Unformatted text preview: he second production unit is 90 percent of the first
production unit cost; the unit cost of the fourth is 90
percent of the unit cost of the second, and so on. In
general, the ratio of C(2Q) to C(Q) is the learning
rate, LR, expressed as a decimal; using the above
equation, b = In (LR)/ln 2, where In is the natural
logarithm.
Learning curve theory may not always be applicable
because, for example, the time rate of production has
no effect on the basic equation. For more detail on
learning curves, including empirical studies and tables
for various learning rates, see Harold Asher, Cost Quantity Relationships in the Airframe Industry, R291,
The Rand Corporation, 1956. a lifecycle cost estimate. One such situation occurs
when the results of different models, whose estimates
are expressed in different year constant dollars, must be
combined. In that case, an appropriate inflation factor
must be applied. Another such situation arises when a
model produces a cost estimate for the first unit of a
hardware item, but the project requires multiple units. In
that case, a learning curve can be applied to the first
unit cost to obtain the required multipleunit estimate.
(See sidebar on learning curve theory.)
A third situation requiring additional calculation
occurs when a model provides a cost estimate of the
total
An Example of a Cost Spreader Function:
The Beta Curve
One technique for spreading estimated acquisition
costs over time is to apply the beta curve. This
fifthdegree polynomial, which was developed at JSC
in the late 1960s, expresses the cumulative cost
fraction as a function of the cumulative time fraction,
T:
Cum Cost Fraction = 10T2(1  T)2(A + BT)
+ T4(5  4T) for 0 ≤T ≤1.
A and B are parameters (with 0 ≤A + B ≤1 ) that
determine the shape of the beta curve. In particular,
these parameters control what fraction of the
cumulative cost has been expended when 50
percent of the cumulative time has been reached.
The figure below shows three examples: with A = 1
and B = 0 as in curve (1), 81 percent of the costs
have been expended at 50 percent of the
cumulative time; with A = 0 and B = 1 as in curve
(2), 50 percent of th...
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This document was uploaded on 02/26/2014 for the course E 515 at University of Louisiana at Lafayette.
 Spring '13
 Mr.Kau
 Systems Engineering, The American, ... ...

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