NASA-Systems Engineering

# The system engineer can use a set of annual cost

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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, R-291, The Rand Corporation, 1956. a life-cycle 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 multiple-unit 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 fifth-degree 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.

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