Learning curves (sometimes called experience curves) are used to analyze a well known and easily observed phenomena: humans become increasingly efficient with experience. As a trivial example, the first time we baked a batch of cookies as children, we undoubtedly were very inefficient in our work -- to say nothing of messy. As we gained experience over time, we probably improved our cookie baking skills in a variety of ways: we became faster, delivered better quality, wasted less, and reduced costs. The same phenomena are regularly observed throughout industry and business. The first time a product is manufactured or a service provided, costs are high, work is inefficient, quality is marginal, and time is wasted. As experienced is acquired, costs decline, efficiency and quality improve, and waste is reduced.
In many situations, this pattern of improvement follows a predictable pattern: for every doubling of production, the "cost" of production (measured in dollars, hours, or in terms of other inputs) declines to some fraction of previous costs. For example, suppose an electronics manufacturer begins production on a new type of oscilloscope. If the first unit manufactured takes 1,000 labor hours to assemble, the second takes 900 hours, and the fourth takes 810 hours, then the manufacturer is learning at a rate of 90%. The first doubling of production (from one unit to two) saw unit production time drop to 90% of initial time (900/1000 = 90%). The second doubling of production (from two to four units) saw unit production time drop from 900 hours to 810 hours for a learning rate of 90% (810/900 = 90%). Assuming that this 90% rate of learning continues, the manufacturer can predict that the eighth unit of produced will take 0.9*810=729 hours to manufacture, the sixteenth unit will take 0.9*729=610 hours, the thirty-second unit will take about 0.9*610=590 hours, and so forth. Note that a learning rate of 70% is better than a learning rate of 90%.
Mathematically this learning phenomena can be expressed as
where
Simple algebra shows that b and R can be calculated as:
Example. A manufacturer of commuter airplanes has started production of a new intermediate-sized aircraft. The wing assembly is particularly difficult to assemble. The first unit manufactured takes a total of 5,000 labor hours to assemble, while the fifth takes 3,500 hours. What rate of learning is occurring? How much labor time do you forecast that the hundredth wing assembly will take?
First, we record that
Now we calculate parameter
and the learning rate
The manufacturer thus has a learning rate of 85.8% (not bad!). To estimate the cost of the hundredth unit, we use m=1 and n=100, and calculate:
Alternatively, we can start with the fifth unit, letting m=5 and n=100:
In either case, we forecast that the hundredth wing assembly will take only 1,815 hours to assemble.
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Stephen R. Lawrence
Associate Professor of Operations Management
Leeds School of Business
University of Colorado
Boulder, CO 80309-0419
Stephen.Lawrence@Colorado.edu