Learning Curves

Technical Supplement 3
Learning Curves

LEARNING OBJECTIVES
After studying this technical supplement, you should be able to:
1. Explain the learning curve concept
2. Identify different uses of learning curves in operations management
3. Calculate the estimated time required to do a task for a given learning curve

LEARNING CURVES AND OPERATIONS MANAGEMENT

As people gainexperience in doing a task, they usually can do the task more quickly. For example, consider the time it might take someone to wash a car for the first time. Then imagine how that person might be able to wash his car in less time as through repetitions he learns to sequence the tasks more efficiently or perhaps as he uses better tools to do the tasks. The same learning effect occurs in manydifferent operational settings.

The learning curve is an analytical tool that can be used to estimate the rate at which cumulative experience allows workers to do tasks faster and with less cost. Operations managers use learning curves to estimate how much the repetitions of a task will enable them to reduce the amount of resources required to accomplish the ask. A learning curve is defined by anequation that contains the rate of improvement (i.e., reduction in costs or reduction in time taken) in performing a task as a function of the cumulative repetitions of the task.

As early as 1925, managers began developing learning curve concepts. The commander at Wright-Patterson Air Force Base in Dayton, Ohio, observed that workers performing manufacturing operations at the base exhibited adefinite learning pattern. He noted that most aircraft manufacturing tasks experienced what he called an 80 percent learning rate, meaning that workers need 20 percent fewer hours to make a part each time their cumulative experience making that part doubled. Thus, if the first part took 100 minutes, the second would require 80 minutes, the fourth would require 64 minutes, and so on. Exhibit 1graphs the reduction in unit time required to complete a task as a function of the number of times that the task is repeated when the organization has an 80 percent learning rate.



Exhibit 1
Learning Curve – 80 Percent Learning Rate
[pic]

The learning curve is also sometimes referred to as an experience curve, a progress function, or an improvement function. Essentially, the learning curveis a mathematical function that can be used to chart the progress of workers as they learn to do their work faster. An operations manager can express the relationship between the amount of time it takes an organization with a learning rate percentage of r to produce the nth item as an equation:

Tn = T1 (nb)

Where:
Tn = time required to complete the nth task
r = learning ratepercentage
b = ln(r)/ln(2)

Example:

Consider the information given in the aircraft manufacturing example above:

T1 = 100 minutes
T2 = 80 minutes
T4 = 64 minutes

What would be the time required to produce the eighth part?

T8 = (100)(8-0.322) = 51.2 minutes since b= ln(0.80)/ln(2) = -0.322

We can verify that this is the correct answer by remembering that thefourth unit required 64 minutes. Since the eighth unit represents a doubling of output beyond the fourth unit, we would expect its task time to be 80 percent of the time required for the fourth unit. Thus, T8 = 64(0.80) = 51.2. This is the same answer given by the learning curve equation above.

Appendix A at the end of this supplement presents a table giving task time values for selectedlearning rates. The appendix shows that the estimated time for the eighth unit produced on an 80% learning curve is 0.512 times the task time required for the first unit. Again this confirms the result we calculated above.

How much time would be required to produce all eight parts?

Note that the table also gives the total time required to produce a cumulative number of units. In our...