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NIST TN 1297: Appendix D3. Equation (A-2)

D.1 Terminology
D.2 Identification of uncertainty components
D.3 Equation (A-2)
D.4 Measurand defined by the measurement method; characterization of test methods; simple calibration
D.5 tp and the quantile t1-α
D.6 Uncertainty and units of the SI; proper use of the SI and quantity and unit symbols
D.7 References

D.3.1 In the most general sense, Eq. (A-2) of Appendix A of this Technical Note, $$y = f(x_1, ~x_2, ~\ldots, ~x_N) ~ .$$ (nist-equation A-2) is a symbolic representation of the procedure (or algorithm) used to obtain the output estimate y, which is the result of the measurement, from the individual input estimates xi. For example, some of the xi may themselves depend on additional input estimates: $$\begin{eqnarray*} x_1 &=& g_1(w_1, ~w_2. ~..., ~w_K)\\x_2 &=& g_2(z_1, ~z_2. ~..., ~z_L)\\  &~& {\rm etc.}\end{eqnarray*}$$

Or the output estimate y may be expressible simply as $$y = x + C_1 + C_2 + \ldots + C_M ~ ,$$ where the Ci are corrections, for example, for the operator, for the ambient temperature, for the laboratory, etc. Some or all of the Ci may be estimated to be near zero based on the available information, but they can still have standard uncertainties that are large enough to contribute significantly to the combined standard uncertainty of the measurement result and which therefore must be evaluated.

NOTE - In some situations, a correction for a particular effect and its standard uncertainty are estimated to be negligible relative to the required combined standard uncertainty of the measurement result, and for added confidence, an experimental test is carried out that confirms the estimate but the standard uncertainty of the test result is not negligible. In such cases, if other evidence indicates that the estimate is in fact reliable, the standard uncertainty of the test result need not be included in the uncertainty budget and both the correction and its standard uncertainty can be taken as negligible.

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Created November 6, 2015, Updated November 15, 2019