U

U

atomic symbol for uranium

u

unit symbol for the unified atomic mass unit

U distribution

A random variable, X, has a U distribution with mean μ and half-width a if it has the probability density function

f(x) =

1 π √ a2 − (x − μ)2

,     for | x − μ | < a     and     f(x) = 0 for | x − μ | ≥ a

If Y is uniformly distributed between −π / 2 and +π / 2, then the quantity X = a × sin(Y) has a U distribution with mean 0 and half-width a.

uncertainty of measurement

“parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand” [VIM]
(see also standard uncertainty, combined standard uncertainty, expanded uncertainty)

Note: Metrologists distinguish between the concepts of error of measurement and uncertainty of measurement.

uncertainty interval

coverage interval

uncertainty-propagation formula (first-order)

The general equation that describes the combined standard uncertainty for an output estimate of a measurement as a function of the standard uncertainties of the input estimates. If the output estimate, y, is calculated from input estimates x₁,x₂,…,x_N, using the equation y = f(x₁,x₂,…,x_N), then the first-order uncertainty propagation formula is written as follows:

uc2(y) =

N ∑ i = 1

(

∂f ∂xi

) 2

u2(xi)

+

2

N − 1 ∑ i = 1

N ∑ j = i + 1

∂f ∂xi

∂f ∂xj

u(xi,xj)

The first-order uncertainty-propagation formula is derived by approximating the function f by a first-order Taylor polynomial.

Note: The GUM refers to the uncertainty-propagation formula as the law of propagation of uncertainty, although it hardly deserves the status of “law.” The term may have gained something in translation from le français.

unified atomic mass unit (u)

non-SI unit of mass, defined as one-twelfth of the rest mass of an atom of ¹²C in its ground state and equal to the atomic mass constant — also called a dalton

Note: Although the unified atomic mass unit is not an SI unit, it is accepted for use with the SI. The name dalton is not accepted for use with the SI.

uniform distribution

rectangular distribution

unit (of measurement)

“particular quantity, defined and adopted by convention, with which other quantities of the same kind are compared in order to express their magnitudes relative to that quantity” [VIM]

unit symbol

symbol of a unit (of measurement)

unsupported

not being replenished by ingrowth

U-qualifier

data validation qualifier applied to a test result to indicate that the result is not significantly different from zero (undetectable)