Range charts
Control Chart of the Range of Duplicates are used to control if the precision of the method remains within the boundaries evaluated during the method validation. The difference between duplicate results is compared to the target uncertainty of the results.
The uncertainty of the range (absolute difference) of replicate values R = |x1 - x2|can be assessed as
If the values of the replicate results can be considered as part of a Gaussian probability distribution, then in only 5 % of the cases the differences will exceed
and in only 0.3 % of the cases will exceed
As in XRF the precision of the results is mainly conditioned by the counting statistics, the precision of the results improves with the increase in the concentration of the element. There are two possible scenarios for a run of analysis: the concentration of the element is similar in all the samples, or the concentration spans within a broad range.
Case 1: The results of duplicate analysis of a control material having the concentration of the element similar to those expected in the unknown samples can serve to assess if the precision correspond to the expected value.
Case 2: Samples contain the element in a broad range of concentration, and therefore the precision of the results changes in a relatively broad range. The quality control manager must request a second run of analysis, this time including duplicates of some of the analyzed samples, as to cover the range of concentrations found during the initial analysis.
Examples of these two charts are provided next.