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Learning Curves

Dr. Everette S. Gardner, Jr.

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Learning Curves 3

Price of Model T, 1909-1923

(in 1958 dollars)

85% slope

1909:

18,000 units$3,300

1923:

8,000,000 units$950

1910

19111912

1913 19141915

1918

1920

1921

1923

Thousands

of $

.8

1

2

31909

4

56

10,000 100,000 1,000,000

Cumulative units produced

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Learning Curves 4

An 80% learning curve

Unit Man hours1ST 1000

2ND 1000 X .80 800

4TH 800 X .80 640

8TH 640 X .80 512

16TH 512 X .80 410

32ND 410 X .80 328

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Learning Curves 5

An 80% learning curve (cont.)

10 20 30 40 50

1000

800

600

400

200

0

Man-hou

rsperunit

Cumulative units produced

1st unit

2nd

4th

8th16th

32nd

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Learning Curves 6

The log - linear method

Exponential form:

yx = kxn

Where

x = unit number

yx= man-hrs. to produce xth unit

k = hrs. to produce first unit

n = log b / log 2

b = learning rate (80%, etc.) expressed as decimal (.8, etc.)

Logarithmic equation:

log yx = log k n (log x)

Learn.xls

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Learning Curves 7

The log - linear method (cont.)

yx log yx

Cum. units Cum. units(x) (log x)

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Learning Curves 8

Example calculations

yx = kxn

, n = log b / log 2

For 80% LC, b = .80

n = log .80 / log 2 = -.3219

Assume k = 1000

y1 = 1000 (1)-.3219 = 1000 (1) = 1000

y2 = 1000 (2)-.3219 = 1000 (.80) = 800

y3 = 1000 (3)-.3219 = 1000 (.7021) = 702

y4 = 1000 (4)-.3219 = 1000 (.6400) = 640y100 = 1000 (100)

-.3219 = 1000 (.2270) = 227

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Learning Curves 9

1 10 100 1000

b = 90%

b = 80%

b = 70%

M

an-hoursper

unit

Cumulative units produced

Typical learning curves

where k = 1 (one hour

required for first unit)

1.00

.10

.01

.001

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Learning Curves 10

Forces behind the learning curve

1. Increased labor efficiency

2. Process innovations and methods improvements

3. Substitution effects

4. Product redesign

5. Standardization

6. Economies of scale

7. Shared experience

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Learning Curves 11

Estimating learning curveparameters

The concept applies to an aggregation rather than to individualoperations

First unit hours rarely known in time to develop curve must

estimate far in advance

Slope can be estimated by least-squares regression

Comparisons should always be made to similar products/processesindustry data usually available

Extensive pre-production planning should result in lower, flattercurve

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Learning Curves 12

Estimating learning curveparameters (cont.)

Man-hrs./

unit

Cumulative units

Little planning

Extensive planning

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Learning Curves 13

Manufacturing strategy and thelearning curve

Capacity expands automatically

Break-even points reduced automatically

Worker compensation plans should account for learning effects

The learning curve is a strategic, not a tactical concept cannot beused as a short-range operating control

A learning curve strategy can reduce the ability to innovate

At some point, the learning curve will plateau

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Learning Curves 14

Manufacturing strategy and thelearning curve (cont.)

Man-hrs.

/u

nit

Cumulative units

b = 1.0

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Learning Curves 15

Learning curve applications Production planning / EOQ planning

Price forecasting

Petrochemicals

Consumer durable goods

Competitive bidding

Income reporting in accounting

Planning warranty maintenance

Washers / dryers

Televisions

Forecasting industrial accidents

Petroleum industry

Mining

Forecasting automobile accidents on new roadways