|
a
|
half‑width of a rectangular distribution of possible values of input quantity
Xi:
|
|
a+
|
upper bound, or upper limit, of input quantity
Xi
|
|
a−
|
lower bound, or lower limit, of input quantity
Xi
|
|
b+
|
upper bound, or upper limit, of the deviation of input quantity
Xi
from its estimate
xi:
|
|
b−
|
lower bound, or lower limit, of the deviation of input quantity
Xi
from its estimate
xi:
|
|
ci
|
partial derivative or sensitivity coefficient:
|
|
f
|
functional relationship between measurand
Y
and input quantities
Xi
on which
Y
depends, and between output estimate
y
and input estimates
xi
on which
y
depends
|
|
∂f∕∂xi
|
partial derivative with respect to input quantity
Xi
of functional relationship
f
between measurand
Y
and input quantities
Xi
on which
Y
depends, evaluated with estimates
xi
for the
Xi:
|
|
k
|
coverage factor used to calculate expanded uncertainty
U = kuc(y)
of output estimate
y
from its combined standard uncertainty
uc(y),
where
U
defines an interval
Y = y ± U
having a high level of confidence
|
|
kp
|
coverage factor used to calculate expanded uncertainty
Up = kpuc(y)
of output estimate
y
from its combined standard uncertainty
uc(y),
where
Up
defines an interval
Y = y ± Up
having a high, specified level of confidence
p
|
|
n
|
number of repeated observations
|
|
N
|
number of input quantities
Xi
on which measurand
Y
depends
|
|
p
|
probability; level of confidence:
|
|
q
|
randomly varying quantity described by a probability distribution
|
|
q‾‾‾
|
arithmetic mean or average of
n
independent repeated observations
qk
of randomly‑varying quantity
q
|
estimate of the expectation or mean
μq
of the probability distribution of
q
|
|
qk
|
kth independent repeated observation of
randomly‑varying quantity
q
|
|
r(xi, xj)
|
estimated correlation coefficient associated with input estimates
xi
and
xj
that estimate input quantities
Xi
and
Xj:
|
|
r(X‾‾‾i, X‾‾‾j)
|
estimated correlation coefficient of input means
X‾‾‾i
and
X‾‾‾j,
determined from
n
independent pairs of repeated simultaneous observations
Xi, k
and
Xj, k
of
Xi
and
Xj:
|
|
r(yi, yj)
|
estimated correlation coefficient associated with output estimates
yi
and
yj
when two or more measurands or output quantities are determined in the same measurement
|
|
s2p
|
combined or pooled estimate of variance
|
|
sp
|
pooled experimental standard deviation, equal to the positive square root of
s2p
|
|
s2(q‾‾‾)
|
experimental variance of the mean
q‾‾‾
|
estimate of the variance
σ2⁄n
of
q‾‾‾:
|
estimated variance obtained from a Type A evaluation
|
|
s(q‾‾‾)
|
experimental standard deviation of the mean
q‾‾‾,
equal to the positive square root of
s2(q‾‾‾)
|
biased estimator of
σ(q‾‾‾)
(see C.2.21, note)
|
standard uncertainty obtained from a Type A evaluation
|
|
s2(qk)
|
experimental variance determined from
n
independent repeated observations
qk
of
q
|
estimate of the variance
σ2
of the probability distribution of
q
|
|
s(qk)
|
experimental standard deviation, equal to the positive square root of
s2(qk)
|
biased estimator of the standard deviation
σ
of the probability distribution of
q
|
|
s2(X‾‾‾i)
|
experimental variance of input mean
X‾‾‾i,
determined from
n
independent repeated observations
Xi, k
of
Xi
|
estimated variance obtained from a Type A evaluation
|
|
s(X‾‾‾i)
|
experimental standard deviation of input mean
X‾‾‾i,
equal to the positive square root of
s2(X‾‾‾i)
|
standard uncertainty obtained from a Type A evaluation
|
|
s(q‾‾‾, r‾‾‾)
|
estimate of the covariance of means
q‾‾‾
and
r‾‾‾
that estimate the expectations
μq
and
μr
of two randomly‑varying quantities
q
and
r,
determined from
n
independent pairs of repeated simultaneous observations
qk
and
rk
of
q
and
r
|
estimated covariance obtained from a Type A evaluation
|
|
s(X‾‾‾i, X‾‾‾j)
|
estimate of the covariance of input means
X‾‾‾i
and
X‾‾‾j,
determined from
n
independent pairs of repeated simultaneous observations
Xi, k
and
Xj, k
of
Xi
and
Xj
|
estimated covariance obtained from a Type A evaluation
|
|
tp(v)
|
t‑factor from the
t‑distribution for
v
degrees of freedom corresponding to a given probability
p
|
|
tp(veff)
|
t‑factor from the
t‑distribution for
veff
degrees of freedom corresponding to a given probability
p,
used to calculate expanded uncertainty
Up
|
|
u2(xi)
|
estimated variance associated with input estimate
xi
that estimates input quantity
Xi
NOTE When
xi
is determined from the arithmetic mean or average of
n
independent repeated observations,
u2(xi) = s2(X‾‾‾i)
is an estimated variance obtained from a Type A evaluation.
