Measurement uncertainty budget

Table 5.3. Measurement uncertainty budget for the measurement of cholesterol in serum by isotope dilution/GCMS...

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. 

Sampling needs to be recognized as the first step in the measurement process and its contribution to the measurement uncertainty budget cannot be ignored [15]. Approaches on how to estimate realistic uncertainties arising from sampling can be found in the Eurachem/EUROLAB/CITAC/Nordtest/AMC guide [16]. 

To assess homogeneity, the distribution of chemical constituents in a matrix is at the core of the investigation. This distribution can range from a random temporal and spatial occurrence at atomic or molecular levels over well defined patterns in crystalline structures to clusters of a chemical of microscopic to macroscopic scale. Although many physical and optical methods as well as analytical chemistry methods are used to visualize and quantify such spatial distributions, the determination of chemical homogeneity in a CRM must be treated as part of the uncertainty budget affecting analytical chemistry measurements. 

In this Chapter we highlight the practical considerations that must be understood by all users of RMs and CRMs we look at some of the issues of traceability and make the CRM user aware of the uncertainty budgets that need to be considered with the use of CRMs. No attempt will be made to advise CRM users on the proper use of statistics in the analytical measurement process and no statistical approaches on the establishment of measurement uncertainty will be given. There are a number of good texts on the subject which should be consulted. These are listed in the Further Reading section of the references at the end of this Chapter and include Miller and Miller (1993) and Taylor s work for NIST (Taylor 1985). 

The proper application of the ISO Guide to the expression of uncertainty in measurement requires that aU sources of rmcertainty are included. In practical terms this means an uncertainty budget has to be developed also by the user. The development of an rmcertainty budget, and the consequences for both analysts and producers is described later in Section 7.2. 

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. 

In their broadest application, CRMs are used as controls to verify in a direct comparison the accuracy of the results of a particular measurement parallel with this verification, traceability may be demonstrated. Under conditions demonstrated to be equal for sample and CRM, agreement of results, e.g. as defined above, is proof. Since such possibilities for a direct comparison between samples and a CRM are rare, the user s claims for accuracy and traceability have to be made by inference. Naturally, the use of several CRMs of similar matrix but different analyte content will strengthen the user s inference. Even so, the user stiU has to assess and account for all uncertainties in this comparison of results. These imcertainty calculations must include beyond the common analytical uncertainty budget (i) a component that reflects material matrix effects, (2) a component that reflects differences in the amount of substance determined, (3) the uncertainty of the certified or reference value(s) used, and 4) the uncertainty of the comparison itself AU this information certainly supports the assertion of accuracy in relation to the CRM. However, the requirement of the imbroken chain of comparisons wiU not be formally fulfilled. 

Each of these error components adds its own uncertainty to the total uncertainty budget of the analytical procedure. Therefore, the different error components are referred to as sources of uncertainty. Depending on the sources of uncertainty taken into account and thus on the conditions of the measurement, the overall MU will be different and another definition of MU will apply. This means that there is no single, straighforward definition of MU. It is rather a concept the interpretation of... 

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... 

If an estimate of the measurement uncertainty has been made and quoted for a single determination, it is possible to infer the measurement uncertainty for repeated determinations by going through the uncertainty budget and... 

Consideration of factors that could contribute to measurement uncertainty from the use in the analysts laboratory revision of the uncertainty budget accordingly... 

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. 

Although every form of training includes teaching the avoidance of blunders, sometimes called spurious errors [8], these errors are unfortunately not always prevented. Nevertheless, the uncertainty budgets of protocols should not include components for possible blunders , because the magnitude of their effects on measurements is completely unpredictable. Such uncertainties are clearly not of a scientific nature. 

In some instances chemists will prepare in-laboratory RMs, generally by dissolution of a pure compound in a solvent to predetermined concentrations or even by dilution of commercially prepared stock solutions. The uncertainties connected with such RMs and relevant procedures must be understood by the analyst and entered into the uncertainty budget for the measurement of the unknown. The analyst then assumes responsibility for the uncertainties of the link of the RM value to the SI, all expressed in the relevant SI units, even when relative uncertainties are used. 

The definition of metrological traceability (see above) stipulates that each link in the chain has a known uncertainty. Nowadays, this concept and its application have been reformulated by the BIPM and recently detailed in the Guide to the expression of uncertainty in measurement (GUM) [26] parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand . Useful explanations are provided in several other guides [26-30] as well as commentaries [e.g. 31-33], The philosophy is to apply a bot-tom-up approach by formulating a function of all input quantities giving the measurand as output. An uncertainty budget of all sources of uncertainty is established. Important items to consider are ... 

The evaluated uncertainty of this substitution, i.e. the uncertainty of K, will limit the uncertainty of the measurement result of the unknown sample and must be taken into account as a contribution to the total uncertainty budget of the result obtained on the unknown sample since ... 

Reference to uncertainty budgets developed according to ISO/GUM principles [8, 9] which are included in each test method. These budgets are used to estimate the uncertainty associated with measurements made using the method. The effects of sample homogeneity and analyte stability are included in the overall estimate of measurement uncertainty. 

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. 

At low count rates the relative uncertainty of the pulser peak area in 1-day measurements remains below 10 3. At counting losses of 30% and at acquisition times of 1 h the relative uncertainty of the counting time does not exceed 1%. To cover the possible influence of systematic effects on the effective duration of the effective acquisition time originating in different counting conditions, a 1% uncertainty is included in the uncertainty budget at count rates exceeding 5000 s1. 

For chemical measurements this involves the need for stated references and a clear uncertainty statement, which should be derived from an uncertainty budget with due regard to the fact that several references, such as amount of substance, mass, volume, time, temperature are generally involved in a single analytical procedure contributing distinct, but different portions to the overall uncertainty. 

This uncertainty budget must not only take into account the uncertainties of all the references used in connection with the analytical procedure, but also the uncertainties from the operation of the laboratory procedure as documented in the validation report. The uncertainty from the measurement procedure is frequently much larger than the uncertainties carried by the references. 

Determination of amount of substance often requires measurements of different properties, for example sample mass, on a balance compared to a mass reference analyte identity by comparison to a reference, perhaps using a spectrometer and a database of known compounds and analyte quantitation by comparison to a different reference, perhaps a reference material. Each property of the result should be traceable, and each may contribute uncertainty to the reported result. Thus, claims of traceability of a result must include not only a description of the references and uncertainty budgets for comparison to them, but also a description of the scope of traceability. 

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. 

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