application of learning curves in the aerospace industry handout

© 2005 BAE Systems

Cost Drivers Learning Event, 2nd November 2005

Learning Curves – Some Alternative Approaches Alan R Jones, BAE Systems

“O! This Learning, what a thing it is.”

William Shakespeare (c.1594, The Taming of The Shrew)

The material presented here is based on a case study presented in the following publication: Jones, A.R. ‘Case Study - Applying Learning Curves in Aircraft Production - Procedures and Experiences’ in Zandin, K (editor) Maynards

Industrial Engineering Handbook, 5th Edition, McGraw-Hill, New York, 2001

© 2005 BAE Systems


Learning Curves – An Alternative Approach

Constituent Elements of Production Learning– Segmentation Theory

Applications– Effect of Output Rate Constraint– “End of Line” Effect– Assessing Loss of Learning– Multi-Ganging of Operations (Parallel Learning)

Cumulative and Cumulative Average Data– Formulae– Examples

© 2005 BAE Systems


Constituent Elements of Production Learning

Background

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34%

6%

11%22%

23%

4%

Tooling Improvements

Manufacturing CostImprovementsQuality Control

Manufacturing Control

Operator Learning

Engineering Changes toAssist Production

Source: P Jefferson, ‘Productivity Comparisons with the USA – where do we differ?’ Aeronautical Journal, Vol 85 No844 May 1981, p.179

Constituent Elements of Production Learning

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Segmenting the Learning Curve: Mathematical Model

Consider 4 cost driver components with values α, β, γ, and δwhere α + β + γ + δ = 1 (or 100%)

Equation of a Unit Learning Curve: TA = T1 Aε

where ε is the learning exponent: ε = log(p)/log(2)with p = the learning percentage expressed as a decimaland TA is the time at Unit A

Expand the exponent: TA = T1 A(α + β + γ + δ) ε

TA = T1 Aαε Aβε Aγε Aδε

In order to model data with breakpoints, re-define the variable A:TA = T1 A1

αε A2βε A3

γε A4δε

For the primary learning (where all cost drivers are “active”), the values of A1 A2 A3 and A4 are all equal

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454510560

454510545

101010510

55555

44444

33333

22222

11111

A4A3A2A1ALogisticsToolingOperatorDesignBuild No

Segmenting the Learning Curve: Mathematical Model

Example based on a production run of 60 units All cost drivers active. Relative learning points are all equal

Impact of constant output rate truncates relative learning for this cost driver

Impact of design freeze truncates relative learning for this cost driver

“End of Line”truncates relative learning for these cost drivers

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Learning Curve Segmentation: Points to Consider

Benefits of Approach:

• Allows discontinuities to be modelled easily (using an on/off switch approach)

• Allows scenarios to be modelled which assume learning rates greater than or less than the “norm” for a particular process or product type

• Allows multiple linear regression techniques to be applied in cost data analysis

Words of Caution:

• As with all modelling techniques, the approach requires calibration for the specific environment in which it is to be applied

• There should be a logical model or explanation of why particular cost drivers have been “switched in or out”

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Effect of Output Rate Constraint on Learning

Application Example

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AverageContents


Number of Operators Average Hours Workedin Time Period

Average Hours spentper Unit in Time Period

Number of Unitsproduced in Time Periodx x=

Constant(For Optimum

Learning)

“Constant”(Effective Upper& Lower Limits)

Reducing(Learning Curve)

Increasing(Rate Ramp-up)

Every operatorperforms same task

on every unit

Constrained by workinghour practices (basic

working week &sustainable overtime

The “Reduced Cost : Increased Output” is in part a natural response of increased product familiarity, and in part a response to market

expectations of affordability etc

© 2005 BAE Systems


AverageContents


Number of Operators Average Hours Workedin Time Period

Average Hours spentper Unit in Time Period

Number of Unitsproduced in Time Periodx x=

Constant(Fixed Output Rate)

Reducing “Constant”(Effective Upper& Lower Limits)

Reducing(Learning Curve)

