Type A uncertainties

Note that the categories relate only to how the estimate was obtained, and not to whether the uncertainty is due to a random or a systematic effect. Type A uncertainty estimates are, by definition, expressed as a standard deviation. Type B uncertainty estimates can take a number of different forms, and may need to be converted to a standard uncertainty prior to combination with other uncertainty estimates. This is discussed later in this section. 

Hoffman and Hammonds (1994) Type A uncertainty Type B uncertainty Uncertainty... 

Aleatory uncertainty The kind of uncertainty resulting from randomness or unpredictability due to stochasticity. Aleatory uncertainty is also known as variability, stochastic uncertainty. Type I or Type A uncertainty, irreducible uncertainty, conflict, and objective uncertainty. 

Knowing which factors contribute to the overall variability it should be possible to improve the analytical methodology. The whole error (first condition) is composed of the systematic error (or bias), unspecified random errors, and a series of errors produced during chemical or physical analyses. Uncertainty, also expressed as standard deviation (type A uncertainty), is a concept for measuring the quality of the analytical procedures (Taylor and Kuyaat, 1994). 

Type A uncertainties (cr ), determined by the counting statistics, and type B uncertainties, based on a scientific judgment are clearly distinguished. Type B uncertainty (cr ) takes into account the uncertainty on the activity of the calibration sources certificates and the uncertainty on the volumetry employed during the preparation of solutions (5.55 %). The total relative uncertainty cr ) spread to 2a (in %) of the activity in Sr is defined in the following general form ... 

In the theory on uncertainty, a distinction between type A and B uncertainties is made. Type A uncertainties are frequency-based estimates of standard deviations (e.g, an SD of the imprecision). Type B uncertainties are uncertainty components for which frequency-based SDs are not available. Instead, the uncertainty is estimated by other approaches or by the opinion of experts. Finally the total uncertainty is derived from a combination of all sources of uncertainty. In this context, it is practical to operate with standard uncertainties (w t), which are equivalent to standard deviations. By multiplication of a standard uncertainty with a coverage factor (k), the uncertainty corresponding to a specified probability level is derived. For example, multiplication with a coverage factor of two yields a probability level of 95% given a normal distribution. When considering the total uncertainty of an analytical result obtained by a routine method, the preanalytical variation, method imprecision, random matrix-related interferences, and uncertainty related to calibration and bias corrections (traceability) should be taken into account. Expressing the uncertainty components as standard uncertainties, we have the general relation ... 

Type A uncertainty is obtained by a set of observed frequency distribution probability density function that is exported Type B uncertainty... 

As in all analytical determinations, the potential for uncertainties affecting results of a testing laboratory from sources outside the laboratory and outside the applied method must be understood and may not be underestimated (Iyengar 1981 Zeisler 1986). According to the ISO terminology, the uncertainties can be divided into Type A (uncertainties evaluated by statistical methods) and Type B (all other). The Type A terms are dependent mostly on the amount and the reaction cross section of the analyte. In the context of this chapter, only the method-specific sources of uncertainty will be treated, with the main emphasis on NAA. 

As is the case in all measurements, the uncertainties from NDP can be divided into Type A (statistical) and Type B (all other). The Type A terms are dependent mostly on the concentration and the neutron cross section of the analyte. While the statistical precision can always be improved by increasing the irradiation time, there are some practical limits. Beam time is in high demand and rarely more than a day can be devoted to a single sample, with 1 h being more typical. There is always some background present and the background subtraction increases the statistical uncertainty. For typical samples of boron in semiconductor materials, the Type A uncertainty is usually about 1% at l[Pg.1611]

However, a new distinction has arisen - Type A and Type B uncertainties. Type A uncertainties are defined as those that have been determined by repeated measurements to assess the magnitude and distribution of the parameter. Type B uncertainties are those whose magnitude has been derived in any other manner. For example, the uncertainty on gamma-ray emission probability is... 

