Measurements and Uncertainty

References A variety of mathematical methods are proposed to cope with hnear (e.g., material balances based on flows) and nonhnear (e.g., energy balances and equilibrium relations) constraints. Methods have been developed to cope with unknown measurement uncertainties and missing measurements. The reference list provides ample insight into these methods. See, in particular, the works by Mah, Crowe, and Madron. However, the methods all require more information than is tvpicaUy known in a plant setting. Therefore, even when automated methods are available, plant-performance analysts are well advised to perform initial adjustments by hand. 

Where you devise original solutions to the measurement of characteristics the theory and development of the method should be documented and retained as evidence of the validity of the measurement method. Any new measurement methods should be proven by rigorous experiment to detect the measurement uncertainty and cumulative effect of the errors in each measurement process. The samples used for proving the method should also be retained so as to provide a means of repeating the measurements should it prove necessary. 

Associated with method validation, but not part of it, are two properties of results that have been previously mentioned. These parameters are measurement uncertainty and metrological traceability. Measurement uncertainty is covered in Chapter 6 and metrological traceability in Chapter 5. If considered at the planning stage of method validation, the information obtained during validation is a valuable input into measurement uncertainty evaluation. Traceability depends on the method s operating procedures and the materials being used. 

After five years as an analyst, Vicki moved within LGC to work on the DTI-funded Valid Analytical Measurement (VAM) programme. In this role, she was responsible for providing advice and developing guidance on method validation, measurement uncertainty and statistics. One of her key projects involved the development of approaches for evaluating the uncertainty in results obtained from chemical test methods. During this time, Vicki also became involved with the development and delivery of training courses on topics such as method validation, measurement uncertainty, quality systems and statistics for analytical chemists. 

Metrology Includes all theoretical and practical aspects of measurement, whatever the measurement uncertainty and field of application. 

Part 2 - Definitions for the use of gauges Part 3 - Definitions for measurement uncertainty and evaluation of gauges 1/80... 

CX/MAS 01/8 (2001), Codex Alimentarius Commission, Codex Committee on Methods of Analysis and Sampling (FAO/WHO), Measurement uncertainty. Relationship between the analytical result, the measurement uncertainty and the specification in Codex standards, agenda item 4a of the 23rd session, Budapest, Hungary, Feb. 26-Mar. 2, 2001. 

King, B. (2001), Meeting the measurement uncertainty and traceability requirements of ISO/IEC standard 17025 in chemical analysis, Fresen. J. And. Chem., 371, 714. 

The result of a chemical measurement is a number, with measurement uncertainty and appropriate units. Analysts are accustomed to working with numbers, calibration graphs have been drawn for years, and a laboratory with any kind of commercial success will generate a lot of data. If the results follow a particular distribution, then this statistical knowledge can be used to... 

The certified value is usually taken as the grand mean of the valid results. The organizer uses standard deviation as the basis for calculating the measurement uncertainty. Results from the laboratories will include their own estimates of measurement uncertainty and statements of the metrological traceability of the results. There is still discussion about the best way to incorporate different measurement uncertainties because there is not an obvious statistical model for the results. One approach is to combine the estimates of measurement uncertainty as a direct geometric average and then use this to calculate an uncertainty of the grand mean. Type A estimates will be divided by /n n is the number of laboratories), but other contributions to the uncertainty are unlikely to be so treated. 

Perhaps this sounds unnecessarily complicated, but an understanding of basic concepts and terms in metrology help us appreciate the importance of metrological traceability, measurement uncertainty, and the like. 

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... 

The standard recognizes the factors that determine the correctness and reliability of test results human factors, accommodation and environment, methods, equipment, sampling, and the handling of test items. In this list, measurement traceability is mentioned, but in fact metrological traceability, with measurement uncertainty and method validation, are really subsumed in methods. (subsection 5.4). The effect of each of these factors on measurement uncertainty will differ considerably among kinds of tests. 

Second, there is no unique scheme of data interpretation. The process of inference always remains arbitrary to some extent. In fact, all the existing DDT data combined still allow for an infinite number of models that could reproduce these data, even if we were to disregard the measurement uncertainties and take the data as absolute numbers. Although this may sound strange, it is less so if we think in terms of degrees of freedom. Let us assume that there are one million measurements of DDT concentration in the environment. Then a model which contains one million adjustable parameters can, in principle, exactly (that is, without residual error) reproduce these data. If we included models with more adjustable parameters than observa-... 

Chemists will have an important reservation concerning this understanding of what constitutes the uncertainty of a measurement. Physicists and engineers may not, but chemists often are subjected to major sampling, stability, blank, and contamination errors. Chemists should include them in their total uncertainty estimates. The distinction between the measurement uncertainty and the degree to which the measured sample fails to represent the relevant larger bulk needs to be debated and discussed for consensus and understanding. 

The detectability limit for any given measurement is defined in terms of measurement uncertainty and for LIFS can be quite small. This limit, however, can be affected by interferences of various kinds and care must be taken in instrument design to avoid difficulties. The dynamic range for LIFS is generally controlled by radiative trapping effects. 

Note 3 In this definition, uncertainty covers both measurement uncertainty and uncertainty associated with the value of a nominal property, such as for identity and sequence. Traceability covers both metrological traceability of a quantity value and traceability of a nominal property value. ... 

Comparison of measurement uncertainty and method validation procedures... 

Measurement uncertainty and its implications for collaborative study method validation and method performance parameters 39... 

H.L. Pardue, The inseparable triad analytical sensitivity, measurement uncertainty, and quantitative resolution, Clin. Chem. 43 (1997) 1831. 

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... 

The limit of detection and/or the limit of quantification are usually provided in the databases as metadata accompanying the concentration values. On the other hand, information about measurement uncertainty (and the method used for calculating the uncertainty) as well as the uncertainty at LOQ are not provided by default, unless this is requested by the customer. 

Eor substances that are not yet defined as priority substances and for which EQS are not finalised, these performance targets cannot be applied. However, the knowledge of the measurement uncertainty and the limit of quantification in relation to predefined targets is important for judging the fitness for purpose of the data (for analysis of trends, comparison of data sets, classification of water bodies for the achievement of good ecological status, for example). 

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