The concept of the learning curve emerged in the aerospace industry as firms attempted to estimate costs for items that were to be developed for a specific purpose and then made repetitively throughout the duration of the project. The assumption was that as additional units are produced, a certain amount of learning occurs such that each subsequent unit takes less time to produce. Plots of production time for subsequent units revealed that learning does indeed take place.

On the standard learning curve, assuming a 90 percent learning curve, when the first unit produced requires 100 hour, the second unit requires 90 percent of 100 or 90 hours. Each successive doubling of the cumulative production yields a 10 percent improvement over the previous time. Thus, the fourth unit produced requires 90 percent of the time required for the second unit (90 hours)--.90x90=81 hours. Further, the eighth unit produced requires 90 percent of the time required for the fourth unit--72.9 hours. To generalize, the concept known as the learning curve was formalized by the following equation:

Y=aXbwhere

Y=time required to produce the Xth unit

a=time required to produce first unit

X=cumulative number of units produced

b=ln(rate of learning)/ln(2) with the rate of learning expressed as a decimal.

Problem 1Your Answers

If a company requires 60 minutes to produce the first unit and operates

on a 90 percent learning curve, how much time is required for the

16th, 32th, 64th, and 200th items.16th=

32nd=

64th=

200th=

Problem 2

If a company requires 60 minutes to produce the first unit and operates

on 70 percent learning curve, how much time is required for the

16th, 32th, 64th, and 200th items.16th=

32nd=

64th=

200th=

Problem 3

If 60 minutes are required to produce the first unit and 48 minutes are

required to produce the 10th unit, how much time is required for the 25th unit?

How much time is required to produce all 25 units (Hint: try this in a spreadsheet)?