It is clear from this simple definition that the accuracy range function A must increase with both random effects and bias magnitude and therefore, is one means of quantifying accuracy as defined above according to ISO GUM. More specifically, suppose that estimates are normally distributed about population mean c with standard deviation . Then we may characterize random measurement effects in terms of the (true) relative standard deviation TRSD and bias of the mean concentration estimate c relative to the true concentration C as: .
(5)
The descriptive definition of Eq. 4 implies that the symmetric accuracy range A increases with both TRSD and bias magnitude |bias|. This feature can be seen directly in the following close approximation to the accuracy range function A, which follows [Ref. 11, 12 for derivation] from the definition in Eq. 4:
(6)
This expression is simple enough for calculation by most hand-held calculators, and it is also a useful starting point for estimating the 95% confidence limit A95% on the accuracy range as measured during a method evaluation, accounting for evaluation errors. b.
Uses of the Symmetric Accuracy Range
method validation. One application of the symmetric accuracy range is for evaluating measurement methods. As mentioned in Chapter E, a method evaluation consists of a number of measurements taken from replicate samplers at each of several controlled and known concentrations covering the range of expected method application. This type of experiment gives information about the samplers’ random errors and also the bias relative to reference concentrations. A confidence limit on the accuracy range can then be computed. One objective in a method suitable for NIOSH application is that the 95% confidence limit A95% not exceed 25%. A includes both the uncertainty (as the term is used by ISO GUM) and the systematic deviation or bias, so that correction of the bias by the sampler vendor or developer is encouraged by the very statement of this objective. See Eqs. 9-11 below for computing A95% when bias is negligible. measurement uncertainty. Suppose then that bias correction has been made. For example, suppose that following evaluation, the sampler is used for future measurement with bias corrected on the basis of its measurement during the evaluation itself. Then computation of the confidence limit A95% is possible accounting for the residual bias which is uncorrectable due to evaluation limitations, but nevertheless will be present in all future measurements. The quantity x A95% in this case forms the counterpart to the expanded uncertainty U of ISO GUM for specifying evaluation confidence at 95%.
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