NIST TN 1297: 2. Classification of Components of Uncertainty

2.1 In general, the result of a measurement is only an approximation or estimate of the value of the specific quantity subject to measurement, that is, the measurand, and thus the result is complete only when accompanied by a quantitative statement of its uncertainty.

2.2 The uncertainty of the result of a measurement generally consists of several components which, in the CIPM approach, may be grouped into two categories according to the method used to estimate their numerical values:

2.3 There is not always a simple correspondence between the classification of uncertainty components into categories A and B and the commonly used classification of uncertainty components as "random" and "systematic." The nature of an uncertainty component is conditioned by the use made of the corresponding quantity, that is, on how that quantity appears in the mathematical model that describes the measurement process. When the corresponding quantity is used in a different way, a "random" component may become a "systematic" component and vice versa. Thus the terms "random uncertainty" and "systematic uncertainty" can be misleading when generally applied. An alternative nomenclature that might be used is

where a random effect is one that gives rise to a possible random error in the current measurement process and a systematic effect is one that gives rise to a possible systematic error in the current measurement process. In principle, an uncertainty component arising from a systematic effect may in some cases be evaluated by method A while in other cases by method B (see subsection 2.2), as may be an uncertainty component arising from a random effect.

NOTE - The difference between error and uncertainty should always be borne in mind. For example, the result of a measurement after correction (see subsection 5.2) can unknowably be very close to the unknown value of the measurand, and thus have negligible error, even though it may have a large uncertainty (see the Guide [2]).

2.4 Basic to the CIPM approach is representing each component of uncertainty that contributes to the uncertainty of a measurement result by an estimated standard deviation, termed standard uncertainty with suggested symbol u_i , and equal to the positive square root of the estimated variance u_i².

2.5 It follows from subsections 2.2 and 2.4 that an uncertainty component in category A is represented by a statistically estimated standard deviation s_i² equal to the positive square root of the statistically estimated variance s_i², and the associated number of degrees of freedom ν_i . For such a component the standard uncertainty is u_i = s_i .

The evaluation of uncertainty by the statistical analysis of series of observations is termed a Type A evaluation (of uncertainty).

2.6 In a similar manner, an uncertainty component in category B is represented by a quantity u_j , which may be considered an approximation to the corresponding standard deviation; it is equal to the positive square root of u_j², which may be considered an approximation to the corresponding variance and which is obtained from an assumed probability distribution based on all the available information (see section 4). Since the quantity u_j² is treated like a variance and u_j like a standard deviation, for such a component the standard uncertainty is simply u_j .

The evaluation of uncertainty by means other than the statistical analysis of series of observations is termed a Type B evaluation (of uncertainty).

2.7 Correlations between components (of either category) are characterized by estimated covariances [see Appendix A, Eq. (A-3)] or estimated correlation coefficients.