Constrained by workinghour practices (basic

working week &sustainable overtime

Reducing the number of operators violates

the premise for optimum learning

A response to market expectations of

affordability etc to drive down costs

Customer contractual limitation or constraint

© 2005 BAE Systems


Example 1: Cumulative Deliveries of Product A

0

50

100

150

200

250

300

350

Years

Cumul

ative

Uni

tsConstant Rate

DeliveriesDelivery Rate

Build-up

117

9.75 per month

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Example 2: Assembly Learning for Product A

1 10 100 1000Cumulative Units

Man

-hou

rs

Actual Regression 5% Confidence Level 95% Confidence Level

Constant RateDeliveries

Delivery RateBuild-up

Breakpoint@ 117

80.4% Learningafter the breakpoint

75.7% Learningup to the breakpoint

22%

78%

Swingometer

© 2005 BAE Systems


Example 2: Cumulative Deliveries of Product B

0

50

100

150

200

250

Years

Cumul

ative

Uni

tsConstant Rate

DeliveriesDelivery Rate

Build-up

60

4 per month

© 2005 BAE Systems


Example 2: Assembly Learning for Product B


Man

-hou

rs

Actual Regression 5% Confidence Level 95% Confidence Level

Constant RateDeliveries

Delivery RateBuild-up

Breakpoint@ 60

87.8% Learningafter the breakpoint

72.1% Learningup to the breakpoint

60%

40%

Swingometer

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Other factors affecting the analysis:

• The examples emanate from different factories with differentmanagement styles and cultural heritage

• One product was essentially for a single customer variant/mark initially followed by small batch export orders

• The other product was a multiple variant/mark international collaboration• The level of continued investment was geared around the known and

perceived market opportunities• The level and timing of engineering change required to introduce export

variants and support customer modifications has to be considered• The underlying manufacturing technology used on the two products was

similar but not identical

© 2005 BAE Systems


“End of Line” Effect on Learning Curves

Application Example

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30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12


Premise:To enable ongoing learning curve reduction once a constant rate of output is achieved requires investment in new or improved technology, process or logistics etc

Cumulative Return on InvestmentReduced saving

per unit

Reduced quantity remaining over which investment can be recovered

Diminishing Return on Investment

© 2005 BAE Systems



0.001

0.01

0.1

1

10

100

1000


Fact

or (C

umul

ativ

e R

etur

n on

Inve

stm

ent)

¾ Quantity

Learning Rate75%80%85%90%

75%80%85%90%

¾ Quantity

Diminishing Cumulative Return on Investment =(Unit Learning Curve Reduction) x (Units Remaining)

It would seem that there is a case that a learning curve will truncate

naturally somewhere between the 60% to 80% point of the total envisaged

production quantity, regardless of the learning curve rate?

© 2005 BAE Systems



1000

10000

100000


Fact

or (C

umul

ativ

e Re

turn

on

Inve

stm

ent)

¾ Quantity

The empirical relationship of the “End of Line”Effect on a learning curve can be attributed to

the “Law of Diminishing Returns”.

It is not unreasonable to expect that a learning curve will truncate naturally

somewhere between the 60% to 80% point of the total envisaged production quantity.

Breakpoint@ Constant Rate

Example:• Constant rate of output at unit 50• 400 units planned in total• 75% Learning Curve

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Assessing Loss of Learning

Application Example

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Assessing Loss of Learning: Anderlohr Method


Man

-hou

rs

Basic AnderlohrSource: Anderlohr, G., ‘What production breaks cost’, Journal of Industrial Engineering,

September 1969, pp.34-36

Consider a Break in Production of 12 months after 50 units

1. Determine how many units have been produced in the previous 12 months

2. Back track up the learning curve by this quantity

3. This defines the re-start position for learning

4. Repeat the learning process (offset by the number of units lost)

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Assessing Loss of Learning: Segmentation Method


Man

-hou

rs

Basic With Re-learning Continued Learning


1. Determine the proportion of learning that will continue by considering the cost drivers that might be affected

3. After the break the continued learning component still applies

4. Factor this by the re-learning component (offset by the number of units lost)

1. Determine the proportion of learning that will continue by considering the cost drivers that might be affected

2. This defines the re-start position for learning after the break

Component subject to Re-Learning

69%

31%

Example

Continued Component of Learning

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Assessing Loss of Learning: Comparison of Methods


