2. Measurement Process Characterization
2.5. Uncertainty analysis

## 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 t-table 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, $$Y$$, $$Y - U \le \mbox{True} \, \mbox{Value} \le Y + U$$