Uncertainty concept

In case of correlated parameters, the corresponding covariances have to be considered. For example, correlated quantities occur in regression and calibration (for the difference between them see Chap. 6), where the coefficients of the linear model y = a + b x show a negative mutual dependence. 

Traditionally, analytical chemists and physicists have treated uncertainties of measurements in slightly different ways. Whereas chemists have oriented towards classical error theory and used their statistics (Kaiser [ 1936] Kaiser and Specker [1956]), physicists commonly use empirical uncertainties (from knowledge and experience) which are consequently added according to the law of error propagation. Both ways are combined in the modern uncertainty concept. Uncertainty of measurement is defined as Parameter, associated with the result of a measurement that characterizes the dispersion of the values that could reasonably be attributed to the measurand (ISO 3534-1 [1993] EURACHEM [1995]). 

Such a parameter may be, e.g., standard deviation, or a given multiple of it, or a one-sided confidence interval attributed to a fixed level of confidence. In general, uncertainty of measurement comprises many components. These uncertainty components are subdivided into 

Occasionally, both these uncertainty components are denoted (i) as type A - and (ii) as type B uncertainties. 

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]). 

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The significance of the uncertainty concept in analytical chemistry has increased in the last century, notwithstanding that at first some conformity was missed. But inconsistencies have been dispelled (see Thompson [1995] AMC [1995]) and operational approaches have been presented by Hund et al. [2001]. Numerous examples of application have been given in EURACHEM [1995]. 

The uncertainty concept is composed of both chemists and physicists approaches of handling of random deviations and substitutes so classical error theories in an advantageous way. 

This model of course makes a lot of assumptions and there are quite a few problems. It is not possible to have appropriate reference standards for all possible chemical measurements, very often there are no common links (i.e. reference to a common basis, which is ideally the SI), laboratories do not always use the standards in an appropriate way and very often the uncertainty concept is not used at all ... 

Section 5.4 of the ISO/IEC standard 17025 (ISO/IEC 2005) requires Testing laboratories shall have and shall apply a procedure to estimate the uncertainty of measurement, and in a test report where applicable, a statement on the estimated uncertainty of measurement information on uncertainty is needed in test reports when it is relevant to the validity or application of the test results, when a client s instruction so requires, or when the uncertainty affects compliance to specification limits (ISO/IEC 2005, section 5.10). Although the reporting clause leaves open the possibility of not including the measurement uncertainty of a result, I believe that the added value to the client of a proper measurement uncertainty statement far outweighs any temporary problems that may be caused by unfamiliarity with the measurement uncertainty concept. 

To assess errors associated with laboratory results in a systematic way, the uncertainty concept has been introduced in laboratory medicine. According to the ISO Guide to the Expression of Uncertainty in Measurement ( GUM )> uncer-... 

The uncertainty concept is directed toward the end user (clinician) of the result, who is concerned about the total error possible, and who is not particularly interested in the question whether the errors are systematic or random. In the outiine of the uncertainty concept it is assumed that any known systematic error components of a measurement method have been corrected, and the specified uncertainty includes the uncertainty associated with correction of the systematic error(s). Although this appears logical, a problem may be that some routine methods have systematic errors dependent on the patient category from which the sample originates. For example, kinetic Jaffe methods for creatinine are subject to positive interference by alpha-keto compounds and to negative interference by bilirubin and its metabolites, which means that the direction of systematic error will be patient dependent and not generally predictable. 

Chapter 10 discusses state and parameter identification. Using uncertainty concepts, an optimal estimate of the state for a linear system is obtained based upon available measurements. The result is the Kalman filter. The Kalman filter is extended for nonlinear systems and discrete-time models. Kalman filtering is also shown to be effective for the estimation of model parameters. 

Although human wonder and minds are the sources of uncertainty in forms of vagueness, dubiousness, incompleteness they also serve to overcome problems through human experience, expert views (Chap. 5). The uncertainty concepts in understanding complex problems are dependent on observations, experiences and conscious expert views. When problems are solved, there is always remaining uncertainty that paves the way for future developments. Thus, scientific solutions cannot be taken as absolute truths in positivistic manner. 

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