2.
Measurement Process Characterization
2.5.
Uncertainty analysis
2.5.7.

Standard and expanded uncertainties


Definition of standard uncertainty

The sensitivity coefficients and standard deviations are combined by
root sum of squares to obtain a 'standard uncertainty'. Given
\(R\) components, the standard uncertainty is:
$$ u = \sqrt{\sum_{i=1}^R a_i^2 s_i^2} $$

Expanded uncertainty assures a high level of confidence

If the purpose of the uncertainty statement is to provide coverage
with a high level of confidence, an expanded uncertainty is
computed as
$$ U = k \cdot u $$
where \(k\) is chosen to be the
\( t_{1\alpha/2, \,\nu}\)
critical value
from the ttable with
\(\nu\) degrees of freedom. For large
degrees of freedom, \(k = 2\) approximates 95 % coverage.

Interpretation of uncertainty statement

The expanded uncertainty defined above is assumed to provide a
high level of coverage for the unknown true value of the measurement
of interest so that for any measurement result, \(Y\),
$$ Y  U \le \mbox{True} \, \mbox{Value} \le Y + U $$
