### ESTIMATING COST MODELS: Improvement and the Learning Curve.

concept of learning and improvement in the activities that people perfonn. Fromour own experience weall know that our fiftieth repetitionis completed in much less time than we needed to accomplish the task the first time.

The learning curve captures the relationship between task perfonnance and task repetition. In general. as output doubles the-unit production time will be reduced to some fixed percentage. the learning curve percentage or learning curve rate. For example. it may take 300 minutes to produce the third unit in a production run involving a task with a 95% learning time curve. In this case the sixth (2 x 3) unit will take 300(0.95) = 285 minutes to produce. Sometimes the learning curve is also known as the progress curve. improvement curve. experience curve. or manufacturing progress function.

Equation2-4 givesan expressionthat can be used for time estimatingin repetitive tasks.

As just given.a learning curve is oftenreferred to by its percentage learning slope. Thus a curve with b = -0.074 is a 95% learning curve because 2^-0.074 = 0.95. This equation uses 2 because the learning curve percentage applies for doubling cumulative production.

The learning curve exponent is calculated using Equation 2-5.

**EXAMPLE 2-9.**
Calculate the time required to produce the hundredth unit of a production run if the first unit took 32.0 minutes to produce and the learning curve rate for production is 80%.

**SOLUTION**
It is particularly important to account for the learning-curve effect if the production run involves a small number of units instead of a large number.When thousands or even millions of units are being produced. early inefficiencies tend to be "averaged out" because of the larger batch sizes. However. in the short run. inefficiencies of the same magnitude can lead to rather poor estimates of production time requirements. and thus production cost estimatesmay be understated.ConsiderExample2-10 and the results that might be observed if the learning-curve effectis ignored.Noticein this example that a "steady state" time is given. Steady state is the time at which the physical constraints of performing the task prevent the achievement of any more learning or improvement.

**EXAMPLE 2-10.**
Estimate the overall labor cost portion due to a task that has a learning-curve rate of 85% and reaches a steady state value after 16units of 5.0minutes per unit. Labor and benefits are $22 per hour, and the task requires two skilledworkers. The overall production run is 20 units.

**SOLUTION**
Because we know the time required for the 16thunit, we can use Equation 2-4 to calculate the time required to produce the first unit.

Now we use Equation 2-4 to calculate the time requirements for each unit in the production run as well as the total production time required.

The Toral cumulative time of the proctuction run is 119.8 minutes (2.0 hours). Thus the total

labor cost wstimate would be:**2.0 hours x $22/hour per worker x 2 workers = $88**

state labor rate, the estimate would be:

**0.083 hours/unit x 20 units x $22/hour per worker x 2 workers = $73.04**

This estiIIl'£lteis understated by about 20% from what the true cost would be

**.**

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