The LEARNC.lng Model

Learning Curve

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The cost, labor, and/or time it takes to perform a task will often decrease the more times it is performed. A manufacturer may need to estimate the cost to produce 1,000 units of a product after prducing only 100. The average unit cost of the first 100 is likely to be considerably higher than the average unit cost of the last 100. Learning curve theory assumes each time the quantity produced doubles, the cost per unit decreases at a constant rate.

In this example, we wish to estimate the cost (in hours) to produce paper based on the cumulative number of tons produced so far. The data is fitted to a curve of the form:

COST( i)=a * VOLUME( i)b

where COST is the dependent variable and VOLUME is the independent variable. By taking logarithms, we can linearize the model:

ln{COST( i)] = ln( a)+b*ln[VOLUME( i)]

We can then use the theory of linear regression to find extimates of ln( a) and b that minimize the sum of the squared prediction errors. Not that since the regression involves only a single independent variable, the formulas for computing the parameters are straightforward. Refer to any theoretical statistics text for a derivation of these formulas.


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