Measurement uncertainty sources

The cause and effect diagram is widely used when identifying the effects on a result, including a chemical analysis result. It is used for example in measurement uncertainty to analyse the uncertainty sources. A cause and effect diagram describes a relationship between variables. The undesirable outcome is shown as an effect, and related causes are shown as leading to, or potentially leading to, this effect. 

The measurement uncertainty of the final result depends on many different contributions (uncertainty sources). The listing in the slide shows some of them, but does not claim complete-... 

The first is the clear and unambiguous specification what has to be measured under which conditions. This sometimes is more tricky than it seems to be, since it is very much connected to the second step, the identification of uncertainty sources. These sources also include parameters that do not directly go into the calculation of the result, but nevertheless influence the result and therefore the uncertainty. 

For the specification of the measurand we need a statement of what we want to measure and at the same time a formula for the result which contains all relevant uncertainty sources. The example in the shde describes the calculation of the result of a determination of the amount of cadmium released from ceramic ware under certain conditions. The result depends on the content of Cd in the extraction solution Co, the volume of the leachate Vl, the surface area ay that is extracted and possibly a dilution factor. These parameters are used to calculate the result. But we also have to consider that the acid concentration, the extraction time and the temperature are influencing the result. Since they are not directly involved in the calculation of the result, we add factors with the value 1. But we assume that this value 1 will have an uncertainty as well. 

To provide a practical, understandable and common way of measurement uncertainty calculations, mainly based on already existing quality control and validation data covering all uncertainty sources in a integral way... 

In the ordinary weighted least squares method, the most probable values of source contributions are achieved by minimizing the weighted sum of squares of the difference between the measured values of the ambient concentration and those calculated from Equation 1 weighted by the analytical uncertainty of those ambient measurements. This solution provides the added benefit of being able to propagate the measured uncertainty of the ambient concentrations through the calculations to come up with a confidence interval around the calculated source contributions. 

Measurement uncertainty is the most important criterium in both method validation and IQC. It is defined as a parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand [14]. The measurand refers to the particular quantity or the concentration of the analyte being measured. The parameter can be a standard deviation or the width of a confidence interval [14, 37]. This confidence interval represents the interval on the measurement scale within which the true value lies with a specified probability, given that all sources of error are taken into account [37]. Within this interval, the result is regarded as being accurate, that is, precise and true [11]. 

The purpose of an analytical method is the deliverance of a qualitative and/or quantitative result with an acceptable uncertainty level. Therefore, theoretically, validation boils down to measuring uncertainty . In practice, method validation is done by evaluating a series of method performance characteristics, such as precision, trueness, selectivity/specificity, linearity, operating range, recovery, LOD, limit of quantification (LOQ), sensitivity, ruggedness/robustness, and applicability. Calibration and traceability have been mentioned also as performance characteristics of a method [2, 4]. To these performance parameters, MU can be added, although MU is a key indicator for both fitness for purpose of a method and constant reliability of analytical results achieved in a laboratory (IQC). MU is a comprehensive parameter covering all sources of error and thus more than method validation alone. 

There are several terms used in measurement uncertainty that must be defined. An uncertainty arising from a particular source, expressed as a standard deviation, is known as the standard measurement uncertainty (u). When several of these are combined to give an overall uncertainty for a particular measurement result, the uncertainty is known as the combined standard measurement uncertainty (uc), and when this figure is multiplied by a coverage factor ( ) to give an interval containing a specified fraction of the distribution attributable to the measurand (e.g., 95%) it is called an expanded measurement uncertainty [U). I discuss these types of uncertainties later in the chapter. 

The top-down approach is often used when there are method validation data from properly conducted interlaboratory studies, and when the laboratory using reproducibility as the measurement uncertainty can demonstrate that such data are applicable to its operations. Chapter 5 describes these types of studies in greater detail. In assigning the reproducibility standard deviation, sR, to the measurement uncertainty from method validation of a standard method, it is assumed that usual laboratory variables (mass, volume, temperature, times, pH) are within normal limits (e.g., 2°C for temperature, 5% for timing of steps, 0.05 for pH). Clause 5.4.6.2 in ISO/ 17025 (ISO/IEC 2005) reads, In those cases where a well-recognized test method specifies limits to the values of the major sources of uncertainty of measurement and specifies the form of presentation of the calculated results, the laboratory is considered to have satisfied this clause by following the test method and reporting instructions. ... 

In fact, difficulties in sourcing and preparing large numbers (>50) of authentic compounds in mixed standards and the time taken for subsequent multilevel calibration of the analytical system with all these standards, can even add to measurement uncertainty in extreme cases. For example, if the time taken for multilevel calibration extends over several days, it is possible for the system response to have drifted significantly over the period reducing confidence in the subsequent data. Other difficult to characterize contributions to variability can also creep in, for example, analyte interactions and the general stability of mixed standards. 

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. 

Before it can prescribe the procedure for the combination of uncertainties, the protocol must treat important matrix effects and their uncertainties. These effects are liable to be disregarded, yet often overshadow other error sources, and thus lead to underestimation of total measurement uncertainty. Ignorance of matrix influence on the measurement will often cause any realistic uncertainty estimate to be so large that the use of a method, instrument or RM would become inappropriate17. At other times, however, substantial improvement can be achieved by introducing additional measurements to quantify and correct for the effect of matrix differences on the measurements. The correction itself will introduce a residual small uncertainty. 

