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Learning CurvesDr. Everette S. Gardner, Jr.
Learning Curves
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Learning curve conceptsPredicts 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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Price of Model T, 1909-1923 (in 1958 dollars)85%
slope1909:18,000 units$3,3001923:8,000,000
units$9501910191119121913191419151918192019211923Thousandsof
$.8123190945610,000100,0001,000,000Cumulative units produced
Learning Curves
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An 80% learning curveUnit Man hours1ST10002ND 1000 X .80 8004TH
800 X .80 6408TH 640 X .80 51216TH 512 X .80 41032ND 410 X .80
328
Learning Curves
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An 80% learning curve (cont.)
10 20 30 40 5010008006004002000Man-hours per unitCumulative
units produced1st unit2nd4th8th16th32nd
Learning Curves
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The log - linear methodExponential form:yx = kxn
Wherex = unit numberyx = man-hrs. to produce xth unit k = hrs.
to produce first unitn = log b / log 2b = learning rate (80%, etc.)
expressed as decimal (.8, etc.)
Logarithmic equation:log yx = log k n (log x)Learn.xls
Learning Curves
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The log - linear method (cont.)
yx log yx
Cum. units Cum. units (x) (log x)
Learning Curves
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Example calculationsyx = kxn, n = log b / log 2
For 80% LC, b = .80
n = log .80 / log 2 = -.3219
Assume k = 1000y1 = 1000 (1)-.3219 = 1000 (1) = 1000y2 = 1000
(2)-.3219 = 1000 (.80) = 800y3 = 1000 (3)-.3219 = 1000 (.7021) =
702y4 = 1000 (4)-.3219 = 1000 (.6400) = 640y100 = 1000 (100)-.3219
= 1000 (.2270) = 227
Learning Curves
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1 10 100 1000
b = 90%b = 80%b = 70%Man-hours per unitCumulative units
producedTypical learning curveswhere k = 1 (one hourrequired for
first unit)1.00.10.01.001
Learning Curves
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Forces behind the learning curve1. 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 parametersThe 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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Estimating learning curve parameters (cont.)
Man-hrs. / unitCumulative unitsLittle planningExtensive
planning
Learning Curves
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Manufacturing strategy and the learning curveCapacity 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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Manufacturing strategy and the learning curve (cont.)
Man-hrs. / unitCumulative unitsb < 1.0b = 1.0
Learning Curves
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Learning curve applicationsProduction planning / EOQ
planning
Price forecastingPetrochemicalsConsumer durable goods
Competitive bidding
Income reporting in accounting
Planning warranty maintenanceWashers / dryersTelevisions
Forecasting industrial accidentsPetroleum industryMining
Forecasting automobile accidents on new roadways
Learning Curves
