## Info

centage decrease was 25 percent. Again, in going from 400 to 800 units, a 25 percent reduction of 17 hours results. We can therefore conclude that, as more units are produced, the rate of change remains constant but the magnitude of the change diminishes.

When the data from Figure 18-1 are plotted on log-log paper, the result is a straight line, which represents the learning curve as shown in Figure 18-2.

There are two fundamental models of the learning curve in general use; the unit curve and the cumulative average curve. Both are shown in Figure 18-2. The unit curve focuses on the hours or cost involved in specific units of production. The theory can be stated as follows: As the total quantity of units produced doubles, the cost per unit decreases by some constant percentage. The constant percentage by which the costs of doubled quantities decrease is called the rate of learning.

The "slope" of the learning curve is related to the rate of learning. It is the difference between 100 percent and the rate of learning. For example, if the hours between doubled quantities are reduced by 20 percent (rate of learning), it would be described as a curve with an 80 percent slope.

To plot a straight line, one must know either two points or one point and the slope of the line. Generally speaking, the latter is more common. The question is whether the company knows the man-hours for the first unit or uses a projected number of man-hours for a target or standard unit to be used for pricing purposes.

The cumulative average curve in Figure 18-2 can be obtained from columns 1 and 3 in Table 18-1. Dividing column 3 by column 1, we find that the average hours for the first 100 units is 196 hours. For 200 units, the average is 149 hours. This becomes important in determining the cost for a manufacturing project.