CHAPTER 3 - Educators

90 CHAPTER 3/COST-ESTIMATION TECHNIQUES
for the 200-MW plant in Example 3-6, we find that the current cost of a 100-MW
plant is
CA = $300 million
0.79 100 MW
200 MW
CA = $300 million × 0.58 = $174 million.
3.4.2 Learning and Improvement
A learning curve is a mathematical model that explains the phenomenon of
increased worker efficiency and improved organizational performance with
repetitive production of a good or service. The learning curve is sometimes
called an experience curve or a manufacturing progress function; fundamentally, it
is an estimating relationship. The learning (improvement) curve effect was first
observed in the aircraft and aerospace industries with respect to labor hours
per unit. However, it applies in many different situations. For example, the
learning curve effect can be used in estimating the professional hours expended
by an engineering staff to accomplish successive detailed designs within a family
of products, as well as in estimating the labor hours required to assemble
automobiles.
The basic concept of learning curves is that some input resources (e.g.,
energy costs, labor hours, material costs, engineering hours) decrease, on a peroutput-unit
basis, as the number of units produced increases. Most learning curves
are based on the assumption that a constant percentage reduction occurs in, say,
labor hours, as the number of units produced is doubled. For example, if 100 labor
hours are required to produce the first output unit and a 90% learning curve is
assumed, then 100(0.9) = 90 labor hours would be required to produce the second
unit. Similarly, 100(0.9) 2 = 81 labor hours would be needed to produce the fourth
unit, 100(0.9) 3 = 72.9 hours to produce the eighth unit, and so on. Therefore, a 90%
learning curve results in a 10% reduction in labor hours each time the production
quantity is doubled.
Equation (3-5) can be used to compute resource requirements assuming a
constant percentage reduction in input resources each time the output quantity
is doubled.
Zu = K(u n ), (3-5)
where u = the output unit number;
Zu = the number of input resource units needed to produce output unit u;
K = the number of input resource units needed to produce the first
output unit;
s = the learning curve slope parameter expressed as a decimal
(s = 0.9 for a 90% learning curve);
log s
n = = the learning curve exponent.
log 2