The relationship between x A95% (with corrected bias) and expanded uncertainty U can be seen most clearly in the case that A95% is significantly smaller than 100%. In this case, Eq. 4 can be rewritten as the approximation: (7) which means that at 95% confidence in the method evaluation, the inequality bracketing the measurand value C holds at probability > 95%. A study using 10,000-point simulations indicates that A95% can be as large as 25%, with method evaluation confidence close to 95% using the approximation of Eq. 7. As can be seen directly, Eq. 7 is the analogue to Eq. 3 when x A95% is adopted as the expanded uncertainty U: .
(8)
In the case that bias is known to equal zero (Technical Note 1 at the end of this chapter), A95% (at 15 degrees of freedom in the evaluation experiment) is simply: .
(9)
Eq. 8 then gives:
(10)
Therefore, the coverage factor k is k = 2.8,
(11)
consistent with the use of k = 3 as a conservative but not excessive value. The user of a method then may report the expanded uncertainty U in a concentration estimate using Eq. 8, knowing the accuracy range confidence limit A95% as reported in the method. Of course, this approach relies on the sense of double confidence—in the evaluation and also in the subsequent application. Note: The European Assessment of Workplace Exposures Technical Committee, CEN TC 137, has adopted a similar viewpoint regarding method performance [20]. In this case, an overall uncertainty, defined as |bias| + 2 × RSD, is used to quantify accuracy. When compared to Eq. 6, the overall uncertainty can be regarded as an approximation to the symmetric accuracy range.
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