Measurement uncertainty evaluation for a non-negative measurand: an alternative to limit of detection

摘要

The interpretation and reporting the results of measurements on materials where the concentration of the analyte is close to or may even be zero has been the subject of much discussion with the use of such concepts as limit of detection (LOD) and limit of quantification (LOQ). While these concepts have taken into account the measurement uncertainty, they have not utilised the fact that the value of the measurand, i.e., the concentration, is constrained to be zero or greater. Taking this into account the distribution of values attributable to the measurand can be derived from the probability density function (PDF) that determines the distribution of the observed values. When this PDF is normal the distribution of the values attributable to the measurand is a truncated t distribution with a lower limit of t(L) = -x(m)/(s/root n), re-normalised so that the total probability is one, where x(m) is the mean of the n observed values and s their standard deviation. When xm(t) much greater than s/root n then the distribution reverts to the unmodified t distribution. The probability that the value of the measurand is above or below a limit can be calculated directly from this truncated t distribution and the interpretation of the result does not require the use of concepts such as LOD and LOQ. Also it deals with the problem of negative observations.