By C. R. Weisbin (auth.), Jeffery Lewins, Martin Becker (eds.)

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Extra resources for Advances in Nuclear Science and Technology: Volume 14 Sensitivity and Uncertainty Analysis of Reactor Performance Parameters

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The method has been available for nearly two centuries; the formulae are laid out below to make explicit the forms of the equations useful for uncertainty evaluation and to accent the approximations typically made. While the variety of least-squares approaches is emphasized here, other choices are available; minimax techniques, which make the maximum absolute difference between input data and result as small as possible, also have been used in crosssection evaluation. Moreover, if data are combined in weighing a specific crucial decision, the loss to the sponsor likely will be greater if the result is wrong in one direction rather than the other; the relatively unbiased result from neither of the mentioned symmetric techniques then will be quite appropriate.

PEELLE 32 c. "Normalized" Uncertainty Matrices. Some nuclear parameters customarily are represented as the product of a mUltiplicity and a normalized spectrum, or as the product of an integral cross-section and an angular distribution expressed in other than a normalized Legendre expansion NM 1 + I n=l a p (11). n n Though no such uncertainty data are included in ENDF/B-V, such data will be required in a complete file. As a specific example, take the fission neutron source spectrum v X(E'), where J X(E')dE' = 1, and assume that X(E') is represented in histogram form with X.

The assertion that oa and ob are independent means that E(oa ob) = D. In such analyses the linear uncertainty quantities like oa often are called disturbances or errors; they correspond not to mistakes but to the differences of unsure sign and magnitude that are represented by the density function. c. The uncertainty Matrix for Discrete Quantities. The concept of covariance is readily extended to the components 19 UNCERTAINTY IN NUCLEAR DATA y. ). ) The elements of the variance-covariance or uncertainty matrix V:: (Vij) are just V.

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