The main problem in evaluating the uncertainty of measurements in coulometry lies in identification of important uncertainty sources and estimation of their contribution (Table 2). With very low instrumental uncertainty, other factors become limiting to the achievable uncertainty, mainly those connected to the chemical processes in the cell and the homogeneity of the material. 

In presentation and interpretation of results, NARL aims for objectivity, clear presentation, and statistical data treatment that is transparent to participants, internationally accepted and metrologically sound. Sources of chemical standards, statements concerning traceability and estimates of measurement uncertainty are included in the study report. 

In the IMEP programme1, Si-traceable values with a full measurement uncertainty according to the Guide to the expression of uncertainty in measurement (GUM) are disseminated by IRMM to field (and other) laboratories by means of appropriately prepared test samples. The uncertainties are the end-product of an evaluation process of all uncertainty sources which is as complete as... 

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. 

This way of evaluating measurement uncertainty, starting from the potential sources of error, was very useful in identifying those components that have a large contribution in the overall uncertainty and in minimizing them as much as possible. Also, good agreement... 

As is often the case, where the RMs are obtained from a non-assured source, it is the responsibility of the user to establish their traceability to appropriate references, at an appropriate level of measurement uncertainty. Usually it will be possible to establish traceability to the SI, but if this is not possible, traceability to other references, such as a higher level RM can be achieved. The traceability issues related to in-house RMs are summarised in Box 4. 

As a consequence, satisfactory performance in IMEP-20 would then mean having a result reported with zeta < 2 and micI < wlab < 0.1-2fref. Laboratories reporting larger uncertainties may not have their experimental procedure under control or may have overestimated some uncertainty components. Laboratories reporting smaller uncertainties are very likely to have either underestimated some of the uncertainty components or not accounted for some uncertainty sources. It has to be emphasized that laboratories with zeta > 3 Prst need to think about the origin of their measurement bias and only subsequently, after corrective measures have been taken, to focus thoroughly on their uncertainty estimation. 

Uncertainty represents the half-width of the interval, where the measurement results lie. If calculated for an analytical procedure and debited sample type, the estimate of measurement uncertainty may apply to results obtained accordingly. The complete uncertainty budget is a powerful tool to identify main sources of errors. Nonetheless, the value of the uncertainty cannot be used to correct a measurement result. In the food sector the evaluation of measurement uncertainty... 

The issues of method validation and assessment of measurement uncertainty in the determination of potentially toxic trace elements in rice are of permanent interest for the scientific community. In this context, the sources of uncertainty associated with the determination of Cd, Cu, Pb, and Zn have been recently estimated in rice through an interlaboratory comparison [30]. Four Brazilian laboratories participated in the proficiency test. The analytical technique used were FAAS, ET-AAS, and ICP-AES. The rice samples were supplied by the Institute for Reference Materials and Measurements (IRMM), Joint Research Center of the European Commission, within the scope of the interlaboratory comparison International Measurement Evaluation Programme (IMEP) 19 Trace Elements in Rice (see also Chapter 7 in this book). Three out of the four laboratories reported values close to the reference values. It was emphasized that, in order to establish a reliable uncertainty budget, all significant sources of uncertainty should be identified. 

In practice the measurement uncertainty for a particular analysis can arise from many sources. Each source will contribute to the overall uncertainty of the measurement and so each source is considered to have its own uncertainty component. 

Bottom-up based on the identification, quantification, and combination of all individual sources of measurement uncertainty... 

It should be noted that the basic and necessary parameters that characterize an analytical result are traceability and measurement uncertainty. An anal3tical result without documented traceability and estimated uncertainty is a source of misinformation. These two parameters are the basic requirements of reliable analytical results. 

Abstract Every analytical result should be expressed with some indication of its quality. The uncertainty as defined by Eurachem ( parameter associated with the result of a measurement that characterises the dispersion of the values that could reasonably be attributed to the,. .., quantity subjected to measurement ) is a good tool to accomplish this goal in quantitative analysis. Eurachem has produced a guide to the estimation of the uncertainty attached to an analytical result. Indeed, the estimation of the total uncertainty by using uncertainty propagation laws is com-ponents-dependent. The estimation of some of those components is based on subjective criteria. The identification of the uncertainty sources and of their importance,... 

Using electrochemical sensors and considering the sources of uncertainty given by Pan [2], viz. homogeneity, recovery, analysis blank, measurement standard, calibration, matrix effect and interferences, measuring instrument, and data processing, the main uncertainty sources i.e., the homogeneity and the matrix effect, are eliminated. 

The main disadvantage of this approach is that it may not readily reveal the main sources of uncertainty for a particular method. In previous studies we have typically found the uncertainty budget to be dominated by the precision and trueness terms [14]. In such cases, if the combined uncertainty for the method is too large, indicating that the method requires improvement, further study may be required to identify the stages in the method which contribute most to the uncertainty. However, the approach detailed here will allow the analyst to obtain, relatively quickly, a sound estimate of measurement uncertainty, with minimum experimental work beyond that required for method validation. 

Therefore, the corrosivity of the cabinet was evaluated as v=Am/S g/m2 for 96 h in the eight experiments. The analysis of the main uncertainty sources according to recommendations [6, 7] was performed (Fig. 1) for evaluation of possible value of uncertainty of corrosivity measurement result. Each main source of uncertainty (mass loss Am, surface area S and duration t) was analysed and calculated separately and these components used for combined and expanded uncertainty calculation. 

Fig. 1 Main uncertainty sources of corrosivity measurement as rate of mass loss in a neutral salt spray cabinet expressed as v=Am/S...

---