Learning Curves
Dr. Everette S. Gardner, Jr.
Learning curve concepts
• Predicts reduction in manufacturing costs or direct
labor hours as cumulative production increases
• Based on empirical evidence rather than theory
Learning Curves
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Thousands
of $
85% slope
6
5
4
3
2
1
.8
10,000
1909
1913 1914
1910
1911
1915
1912
1920
1918
1923
1921
100,000
1,000,000
Cumulative units produced
1923:
8,000,000 units
$950
1909:
18,000 units
$3,300
Price of Model T, 1909-1923
(in 1958 dollars)
Learning Curves
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An 80% learning curve
Unit
1ST
2ND
4TH
8TH
16TH
32ND
1000 X .80
800 X .80
640 X .80
512 X .80
410 X .80
Man hours
1000
800
640
512
410
328
Learning Curves
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An 80% learning curve (cont.)
Man-hours per unit
1000
800
600
1st unit
2nd
4th
8th
16th
400
32nd
200
0
10
20
30
40
50
Cumulative units produced
Learning Curves
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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)
Learning Curves
Learn.xls
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The log - linear method (cont.)
yx
log yx
Cum. units
(x)
Cum. units
(log x)
Learning Curves
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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) = 640
y100 = 1000 (100)-.3219 = 1000 (.2270) = 227
Learning Curves
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Man-hours per unit
1.00
b = 90%
.10
b = 80%
b = 70%
.01
.001
1
10
100
1000
Cumulative units produced
Typical learning curves
where k = 1 (one hour
required for first unit)
Learning Curves
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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
Learning Curves
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Estimating learning curve
parameters
• The concept applies to an aggregation rather than to individual
operations
• 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/processes –
industry data usually available
• Extensive pre-production planning should result in lower, flatter
curve
Learning Curves
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Man-hrs. / unit
Estimating learning curve
parameters (cont.)
Little planning
Extensive planning
Cumulative units
Learning Curves
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Manufacturing strategy and the
learning 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 be
used as a short-range operating control
• A learning curve strategy can reduce the ability to innovate
• At some point, the learning curve will “plateau”
Learning Curves
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Man-hrs. / unit
Manufacturing strategy and the
learning curve (cont.)
b = 1.0
Cumulative units
Learning Curves
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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
Learning Curves
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