|
|
u(xi)
|
standard uncertainty of input estimate
xi
that estimates input quantity
Xi,
equal to the positive square root of
u2(xi)
NOTE When
xi
is determined from the arithmetic mean or average of
n
independent repeated observations,
u(xi) = s(X‾‾‾i)
is a standard uncertainty obtained from a Type A evaluation.
|
|
u(xi, xj)
|
estimated covariance associated with two input estimates
xi
and
xj
that estimate input quantities
Xi
and
Xj
NOTE When
xi
and
xj
are determined from
n
independent pairs of repeated simultaneous observations,
u(xi, xj) = s(X‾‾‾i, X‾‾‾j)
is an estimated covariance obtained from a Type A evaluation.
|
|
u2c(y)
|
combined variance associated with output estimate
y
|
|
uc(y)
|
combined standard uncertainty of output estimate
y,
equal to the positive square root of
u2c(y)
|
|
ucA(y)
|
combined standard uncertainty of output estimate
y
determined from standard uncertainties and estimated covariances obtained from Type A evaluations alone
|
|
ucB(y)
|
combined standard uncertainty of output estimate
y
determined from standard uncertainties and estimated covariances obtained from Type B evaluations alone
|
|
uc(yi)
|
combined standard uncertainty of output estimate
yi
when two or more measurands or output quantities are determined in the same measurement
|
|
u2i(y)
|
component of combined variance
u2c(y)
associated with output estimate
y
generated by estimated variance
u2(xi)
associated with input estimate
xi:
|
|
ui(y)
|
component of combined standard uncertainty
uc(y)
of output estimate
y
generated by the standard uncertainty of input estimate
xi:
|
|
u(yi, yj)
|
estimated covariance associated with output estimates
yi
and
yj
determined in the same measurement
|
|
u(xi)∕
│xi│
|
relative standard uncertainty of input estimate
xi
|
|
uc(y)∕
│y│
|
relative combined standard uncertainty of output estimate
y
|
|
[u(xi)∕xi]2
|
estimated relative variance associated with input estimate
xi
|
|
[uc(y)∕y]2
|
relative combined variance associated with output estimate
y
|
|
|
estimated relative covariance associated with input estimates
xi
and
xj
|
|
U
|
expanded uncertainty of output estimate
y
that defines an interval
Y = y ± U
having a high level of confidence, equal to coverage factor
k
times the combined standard uncertainty
uc(y)
of
y:
|
|
Up
|
expanded uncertainty of output estimate
y
that defines an interval
Y = y ± Up
having a high, specified level of confidence
p,
equal to coverage factor
kp
times the combined standard uncertainty
uc(y)
of
y:
|
|
xi
|
estimate of input quantity
Xi
NOTE When
xi
is determined from the arithmetic mean or average of
n
independent repeated observations,
xi = X‾‾‾i.
|
|
Xi
|
ith input quantity on which measurand
Y
depends
NOTE Xi
may be the physical quantity or the random variable (see 4.1.1,
Note 1).
|
|
X‾‾‾i
|
estimate of the value of input quantity
Xi,
equal to the arithmetic mean or average of
n
independent repeated observations
Xi, k
of
Xi
|
|
Xi, k
|
kth independent repeated observation of
Xi
|
|
y
|
estimate of measurand
Y
|
result of a measurement
|
output estimate
|
|
yi
|
estimate of measurand
Yi
when two or more measurands are determined in the same measurement
|
|
Y
|
a measurand
|
|
|
estimated relative uncertainty of standard uncertainty
u(xi)
of input estimate
xi
|
|
μq
|
expectation or mean of the probability distribution of randomly‑varying quantity
q
|
|
v
|
degrees of freedom (general)
|
|
vi
|
degrees of freedom, or effective degrees of freedom, of standard uncertainty
u(xi)
of input estimate
xi
|
|
veff
|
effective degrees of freedom of
uc(y),
used to obtain
tp(veff)
for calculating expanded uncertainty
Up
|
|
veffA
|
effective degrees of freedom of a combined standard uncertainty determined from standard uncertainties obtained
from Type A evaluations alone
|
|
veffB
|
effective degrees of freedom of a combined standard uncertainty determined from standard uncertainties obtained
from Type B evaluations alone
|
|
σ2
|
variance of a probabiIity distribution of (for example) a randomly‑varying quantity
q,
estimated by
s2(qk)
|
|
σ
|
standard deviation of a probability distribution, equal to the positive square root of
σ2
|
s(qk)
is a biased estimator of
σ
|
|
σ2(q‾‾‾)
|
variance of
q‾‾‾,
equal to
σ2∕n,
estimated by
s2(q‾‾‾) = s2(qk)∕n
|
|
σ(q‾‾‾)
|
standard deviation of
q‾‾‾,
equal to the positive square root of
σ2(q‾‾‾)
|
s(q‾‾‾)
is a biased estimator of
σ(q‾‾‾)
|
|
σ2[s(q‾‾‾)]
|
variance of experimental standard deviation
s(q‾‾‾)
of
q‾‾‾
|
|
σ[s(q‾‾‾)]
|
standard deviation of experimental standard deviation
s(q‾‾‾)
of
q‾‾‾,
equal to the positive square root of
σ2[s(q‾‾‾)]
|
