Value of the measurand

It is an important fact, that it is understood that the result of the measurement is the best estimate of the value of the measurand, and that all components of uncertainty, including those arising from systematic effects, such as components associated with corrections and reference standards, contribute to the dispersion" (ISO 3534-1 [1993]). Therefore, uncertainty marks the limits within which a result is accurate, i.e. precise and true (Fleming et al. [1996]). 

Accuracy is defined in the name of BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, and OIML as the closeness of agreement between the result of a measurement and the true value of the measurand (ISO 3534-1 [1993] Fleming et al. [1996b]). Accuracy characterizes the absence of a relevant bias of a measured value. As can be seen from Fig. 4.1, accuracy is a measure that combines the effects of both random and systematic deviations. Therefore, a bias can only be detected if it exceeds the range of random error. 

Closeness of agreement between the result of a measurement and a true value of the measurand . 

Specification of the Measurand In the context of uncertainty estimation, specification of the measurand" requires both a clear and unambiguous statement of what is being measured, and a quantitative expression relating the value of the measurand to the parameters on which it depends. 

The quantitative expression means how the parameter is connected to the value of the measurand in terms of a formula, e g. 

It cannot be overemphasized that MU is different from error. The error of an individual analytical result, the difference between the result and the true value of the measurand, is always a single value [38]. Part of the value of a known error, the systematic error, can be used to correct a result. This means that after correction the result of an analysis may be very close to the true value. However, the uncertainty of the measurement may still be very large because there is doubt or limited knowledge about how close the result is to the value. Uncertainty is expressed as a range and applies to an analytical procedure and a specific sample type but to different determinations and thus measurement results. The value of the uncertainty cannot be used to correct a measurement result. 

The term measurand, which might be new to some readers, is the quantity intended to be measured, so it is correct to say of a numerical result that it is the value of the measurand. Do not confuse measurand with analyte. A test material is composed of the analyte and the matrix, and so the measurand is physically embodied in the analyte. For example, if the measurand is the... 

The test material is chosen to fulfill the aims of the study. In a proficiency testing scheme or a method validation study, the test material is usually as near as possible to typical field samples. There is no advantage in competently analyzing an artificial sample if the same laboratory has difficulty with real samples. The organizing laboratory must know the composition of the test material, and must be sure that the analyte for which a quantity is to be measured is present in about the desired amount. For pure materials this is not a problem, but for natural test materials or complex matrix materials, the organizing laboratory may have to do some analyses before the samples can be sent out to the participants. If the value of the measurand is to be established by an independent laboratory before the study, then the identity requirement is also fulfilled when the measurand is stated. 

Samples distributed for analysis should have known quantity values with estimated measurement uncertainties, although, of course, these are not released to the participants until after the tests. The value of the measurand ( assigned) can be assigned by... 

Post-hoc consensus does not independently establish the value of the measurand, and although it provides internal consistency, comparison with other testing rounds and proficiency tests should be made with care. In some cases the outliers from the consensus mean in a round may be the only ones with the correct answer. When an empirical method is used to establish the assigned value, this method should be made known to the participants in advance. Where the assigned value is provided with an uncertainty (as it would be in cases 1-3 above), the uncertainty should be small compared to... 

Measurement uncertainty characterizes the extent to which the unknown value of the measurand is known after measurement, taking account of the information given by the measurement. Compared with earlier, more complicated definitions, the current definition of measurement uncertainty is quite simple, although it does not give much guidance on how it is to be estimated. What information should be used, and how should one use it ... 

Analytical chemistry has been helped in recent years by the ubiquity of DNA evidence. Here the measurement uncertainty is not the issue, but simply the probability that a particular electrophoretic pattern could come from someone other than the defendant. Statements such as It is 1,000,000 times more likely that the DNA found at the crime scene came from Mr. X, than came from an unrelated, white male are put to juries, and it has been shown that mostly, with good direction from the judge, the message has been understood. In the next section I explore the consequences of treating the quoted measurement result with its uncertainty as an interval containing the value of the measurand with a certain probability. 

Suppose a very large number of measurements could be made under conditions of measurement that allow all possible variation that could occur, including systematic effects from calibrations of balances, glassware, and so on. Also suppose that the material being measured was identical for all of these measurements, which were correctly applied with any identified systematic effects corrected for. The reality of measurement uncertainty is that these measurements would not be identical but would scatter around the value of the measurand. In the absence of any other information, this dispersion is assumed to be normally distributed, which can be described by two parameters, the mean (p) and the standard deviation (cr). It is not... 

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. 

For a measurement result to be metrologically traceable, the measurement uncertainty at each level of the calibration hierarchy must be known. Therefore, a calibration standard must have a known uncertainty concerning the quantity value. For a CRM this is included in the certificate. The uncertainty is usually in the form of a confidence interval (expanded uncertainty see chapter 6), which is a range about the certified value that contains the value of the measurand witha particular degree of confidence (usually 95%). There should be sufficient information to convert this confidence interval to a standard uncertainty. Usually the coverage factor ( see chapter 6) is 2, corresponding to infinite degrees of freedom in the calculation of measurement uncertainty, and so the confidence interval can be divided by 2 to obtain uc, the combined standard uncertainty. Suppose this CRM is used to calibrate... 

Minimum value of the measurand at which the presence of the analyte can be determined with a given probability of a false negative, and in the absence of the analyte, at a given probability of a false positive Minimum value that can be obtained with a specified measurement uncertainty... 

Range of values of the measurand in which the validation holds... 

Selectivity is a measure of the extent to which the result gives the value of the measurand and only of the measurand. If a method is 100% selective, it is said to be specific to the measurand. There are many ways of ensuring selectivity, and it is a basic characteristic of the analytical method. Chromatography, in general separation science, is a powerful analytical tool... 

Measurement uncertainty is the key to understanding modern approaches to quality assurance in analytical chemistry. A proper measurement uncertainty gives a range in which the value of the measurand is considered to... 

More recently, proficiency evaluation programs have produced similar traceability linkages, but with a novel twist. The proficiency test material (transfer standard) is sent without attachment of results. The laboratory under test receives both an independent confirmation of measurement ability and, indirectly, a traceability linkage when the test is concluded and the assigned value of the measurand is disclosed. It is unlikely that proficiency evaluation will supplant traditional forms of providing traceability links. However, the concept does provide metrologists with an additional tool. 

The expanded uncertainty provides the range within which the value of the measurand is believed to be for a particular level of confidence (see Section 6.2). 

Calibration The set of operations which establish, under specified conditions, the relationship between values indicated by a measuring instrument or measuring system and the corresponding known values of the measurand. 

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