.6

500.900.

66

LSLUSLTolerance

CP

Cp is missing a key element It only really makes sense when the process remains centered.

Specification RangeLSL USL

Process Range

• Cpk was created to address instances when the process mean is not centered relative to the specification limits.

Indices of Capability - Cpk

LSL USL

Cp= 2.0 Cpk=2.0

Cp= 2.0 Cpk=<1

Cp= 2.0 Cpk= 0

Cp= 2.0 Cpk< -1

Incr

ease

in r

ejec

ts

Potential RealCapability Capability

How can we calculate Cpk ?

m = process center

= short-term standard deviation

m = midpoint of specification

STSTplpupk

LSLUSLCCC

3,

3min),min(

MINITABSTATQUALITY TOOLS Capability Analysis

2

LSLUSLm

2/)(

||

LSLUSL

mk

)1( kCC ppk






You can’t improve what you don’t measure? But what characteristics do Six Sigma metrics have?

METRIC:1. Must have a scale

2. Must have a goal, or standard

3. Compensation or other forms of recognition must be attached to actual performance compared to goal.

4. The metric is reported and reviewed vertically and horizontally throughout the organization on a regular basis.

5. The metric must be able to be pooled horizontally and vertically within the enterprise.

6. The metric must be strongly correlated with one or more of the 12 dimensions of quality at the business, operations, and/or process level of the organization.

12 Dimensions of Quality Metrics

Aligned Owned Predictive Actionable

Minimal Simple Correlated Transformative

Standardized Contextual Reinforced Validated

What defects are we measuring? And what’s the difference?

• Unit = item, service, product, transaction delivered to customer.• Defect = failure to meet customer req. or a performance standard• Defective = unit that contains at least one defect• Defect opportunity = opportunities for a unit to be defective

• With DPMO, look up Long-term and Short-term Sigma in the Sigma Conversion Table (Table VIII in Appendix A)

unitsofNo

defectsofNounitperDefectDPU

.

.

610*.

..

iesopportunitofNo

defectsofNooppmillionperDefectDPMO

DPU/ DPMOExample 9.4

• Bank branch receives 300 mortgage applications per business day.• Report shows that these applications contained 50 defects.• Each application as 14 key fields (defect opportunities).

Calculate the DPU, DPO and Sigma Level:

Look up 11,904.76 in the Sigma Conversion Table (Table VIII in appendix)

What is the range for the Short-term and Long-term Sigma?

1667.0300

50

.

.

unitsofNo

defectsofNoDPU

76.1190410*14300

50 6

DPMO

DPU/ DPMO Example 9.7

• Office receives 4500 engineering permit applications per day.• Audit shows that these applications contained 300 defects.• Each application as 12 key fields (defect opportunities).

Calculate the DPU, DPO and Sigma Level:

Look up 5,555.56 in the Sigma Conversion Table

Short-term sigma = 4s - 4.1 sLong-term sigma = 2.5 s - 2.6s

0667.04500

300

.

.

unitsofNo

defectsofNoDPU

56.555510*124500

300 6

DPMO

Capability vs. Performance

• For indicating the level of long-term performance that a process can achieve we use:

LT6 or spread Process

tolerance ionSpecificatP index ePerformanc p

LTLTplpupk

LSLUSLPPP

3,

3min),min(

Equivalent Mean Offset

Short-Term CapabilityLong-Term Performance

1.5

LSL

LSL

USL

USL






What is meant by yield?

• “Yield” can be viewed as the ratio of output to input:

• A successful unit would mean it is free of any type on nonconformity (or defect).

• EXAMPLE: Process 100 units, 90 are successful.

• Called FTY (Final Test Yield)

I

O

Input

OutputYield

90.0100

90Yield

But…yield is a flawed conceptIt doesn’t account for rework and replacement

• We must look at a process map and measure IPY (In Process Yield) at each step.

• RTY (Rolled Throughput Yield) is calculated by multiplying together they IPY.

RTP = IPY1 x IPY2 x IPY3 x…x IPYn

• This could be considered a true assessment of process effectiveness.

processthisinstartedUnits

processnexttoshippedUnitsIPY

Example of Yield vs. RTY

• Bank with 280 deposits a day. Each slip as 5 defect opportunities. They get a lot of complaints, but they can’t understand why since the # of defects per final confirmation is low.

START

END

Customer gives deposit slip .

Bank associate processes deposit

Enters deposit in electronic system

System generates deposit

confirmation

Customer obtains confirmation

FIRST: create a flow chart


SECOND: Note the defects per step, and calculate the DPU, IPY for each.

IPY = e-DPU

Since there are multiple defect opportunities per unit.

START

END





confirmation


Defs DPU IPY

5 5/280= .0179 .9823

6 6/280= .0214 .9788

3 3/280= .0107 .9893

4 4/280= .0143 .9858

2 2/280= .0071 .9929

.0714

9311.1

k

IPYRTY

9311.0714. eeRTY TotalDPU


SECOND: Note the defects per step, and calculate the DPU, IPY for each.

IPY = e-DPU

Since there are multiple defect opportunities per unit.

START

END





confirmation


Defs DPU IPY

50 50/280= .1786 .8364

6 6/280= .0214 .9788

3 3/280= .0107 .9893

4 4/280= .0143 .9858

2 2/280= .0071 .9929

.2321

7928.1

k

IPYRTY

7928.2321. eeRTY TotalDPU






The Hidden Factory• The hidden factory is used

to designate all work performed above and beyond to produce a good unit of output and is not explicitly identified. Can include the costs for rework, scrap, excess floor space and equipment.

• Estimated that 30% of an organization’s resources go to the hidden factory.

START

END





confirmation


InspectionFailure

Analysis

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InspectionFailure

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InspectionFailure

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InspectionFailure

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InspectionFailure

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Chapter 9 Capability and Rolled Throughput Yield