Man

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Basic Anderlohr Segmentation


Anderlohr method always lags the segmentation method for

the same re-start value

Anderlohr Method

Segmentation Method

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Assessing Loss of Learning: Comparison of Methods

Practical Considerations:

• Small breaks in production will be more difficult to detect further down the curve due to potential “noise” in the actual data

• The Anderlohr Method assumes that the rate of learning loss is equivalent to the rate of learning gain. This is not necessarily the case, but a modified approach which “backtracks” only a proportion of the “lost”learning could be adopted

• What happens when the break in production occurs during the latter stages of the production run (often the case)? The learning curve may have “bottomed out” by this stage

• Either approach could be applied to other cases of learning loss other than time breaks; for example, a physical relocation or new start-up.

Consider the following example using the cost driver segmentation method

© 2005 BAE Systems


Example 3: Cumulative Deliveries of Product C

800

820

840

860

880

900

920

940

960

980

1000

Years

Cumul

ative

Uni

ts3-Year BreakIn Production

2 per month@ peak

2 per month@ end of line

© 2005 BAE Systems


Example 3: Assembly Learning for Product C

700 750 800 850 900 950 1000Cumulative Units

Man

-hou

rs

Actual Regression

Re-learningRate restricted learning

Break in Production

29%

71%

Swingometer

22%

78%

Swingometer

© 2005 BAE Systems


Multi-Ganging of Operations: Parallel Learning

1 10 100Cumulative Units

Man

-hou

rs

Common Learning Series Working 2-Gangs 4-Gangs 8-Gangs

Multi-Gang parallel working has the effect of deferring learning curve reduction by a proportion of the lost operator contribution

This has the apparent effect of reducing the observed learning and

increasing the theoretical First Unit Value

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Cumulative Average Data

Cumulative Average Model:

• The formula for the Cumulative Average version of a Learning Curve is the same as that for a Unit Learning Curve:

TA = T1 Aε

where ε is the learning exponent: ε = log(p)/log(2)with p = the learning percentage expressed as a decimaland TA is the Cumulative Average Time at Unit A

• The Cumulative Average version will be inherently “smoother” than its Unit counterpart, but the rate of learning indicated will be very similar for higher quantities (greater than 30 – depending on the accuracy required)

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Cumulative Average Data


Man

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Unit Unit Cum Ave Unit Regression

Cumulative Average Curve runs parallel to the Unit

Curve for larger quantities

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Cumulative Data Approximation Formulae

Cumulative Data Approximations for a Unit Learning Curve:

For a positive error1, CA ~ T1 [ (A + 0.5)ε+1 - 0.5ε+1 ]

(ε + 1)

For a negative error2, CA ~ T1 (Aε+1 - 1) + T1 (Aε + 1)

(ε + 1) 2

where ε is the learning exponent: ε = log(p)/log(2)with p = the learning percentage expressed as a decimal

Source: 1. Conway, R.W. and Schultz, A.Jr., ‘The Manufacturing Progress Function’, Journal of Industrial Engineering, Jan-Feb 1959, pp.39-542. Jones, A.R. ‘Case Study - Applying Learning Curves in Aircraft Production - Procedures and Experiences’ in Zandin, K (editor)

Maynards Industrial Engineering Handbook, 5th Edition, McGraw-Hill, New York, 2001

© 2005 BAE Systems


Cumulative Data Approximation Formulae Error

Source: Jones, A.R. ‘Case Study - Applying Learning Curves in Aircraft Production - Procedures and Experiences’ in Zandin, K (editor) Maynards Industrial Engineering Handbook, 5th Edition, McGraw-Hill, New York, 2001

-2.50%

-2.00%

-1.50%

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

0 10 20 30 40 50 60 70 80 90 100

Cumulative Units

% Error

Jones Approximation

Cauchy-Schwartz Approximation80% learning curve

75% learning curve

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Cumulative Data Equivalent Unit Completion Method

0 . 1 1 1 0 1 0 0Cumulative Units

Man

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rs

0

10

20

30

40

50

60

Cumulative Units

Calendar Time

Cumulative Average

Unit Learning Curve

Cumulative Average based onEquivalent Unit Completions

application of learning curves in the aerospace industry handout

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