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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 to 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*u

where k is chosen to be the t1-α/2,ν critical value from the t-table with ν 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 <= True Value <= Y + U
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