## N

Tables are widely available with both unit and total values for the learning ' curves, and have been calculated for many different improvement ratios (learning rates—e.g., see |26|). -

In the example of the electronic device just given, assume that after producing the twentieth unit, there is no significant further improvement (i.e., assembly time has reached a steady state at 70 hours). Further assume that previous study established that the usual learning rate for assemblers in this plant is about 85 percent We can estimate the time required for the first unit by letting T„ = 70 hours by the unit « = 20. Then r = log .85/1 og2 = - . 1626/.693 = -.235

Now we know the time for the initial unit. Using a table that shows the total time multipler (see (26, p. 347-348] for example), we can find the appropriate total time multiplier for this example—the multiplier for 20 units given a learning rate of 85 percent. With this multiplier, 12.40, we can calculate the total time required to build all 20 units. It is

The last 5 units are produced in the steady-state time of seventy hours each. Thus the total assembly time is

We can now refigure the direct labor cost.

Our first estimate, which ignored learning effects, understated the cost by or about 17 percent. Figure 7-4 illustrates this source of the error.

The conclusion is simple. For any task where labor is a significant cost factor and the production run is reasonably short, the PM should take the learning curve into account when estimating costs. The implications of this conclusion should not be overlooked. We do not often think of projects as "production," but they are. Research |16] has shown that the learning curve effect is important to decisions about the role of engineering consultants on computer-assisted design (CAD) projects. The failure to consider performance improvement is a significant cause of project cost underestimation.

The number of things that can produce errors in cost estimates is almost without limit, but some problems occur with particularly high frequency. Changes in resource prices is one of these. The most commonly used solution to this problem is to increase all cost estimates by some fixed percentage. A more useful approach is to identify each input that accounts for a significant portion of project cost and estimate the direction and rate of price change for each.

The determination of which inputs account for a "significant" portion of project cost is not difficult, though it may be somewhat arbitrary. Suppose, for example, that our initial, rough cost estimate (with no provision for future price changes) for