**Learning Curve and Learning Curve Effect**

"Learning curves" were first observed by the 19th century German psychologist Hermann Ebbinghaus investigating the difficulty of memorizing varying numbers of verbal stimuli. Subsequent learning about the complex processes of learning are discussed in the Learning curve article.

Experience shows that the more times a task has been performed, the less time is required on each subsequent iteration. This relationship was probably first quantified in 1936 at Wright-Patterson Air Force Base in the United States, where it was determined that every time total aircraft production doubled, the required labour time decreased by 10 to 15 percent. Subsequent empirical studies from other industries have yielded different values ranging from only a couple of percent up to 30 percent, but in most cases it is a constant percentage: It did not vary at different scales of operation. The Learning Curve model posits that for each doubling of the total quantity of items produced, costs decrease by the same proportion, as described by Equations 1 and 2. The equations have the same equation form. The two equations differ only in the definition of the Y term, but this difference can make a significant difference in the outcome of an estimate.

1. This equation describes the basis for what is called the **unit curve**. In this equation, Y represents the cost of a specified unit in a production run. For example, If a production run has generated 200 units, the total cost can be derived by taking the equation below and applying it 200 times (for units 1 to 200) and then summing the 200 values. This is cumbersome and requires the use of a computer or published tables of predetermined values.

where

- is the number of direct labour hours to produce the first unit
- is the number of direct labour hours to produce the
**xth**unit - is the unit number
- is the learning percentage

2. This equation describes the basis for the **cumulative average** or cum average curve. In this equation, Y represents the average cost of different quantities (X) of units. The significance of the "cum" in cum average is that the average costs are computed for X cumulative units. Therefore, the total cost for X units is the product of X times the cum average cost. For example, to compute the total costs of units 1 to 200, an analyst could compute the cumulative average cost of unit 200 and multiply this value by 200. This is a much easier calculation than in the case of the unit curve.

where

- is the number of direct labour hours to produce the first unit
- is the average number of direct labour hours to produce
**First xth**units - is the unit number
- is the learning percentage

Read more about this topic: Experience Curve Effects

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