Calibration uncertainty budgeting

On most occasions CRMs are used as Quality Control materials, rather than as calibrations . As outlined above, this common application adds significantly to the user s uncertainty budget, since at a minimum it is necessary to consider at least two independent measurement events (Um). so increasing the combined uncertainty of the results. Again this process rapidly increases the combined uncertainty with increasing complexity of the analytical system and so the usefulness of a control analysis may be downgraded when a correct uncertainty budget is formulated. 

When making a chemical measurement by taking a certain amount of the test material, working it up in a form that can be analyzed, calibrating the instrument, and performing the measurement, analysts understand that there will be some doubt about the result. Contributions to uncertainty derive from each step in the analysis, and even from the basis on which the analysis is carried out. An uncertainty budget documents the history of the assessment... 

The protocol must present an uncertainty budget. Its components should be carefully estimated, and may be stated in standard uncertainties, but expanded uncertainties can have great utility, provided the k factor is carefully chosen and indicated [2, 4, 6]13. All supposa-ble uncertainty sources (of types A and B)14, must be considered. Uncertainty components are concerned with contaminations, matrix effects, corrections, lack of stability or of stoichiometry, impurities in reagents, instrument non-linearities and calibrations, inherent uncertainties in standard methods, and uncertainties from subsample selection. Explicitly excluded may have to be sample selection in the field before submission to the laboratory and contamination prior to sample submission to the laboratory. The responsibility for adhering to the protocol s procedures, for which the planned complete uncertainty budget applies, rests with the laboratory and the analyst in charge of the measurement. 

Obviously a small absorbance uncertainty is caused by the lowest concentration but there are many other sources of error. In this respect, it is the authors opinion that calibrating and validating the metrological performances of photometric systems is a necessary condition but not on its own sufficient to achieve traceability in this field. In fact, a measurement uncertainty budget takes into consideration all uncertainties due to the way in which instrumentation is used, the CRMs and calibration of the system. 

For a measurement of pH with cell (I) to be traceable to the SI, an uncertainty for the Bates-Guggenheim convention must be estimated. One possibility is to estimate a reasonable uncertainty contribution due to a variation of the ion size parameter. An uncertainty contribution of 0.01 in pH should cover the entire variation. When this contribution is included in the uncertainty budget, the uncertainty at the top of the traceability chain is too high to derive secondary standards as used to calibrate pH meter-electrode assemblies. 

It is of main importance to set up a total uncertainty budget following the GUM and EURACHEM guidelines for combined uncertainty to identify the main sources of uncertainty [40, 41]. Results from different laboratories or from the same laboratory at different times have to be comparable with conbdence. This is achieved if all laboratories are using the same stated reference. In many cases, this is achieved by establishing a chain of calibrations leading to primary national or international standards, ideally the SI units of measurement [79]. The SI system provides an international infrastructure for realizing comparable measurements by the use of traceable measurements. 

When the operator has determined the totality of the uncertainty budget within the possibilities offered by his laboratory, the uncertainty due to the presence of (a) possible systematic error(s) or bias remains. Only one possibility exists to detect such a bias. It lies in external help. Comparing the results of the test method to another method developed in-house involves the risk of having an unknown laboratory bias, e g. biased primary calibrants etc. Therefore, it is more appropriate to look for external help. This can come from the comparison of results obtained on a reference sample with those obtained on the same sample by another laboratory or by analysing a certified reference material. Both possibilities will be dealt with in the next two chapters of this book. 

Uncertainty and traceability appear to be different concepts, but, in fact, they are identical twins. If a measurement is traceable, an uncertainty budget can be made that includes the calibration of the reference standard. The uncertainty of this reference standard can only be properly stated if it is traceable to a primary standard. On the other hand, if no uncertainty calculation can be made, a measurement cannot be traceable, and if a measurement is not traceable, no uncertainty can be calculated as the uncertainty of the used references is not known. 

A measurement assurance program that supports the validity of the uncertainty budget. Such a program might include such activities as operator training, periodic instrument calibrations, maintenance of laboratory environments within specified limits, and so on. 

When we consider the efficiency, e, we find we have a separate uncertainty budget to consider taking into account all of the factors involved in preparing the efficiency calibration reference source and the measurement of the cahbration data. This would take into account the uncertainty of the certified source from which the calibration source was prepared aud the uncertainty of interpolation of the cahbration curve. 

One of the key concerns of analytical science is how good are the numbers produced . Even with an adequately developed, optimised and collaboratively tested method which has been carried out on qualified and calibrated equipment the question remains. Recently it has become fashionable to extend the concepts of the physical metrology into analytical measurements and to quantify confidence in terms of the much more negative uncertainty.It is based on the bottom-up principle or the so called error budget approach. This approach is based on the theory that if the variance contributions of all sources of error involved in analytical processes then it is possible to calculate the overall process... 

There wiU, of course, also be uncertainties introduced when preparing the calibration source. However, they will be a constant amount on each calibration point and it would not be useful to include them in the weighting process. In fact, little more than weighing will be involved in most cases and the extra uncertainty is likely to be small. Nevertheless, it should be accounted for by combining with the interpolation uncertainty. Note that the individual uncertainties on the amount of each nuclide in the reference material do not appear directly in the budget. These will contribute to the scatter on the calibration curve. On the other hand, if individual efficiencies, for particular gamma-rays of particular nuclides are used, the uncertainty on the amount of nuclide in the calibration source should be taken into account. 

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