Systematic measurement uncertainties

Accuracy is often used to describe the overall doubt about a measurement result. It is made up of contributions from both bias and precision. There are a number of definitions in the Standards dealing with quality of measurements [3-5]. They are only different in the detail. The definition of accuracy in ISO 5725-1 1994, is The closeness of agreement between a test result and the accepted reference value . This means it is only appropriate to use this term when discussing a single result. The term accuracy , when applied to a set of observed values, describes the consequence of a combination of random variations and a common systematic error or bias component. It is preferable to express the quality of a result as its uncertainty, which is an estimate of the range of values within which, with a specified degree of confidence, the true value is estimated to lie. For example, the concentration of cadmium in river water is quoted as 83.2 2.2 nmol l-1 this indicates the interval bracketing the best estimate of the true value. Measurement uncertainty is discussed in detail in Chapter 6. 

This chapter deals with handling the data generated by analytical methods. The first section describes the key statistical parameters used to summarize and describe data sets. These parameters are important, as they are essential for many of the quality assurance activities described in this book. It is impossible to carry out effective method validation, evaluate measurement uncertainty, construct and interpret control charts or evaluate the data from proficiency testing schemes without some knowledge of basic statistics. This chapter also describes the use of control charts in monitoring the performance of measurements over a period of time. Finally, the concept of measurement uncertainty is introduced. The importance of evaluating uncertainty is explained and a systematic approach to evaluating uncertainty is described. 

In any experiment, therefore, all significant systematic errors should be measured and corrected for, and the random errors, including those pertaining to the bias corrections, estimated and combined in the measurement uncertainty. 

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... 

Systematic effects are estimated by repeated measurements of a CRM, suitably matrix matched. Any difference between the CRM and a routine sample for which the measurement uncertainty is being estimated should be considered and an appropriate uncertainty component added. Suppose a concentration measurement is routinely made in a laboratory that includes measurement of a CRM in the same run as calibration standards and unknowns. The bias (6) is given by... 

As reproducibility standard deviation from interlaboratory method validation studies has been suggested as a basis for the estimation of measurement uncertainty if it is known sR can be compared with a GUM estimate. It may be that with good bias correction, the estimate may be less than the reproducibility, which tends to average out all systematic effects including ones not relevant to the present measurement. Another touchstone is the Horwitz relation discussed in section 6.5.4. A rule of thumb is that the reproducibility of a method (and therefore the estimated measurement uncertainty) should fall well within a factor of two of the Horwitz value. 

The analyst conducting a method validation must assess any systematic effects that need to be corrected for or included in the measurement uncertainty of the results. The interplay between random and systematic error is complex and something of a moveable feast. The unique contribution of each analyst to the result of a chemical measurement is systematic, but in a large... 

This thus requires a sampling plan that reflects the data quality objectives and analytical measurement subjected to the laboratory quality system (Swyngedouw and Lessard, 2007). The measurement uncertainty can be controlled and evaluated (Eurachem, 2000). The sampling variance may contain systematic and random components of error from population representation and sampling protocol. Note that the errors are separate and additive. This means that the laboratory cannot compensate for sampling errors. 

Analysts and end users of the measurement results should be aware of the new dimension of the procedure validation definition given in ISO/IEC 17025, which requires that a procedure s performance parameters are fit for a specific intended use. In other words this means that the work of an analyst is not finished when performance capabilities of a specific method (or preferably procedure ) are evaluated, but he/she has to go a step further and check whether these characteristics are in compliance with the client s needs. Of course, it is up to the client to specify his/her re-quirements/properties the result should have. Furthermore, ISO/IEC 17025 is introducing evaluation of measurement uncertainty as a mean of performing validation through systematic assessment of all quantities influencing the result. 

It is notable that such kinds of error sources are fairly treated using the concept of measurement uncertainty which makes no difference between random and systematic . When simulated samples with known analyte content can be prepared, the effect of the matrix is a matter of direct investigation in respect of its chemical composition as well as physical properties that influence the result and may be at different levels for analytical samples and a calibration standard. It has long since been suggested in examination of matrix effects [26, 27] that the influence of matrix factors be varied (at least) at two levels corresponding to their upper and lower limits in accordance with an appropriate experimental design. The results from such an experiment enable the main effects of the factors and also interaction effects to be estimated as coefficients in a polynomial regression model, with the variance of matrix-induced error found by statistical analysis. This variance is simply the (squared) standard uncertainty we seek for the matrix effects. 

