JCGM 100:2008, GUM 1995 with minor corrections
Evaluation of measurement data — Guide to the expression of uncertainty in measurement
Type A evaluation (of uncertainty)
method of evaluation of uncertainty by the statistical analysis of series of observations
Type B evaluation (of uncertainty)
method of evaluation of uncertainty by means other than the statistical analysis of series of observations
These categories apply to uncertainty and are not substitutes for the words “random” and “systematic”. The uncertainty of a correction for a known systematic effect may in some cases be obtained by a Type A evaluation while in other cases by a Type B evaluation, as may the uncertainty characterizing a random effect.
The purpose of the Type A and Type B classification is to indicate the two different ways of evaluating uncertainty components and is for convenience of discussion only; the classification is not meant to indicate that there is any difference in the nature of the components resulting from the two types of evaluation. Both types of evaluation are based on probability distributions, and the uncertainty components resulting from either type are quantified by variances or standard deviations.
The estimated variance u^2 characterizing an uncertainty component obtained from a Type A evaluation is calculated from series of repeated observations and is the familiar statistically estimated variance s^2 . The estimated standard deviation u, the positive square root of u^2, is thus u = s and for convenience is sometimes called a Type A standard uncertainty. For an uncertainty component obtained from a Type B evaluation, the estimated variance u^2 is evaluated using available knowledge, and the estimated standard deviation u is sometimes called a Type B standard uncertainty.
Thus a Type A standard uncertainty is obtained from a probability density function derived from an observed frequency distribution , while a Type B standard uncertainty is obtained from an assumed probability density function based on the degree of belief that an event will occur [often called subjective probability ]. Both approaches employ recognized interpretations of probability.
A Type B evaluation of an uncertainty component is usually based on a pool of comparatively reliable information.
For an estimate xi of an input quantity Xi that has not been obtained from repeated observations, the associated estimated variance u^2(xi) or the standard uncertainty u(xi) is evaluated by scientific judgement based on all of the available information on the possible variability of Xi . The pool of information may include
- previous measurement data;
- experience with or general knowledge of the behaviour and properties of relevant materials and instruments;
- manufacturer's specifications;
- data provided in calibration and other certificates;
- uncertainties assigned to reference data taken from handbooks.
For convenience, u^2(xi) and u(xi) evaluated in this way are sometimes called a Type B variance and a Type B standard uncertainty, respectively.