# Appendix D

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.2 Identification of uncertainty components

D.2.1 The NIST policy on expressing measurement uncertainty states that all components of standard uncertainty "should be identified according to the method used to estimate their numerical values: A. those which are evaluated by statistical methods, B. those which are evaluated by other means."

Such identification will usually be readily apparent in the "detailed description of how each component of standard uncertainty was evaluated" that is required by the NIST policy. However, such identification can also be given in a table which lists the components of standard uncertainty. Tables D.1 and D.2, which are based on the end-gauge calibration example of the Guide (subclause H.1), are two examples of such tables.

Table D.1 - Uncertainty Budget: End-Gauge Calibration
Source of uncertainty Standard uncertainty
(nm)
Calibration of standard end gauge 25(B)
Measured difference between end gauges:
repeated observations
random effects of comparator
systematic effects of comparator
5.8 (A)
3.9 (A)
6.7 (B)
Thermal expansion of standard end gauge 1.7 (B)
Temperature of test bed:
mean temperature of bed
cyclic variation of temperature of room
5.8 (A)
10.2 (B)
Difference in expansion coefficients of end gauges 2.9 (B)
Difference in temperatures of end gauges 16.6 (B)
Combined standard uncertainty: uc(l) = 34 nm

D.2.2 In Table D.1, the method used to evaluate a particular standard uncertainty is shown in parentheses. In Table D.2, the method is indicated by using different columns. The latter table also shows how one can indicate whether a component arose from a random effect in the current measurement process or from a systematic effect in the current measurement process, assuming that such information is believed to be useful to the reader.

Table D.2 - Uncertainty Budget: End-Gauge Calibration
Source of uncertainty Standard uncertainties
from random effects in the
current measurement process
(nm)
Standard uncertainties
from systematic effects in the
current measurement process
(nm)
Type A
evaluation
Type B
evaluation
Type A
evaluation
Type B
evaluation
Calibration of standard end gauge       25
Measured difference between end gauges:
repeated observations 5.8
random effects of comparator     3.9
systematic effects of comparator       6.7
Thermal expansion of standard end gauge       1.7
Temperature of test bed:
mean temperature of bed 5.8
cyclic variation of temperature of room       10.2
Difference in expansion coefficients of end gauges       2.9
Difference in temperatures of end gauges   16.6
Combined standard uncertainty: uc(l) = 34 nm

If a standard uncertainty is obtained from a source outside of the current measurement process and the nature of its individual components are unknown (which will often be the case), it may be classified as having been obtained from a Type B evaluation. If the standard uncertainty from an outside source is known to be composed of components obtained from both Type A and Type B evaluations but the magnitudes of the individual components are unknown, then one may indicate this by using (A,B) rather than (B) in a table such as D.1.

On the other hand, a standard uncertainty known to be composed of components obtained from Type A evaluations alone should be classified as a Type A standard uncertainty, while a standard uncertainty known to be composed of components obtained from Type B evaluations alone should be classified as a Type B standard uncertainty.

In this same vein, if the combined standard uncertainty uc(y) of the measurement result y is obtained from Type A standard uncertainties (and covariances) only, it too may be considered Type A, even though no direct observations were made of the measurand Y of which the measurement result y is an estimate. Similarly, if a combined standard uncertainty is obtained from Type B standard uncertainties (and covariances) only, it too may be considered Type B.