We have every reason to consider the estimation of measurement uncertainty in an analytical procedure followed by the judgement of compliance with a target uncertainty value as a kind of validation. This is in full agreement with ISO 17025 that points to several ways of validation, among them systematic assessment of the factors influencing the result and assessment of the uncertainty of the results... [31]. In line with this is also a statistical modelling approach to the validation process that has recently been developed and exemplified as applied to in-house [32] and interlaboratory [33] validation studies. 

Grand mean The mean of all the data (used in ANOVA). (Section 4.2) Gross error A result that is so removed from the true value that it cannot be accounted for in terms of measurement uncertainty and known systematic errors. In other words, a blunder. (Section 1.7) Grubbs s test A statistical test to determine whether a datum is an outlier. The G value for a suspected outlier can be calculated using G = ( vsuspect — x /s). If G is greater than the critical G value for a stated probability (G0.05",n) the null hypothesis, that the datum is not... 

Consider what the consequences of setting the probability level for acceptance of H0 at 90, 95, and 99% might be. As an example suppose an analytical method has been used to analyze a certified reference material for the element zinc, that is, a material whose amount of substance of zinc has been established to a high metrological standard with low measurement uncertainty, with a view to deciding if there is any significant systematic error in the method. The mean of n measurement results has been determined and suppose that the population standard deviation (a), and therefore the standard deviation of the... 

To improve the statistical precision, replicate samples are processed for each set of conditions. Our error analysis methods have been described previously (28, 54). The cited measurement uncertainties represent single standard deviations at the 68% confidence level. In the case of yield branching ratios these uncertainties follow directly from statistical random error analysis. Speculative estimates of the contributions from possible systematic mechanistic errors have not been included. 

Systematic measurement errors may reside implicitly in the customary reporting of pH and ten erature. Chemical hydrogen exchange rates can vary by a factor of ten for each pH unit (see Section 1.2.2) [42]. When pH is recorded to the nearest tenth unit, the expanded uncertainty of the exchange rate coefficient, is no less than 10%. This uncertainty can be reduced substantially. Modern, commercially available pH probes that are calibrated with two-point bracketing have an expanded uncertainty of t/ j(pH) 0.02. When pH is determined at this accuracy, the contribution of f/ j(pH) to the expanded uncertainty of This uncertainty contribution is halved when the... 

When an analytical laboratory is supplied with a sample and requested to determine the concentrations of one of its constituents, it will doubtless estimate, or perhaps know from experience, the extent of the major random and systematic errors occurring. The customer supplying the sample may well want this information summarized in a single statement, giving the range within which the true concentration is reasonably likely to lie. This range, which should be given with a probability (i.e. it is 95% probable that the concentration lies between. .. and. .. ), is called the uncertainty of the measurement. Uncertainty estimates are now very widely used in analytical chemistry, and are discussed in more detail in Chapter 4. 

Every measurement process renders values that are not centered at the true value but show some offset from it. These differences are often called errors. There are two types of error, systematic and random. A systematic error is a constant offset, whereas a random error is different between subsequent measurements, and this difference cannot be predicted. One approach of expressing the information gained from an experiment is to provide a best estimate of the measurand and information about systematic and random error values (in the form of an error analysis see, for example, Bevington and Robinson, 2003 Taylor, 1997). Another approach, the GUM approach, is to express the result of a measurement as a best estimate of the measurand together with an associated measurement uncertainty, which combines systematic and random errors on a common probabilistic basis. Figure 6.28 explains graphically the definitions for random and systematic errors and the corrections applied to the latter. Figure 6.29 shows the treatment of systematic and random errors in the course of an uncertainty analysis. 

Figure 6.29 Systematic and random errors and their treatment in the determination of the measurement uncertainty. According to Hernia, 1996.)...

Description The term accuracy combines precision and trueness (i.e., the effects of random and systematic factors, respectively). Suppose the results produced by the application of a method show zero or very low bias (i.e., are true ), their accuracy becomes equivalent to their precision [27]. In general, accuracy is not a quantity and is not given a numerical value. Due to the worldwide concept of measurement uncertainty as expressed in ISO [33] and EURACHEM [34] documents, it is recommended to use the clearer and less ambiguous term uncertainty instead of accuracy. ... 

Note 1 The reference quantity value for a systematic measurement error is a true quantity value, or a measured quantity value of a measurement standard of negligible measurement uncertainty, or a conventional quantity value. 

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