Download - 7 Learning Curves
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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