8 Summary of procedure for evaluating and expressing uncertainty
The steps to be followed for evaluating and expressing the uncertainty of the result of a measurement as presented in
this Guide may be summarized as follows:

Express mathematically the relationship between the measurand
Y
and the input quantities
X_{i}
on which
Y
depends:
Y = f(X_{1}, X_{2}, ..., X_{N}).
The function
f
should contain every quantity, including all corrections and correction factors, that can contribute
a significant component of uncertainty to the result of the measurement (see
4.1.1 and 4.1.2).

Determine
x_{i},
the estimated value of input quantity
X_{i},
either on the basis of the statistical analysis of series of observations or by other means (see
4.1.3).

Evaluate the standard uncertainty
u(x_{i})
of each input estimate
x_{i}.
For an input estimate obtained from the statistical analysis of series of observations, the standard uncertainty is
evaluated as described in 4.2 (Type A evaluation of standard uncertainty). For an
input estimate obtained by other means, the standard uncertainty
u(x_{i})
is evaluated as described in 4.3 (Type B evaluation of standard uncertainty).

Evaluate the covariances associated with any input estimates that are correlated (see
5.2).

Calculate the result of the measurement, that is, the estimate
y
of the measurand
Y,
from the functional relationship
f
using for the input quantities
X_{i}
the estimates
x_{i}
obtained in step 2 (see 4.1.4).

Determine the combined standard uncertainty
u_{c}(y)
of the measurement result
y
from the standard uncertainties and covariances associated with the input estimates, as described in
Clause 5. If the measurement determines simultaneously more than one output quantity, calculate
their covariances (see 7.2.5, H.2,
H.3, and H.4).

If it is necessary to give an expanded uncertainty
U,
whose purpose is to provide an interval
y − U
to
y + U
that may be expected to encompass a large fraction of the distribution of values that could reasonably be attributed
to the measurand
Y,
multiply the combined standard uncertainty
u_{c}(y)
by a coverage factor
k,
typically in the range 2 to 3, to obtain
U = ku_{c}(y).
Select
k
on the basis of the level of confidence required of the interval
(see 6.2, 6.3, and especially
Annex G, which
discusses the selection of a value of
k,
that produces an interval having a level of confidence close to a specified value).

Report the result of the measurement
y
together with its combined standard uncertainty
u_{c}(y)
or expanded uncertainty
U
as discussed in 7.2.1 and 7.2.3; use one of the formats
recommended in 7.2.2 and 7.2.4. Describe, as
outlined also in Clause 7, how
y
and
u_{c}(y)
or
U
were obtained.