Uncertainty source

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. 

In the 2" step we try to figure out all relevant uncertainty sources that infln-ence the parameters identified in step 1. The figure shows a fishbone or Ishikawa diagram that is helpful to get an overview. 

Identification of uncertainty sources Could be described e.g. by a fishbone diagram... 

When we quantify the uncertainty sources or groups of sources we have to consider that we can assume some to be normally distributed. In this case we get the standard uncertainty directly from the standard deviation. 

As already mentioned the modelling approach described in the GUM is difficult to translate into analytical chemistry because the testing procedures are very complex and it is a huge effort to identify and quantify all uncertainty sources. For routine laboratories often handling dozens or even hundreds of different test methods it is nearly impossible to cope that with the modelling approach. 

Chemical analyses often are very complex testing procedures with lots of uncertainty sources that can hardly be quantified separately... 

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... 

To construct a cause-and-effect diagram of uncertainty sources from the information contained in the procedures and equations of an analytical method, follow these steps. First, draw a horizontal right-facing arrow in the middle of a sheet of paper. Label the arrow end with the symbol for the measurand. Starting from the sources identified by the equation for the value of the measurand, draw arrows to this line at about 45°, one for each of the quantities in your equation plus any other sources identified that are not already counted, plus one for repeatability. Label the start of each arrow with a symbol for the quantity. Figure 6.3 shows a draft cause-and-effect diagram for the purity of the acid. 

Equation (4.20) was proposed by Hoskuldsson [65] many years ago and has been adopted by the American Society for Testing and Materials (ASTM) [59]. It generalises the univariate expression to the multivariate context and concisely describes the error propagated from three uncertainty sources to the standard error of the predicted concentration calibration concentration errors, errors in calibration instrumental signals and errors in test sample signals. Equations (4.19) and (4.20) assume that calibrations standards are representative of the test or future samples. However, if the test or future (real) sample presents uncalibrated components or spectral artefacts, the residuals will be abnormally large. In this case, the sample should be classified as an outlier and the analyte concentration cannot be predicted by the current model. This constitutes the basis of the excellent outlier detection capabilities of first-order multivariate methodologies. 

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. 

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 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... 

Identifying uncertainty sources specified in the SOP, including sources arising from chemical assumptions,... 

Currently, there are inconsistencies in the application and methodology for uncertainty analysis in exposure assessment. While several sophisticated quantitative techniques exist, their general application is hampered not only by their complexity (and resulting need for considerable supporting information) but also by the lack of methodology to facilitate the specification of uncertainty sources prior to the quantification of their specific weight. 

The uncertainty of this parameter has not been considered The standard value is questionable because of variation and changes over age and sex. However, within the model, it is not a major source of uncertainty, since additional information on variation in this parameter will not contribute to major changes in the exposure result. A possible 1-2% error in this parameter (used in the denominator of the model) is considered Low in contrast to the major uncertainty sources (e.g. variation in fish-eating habits in the population, mixture of different fish species and degree of contamination associated with regional origin). 

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. 

The uncertainty ucrm which can be attached to a certified value in a CRM is given by the combination of all uncertainty sources relevant to the user (31, 32). 

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,... 

The uncertainty estimation can be divided into four steps [1] (1) specification, (2) identification of uncertainty sources, (3) quantification of uncertainty components, and (4) total uncertainty estimation. 

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. 

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...

The analysis of uncertainty sources and components reveals that the uncertainty value of the spray cabinet corrosivity depends on the measurements of the surface area of the RS and mass loss in the corrosion processes. 

Having estimated the uncertainty as outlined, additional uncertainty sources should be considered. If the comparison was undertaken within a short time period, one might consider adding an additional long-term imprecision component as a variance component to the standard uncertainty expression. 

A procedure is presented for estimation of uncertainty in measurement of the pK(a> of a weak acid by potentiometric titration. The procedure is based on the ISO GUM. The core of the procedure is a mathematical model that involves 40 input parameters. A novel approach is used for taking into account the purity of the acid, the impurities are not treated as inert compounds only, and their possible acidic dissociation is also taken into account. Application to an example of practical pK(a> determination is presented. Altogether, 67 different sources of uncertainty are identified and quantified within the example. The relative importance of different uncertainty sources is discussed. The most important source of uncertainty (with the experimental set-up of the example) is the uncertainty of the pH measurement followed by the accuracy of the burette and the uncertainty of weighing. The procedure gives uncertainty separately for each point of the titration curve. The uncertainty depends on the amount of the titrant added, being lowest in the central part of the titration curve. The possibilities of reducing the uncertainty and interpreting the drift of the pKJa) values obtained from the same curve are discussed. 

The second step is to identify or to list all possible sources of uncertainty for the method, and to ensure that uncertainty sources of the same nature are grouped together to avoid their inclusion in duplicate in the estimation. A cause and effect diagram can serve as a useful tool to elaborate this step. The list, or the cause-and-effect diagram (Fig. 9.3), is developed initially on the basis of factors in the mathematical expression [Eq. (9.1)] that is utilized to calculate the result of the analysis and with reference to the method protocol (Fig. 9.2). The individual components for the uncertainty budget are listed in Table 9.1. 

Since no certified reference material was available for this matrix-analyte combination, the method recovery R) in this example is an estimate of the recovery obtained from spiking a blank sample, as described by Barwick and Ellison. Two uncertainty sources are considered in the estimation of uncertainty associated with the recovery u R)-, these are the recovery uncertainty due to the sample preparation method u R ), and that due to variation in sample matrices u Rs), as described by Leung et al. An... 

The penultimate step in the procedure is to calculate the combined uncertainty of the method, which is expressed as the relative uncertainty, from the standard uncertainty values of main uncertainty sources. Erom Table 9.1, the main contributing sources to the overall relative standard uncertainty for the example given are the preparation of calibrators (RSUcai = 0.0209), the sample preparation (RSUsampie = 0.00509), the method precision (RSUprec =... 

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