### Can we estimate uncertainty by replicates?

The method traditionally practiced by most test laboratories in the estimation of measurement uncertainty is by the ISO GUM (ISO/IEC Guide 98-3) approach, which is quite tedious and time consuming to study and gather uncertainty contributions from each and every step of the test method. An alternative way of looking at uncertainty is to attempt to study the overall performance of the analytical procedure by involving replication of the whole procedure to give a direct estimate of the uncertainty for the final test result. This is the so-called ‘top-down’ approach.

We may use the data from inter-laboratory study, in-house validation or ongoing quality control. This approach is particularly appropriate where individual effects are poorly understood in terms of their quantitative theoretical models which are capable of predicting the behavior of analytical results for particular sample types. By this approach, it is suffice to consider reproducibility from inter-laboratory data or long-term within-laboratory precision as recommended by ISO 21748, ISO 11352 and ASTM D 6299.

However, one must be aware of that by repeatedly analyzing a given sample over several times will not be a good estimate of the uncertainty unless the following conditions are fulfilled:

- There must be no perceptible bias or systematic error in the procedure. That is to say that the difference between the expected results and the true or reference value must be negligible in relation to twice of the standard deviation with 95% confidence. This condition is usually (but not always) fulfilled in analytical chemistry.

- The replication has to explore all of the possible variations in the execution of the method by engaging different analysts on different days using different equipment on a similar sample. If not, at least all of the variations of important magnitude are considered. Such condition may not be easily met by replication under repeatability conditions (i.e. repeated testing within laboratory), because such variations would be laboratory-specific to a great extent.

The conclusion is that replicated data by a single analyst on same equipment over a short period of time are not sufficient for uncertainty estimation. If the top-down approach is to be followed, we must obtain a good estimate of the long-term precision of the analytical method. This can be done for example, by studying the precision for a typical test method used as a QC material over a reasonable period of time. We may also use a published reproducibility standard deviation for the method in use, provided we document proof that we are able to follow the procedure closely and competently.

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