The purpose of the expanded uncertainty U is to provide intervals, which generally contain measurand values (often referred to as the true values). In particular, given a concentration estimate (hats, as here, indicate estimates), the measurand value C is bracketed at better than 95% confidence by intervals of the type: ,
(3)
at 95% confidence in the method evaluation. The coverage factor k is intended to account for both (1) the fluctuation of the measurement about the measurand value and (2) the uncertainty in the assessment of this fluctuation. Note: Requiring only mean confidence in the evaluation leads to k given in terms of a Student-t quantile. Here, however, in fixing the method evaluation confidence (e.g., at 95%), the chi-square distribution takes the place of the Student-t distribution. Double confidence levels (in the measurement and evaluation) directly relate to a well-developed [11-19] statistical theory of tolerance or prediction intervals. Another point of ISO GUM is semantic. Uncertainty, as in common usage, covers only what is unknown about a measurement. The known but uncorrected systematic deviation or bias relative to reference concentrations does not enter into measurement uncertainty. A related concept, accuracy, is defined qualitatively within ISO GUM as the “closeness of agreement between the result of a measurement and a true value of the measurand”. Accuracy can have both random and systematic components. It is not surprising then that if a bias correction is made and if accuracy is quantified reasonably, the expanded uncertainty and an accuracy confidence limit can be equivalent. As mentioned above, another aspect of ISO GUM deals with influence factors. If measurement results are expected to be sensitive to an environmental factor (e.g., ambient temperature), then the effect of such a factor on the measurement method must be measured in the laboratory. Given estimates of the environmental variations expected during method application, influence components of the combined uncertainty can be estimated for inclusion in the uncertainty budget of Eq. 1. Table 1 lists several influence factors, which may or may not be significant.
3.
THE SYMMETRIC ACCURACY RANGE A AS USED BY NIOSH a.
Definition and its Approximation
The symmetric accuracy range A is defined as the fractional range, symmetric about the true concentration C, within which 95% of sampler measurements are to be found. Another way of saying this is: for 95% of measurements
3/15/03
212
(4)
NIOSH Manual of Analytical Methods