The user can find suitable materials in a number of different ways. For instance any of the above measurands can be chosen and a search made within a specific matrix type. A list of the measurand values in all materials of the selected matrix classification sorted by decreasing concentration will be produced, including the uncertainties in percent, the certification status and the material identification code. Other search methods are possible, selection by material gives a table with values of all measurands in the chosen material in alphabetical order and additional information about the price, the unit size, the issuing date, the supphers and the exact material name. A further option is to list all materials from a producer. 

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

Semantic uncertainty is the type of uncertainty for which we shall need fuzzy logic. Expressed by phrases such as "acidic" or "much weaker," this is imprecision in the description of an event, state, or object rather than its measurement. Fuzzy logic offers a way to make credible deductions from uncertain statements. We shall illustrate this with a simple example. 

Also under the IPCS harmonization project, a working group is preparing a harmonized set of principles for the treatment of uncertainty in exposure assessment. The document will review the types of uncertainty analyses used in exposure assessments, evaluate their effectiveness in giving decision-makers the types of information they need, and derive a set of principles for uncertainty analysis (WHO/IPCS 2006). 

Type A evaluation (of uncertainty) Method of evaluation of uncertainty by the statistical analysis of series of observations. 

Uncertainties from some sources may be quantified by doing experiments. From the results of repeated measurements we get a standard deviation which we can use directly as an estimate for the standard uncertainty. This is called type A evaluation of uncertainties. 

A probabilistic risk assessment (PRA) deals with many types of uncertainties. In addition to the uncertainties associated with the model itself and model input, there is also the meta-uncertainty about whether the entire PRA process has been performed properly. Employment of sophisticated mathematical and statistical methods may easily convey the false impression of accuracy, especially when numerical results are presented with a high number of significant figures. But those who produce PR As, and those who evaluate them, should exert caution there are many possible pitfalls, traps, and potential swindles that can arise. Because of the potential for generating seemingly correct results that are far from the intended model of reality, it is imperative that the PRA practitioner carefully evaluates not only model input data but also the assumptions used in the PRA, the model itself, and the calculations inherent within the model. This chapter presents information on performing PRA in a manner that will minimize the introduction of errors associated with the PRA process. 

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. 

There are several terms used in measurement uncertainty that must be defined. An uncertainty arising from a particular source, expressed as a standard deviation, is known as the standard measurement uncertainty (u). When several of these are combined to give an overall uncertainty for a particular measurement result, the uncertainty is known as the combined standard measurement uncertainty (uc), and when this figure is multiplied by a coverage factor ( ) to give an interval containing a specified fraction of the distribution attributable to the measurand (e.g., 95%) it is called an expanded measurement uncertainty [U). I discuss these types of uncertainties later in the chapter. 

Specifying the measurand implies that the measurement method and relevant equations are specified. This provides a template for examining sources of Type uncertainties. For example, a simple titration from which the concentration of an acid is to be measured by the formula... 

Note that repeatability precision (r) is included in the equation for the measurand with a nominal value of 1 and standard uncertainty the Type A standard deviation from repeated measurements. 

There is a problem when some components of the combined standard uncertainty are assessed from measurements or estimates with finite degrees of freedom. A type A estimate from a standard deviation of n repeated measurements has n - 1 degrees of freedom. Usually Type estimates will be based on data that have essentially infinite degrees of freedom, but if the standard uncertainty is open to doubt, the effective degrees of freedom can be determined from... 

Measurement uncertainty Type A effects [repeatability and reproducibility precision] Type effects... 

Values of K0 estimated in this way for several nonpolar molecules in type-A zeolite and in chabazite are compared with experimental data in Table I. For most of the hydrocarbons in both zeolites the predicted and experimental values agree to within about 35%. The accuracy with which the experimental values of K0 are known is not high since these values are calculated from the intercepts of plots of In K vs. l/T. A variation in K0 of 35% corresponds only to an error of about 0.25 kcal/mole in the value of qo, and this is of the same order as the experimental uncertainty. 

Table III presents the rotational analysis for compounds 3-7, in the three staggered orientations for the hydroxymethyl side chain to give conformers of types a, b, and c. The ranges in rotation expected for certain conformations results from the above-mentioned uncertainty in the value for OH/Or (exo).

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