Specification of uncertainty

Currently, there are inconsistencies in the application and methodology for uncertainty analysis in exposure assessment. While several sophisticated quantitative techniques exist, their general application is hampered not only by their complexity (and resulting need for considerable supporting information) but also by the lack of methodology to facilitate the specification of uncertainty sources prior to the quantification of their specific weight. 

Data, expert judgement or both should be used to inform the specification of uncertainties for ... 

The comparison makes use of generic specifications of uncertainties for tank-gauging equipment, storage tanks, and installation. The data used are assumed to be manufacturer independent. 

The degree of uncertainty of 10 per cent or more, inseparable from estimates of specific surface from adsorption isotherms, even those of nitrogen, may seem disappointing. In fact, however, attainment of this level of accuracy is a notable achievement in a field where, prior to the development of the BET method, even the order of magnitude of the specific surface of highly disperse solids was in doubt. The adsorption method still provides the only means of determining the specific surface of a mass of non-... 

Effect of Uncertainties in Thermal Design Parameters. The parameters that are used ia the basic siting calculations of a heat exchanger iaclude heat-transfer coefficients tube dimensions, eg, tube diameter and wall thickness and physical properties, eg, thermal conductivity, density, viscosity, and specific heat. Nominal or mean values of these parameters are used ia the basic siting calculations. In reaUty, there are uncertainties ia these nominal values. For example, heat-transfer correlations from which one computes convective heat-transfer coefficients have data spreads around the mean values. Because heat-transfer tubes caimot be produced ia precise dimensions, tube wall thickness varies over a range of the mean value. In addition, the thermal conductivity of tube wall material cannot be measured exactiy, a dding to the uncertainty ia the design and performance calculations. 

The problem is defined during process development as information becomes available and decisions are made. Initially, the definition is limited, vague, and brief and economic analysis involves a high level of uncertainty. As the project evolves, the definition becomes more complete, more highly specific, and lengthier. At the same time, the economic assessment tends to exhibit less uncertainty. 

There are a variety of ways to express absolute QRA results. Absolute frequency results are estimates of the statistical likelihood of an accident occurring. Table 3 contains examples of typical statements of absolute frequency estimates. These estimates for complex system failures are usually synthesized using basic equipment failure and operator error data. Depending upon the availability, specificity, and quality of failure data, the estimates may have considerable statistical uncertainty (e.g., factors of 10 or more because of uncertainties in the input data alone). When reporting single-point estimates or best estimates of the expected frequency of rare events (i.e., events not expected to occur within the operating life of a plant), analysts sometimes provide a measure of the sensitivity of the results arising from data uncertainties. 

The RfD is derived from the NOAEL (or LOAEL) for the critical toxic effect by consistent application of uncertainty factors (UFs) and a modifying factor (ME). The uncertainty factors generally consist of multiples of 10 (although values less than 10 are sometimes used), with each factor representing a specific area of uncertainty inherent in the extrapolation from the available data. The bases for application of different uncertainty factors are explained below. 

It is regrettable that the evidence afforded by reaction kinetics is rarely, if ever, uniquely consistent with a single mechanism or a single explanation. The results for nucleophilic aromatic substitution reactions are no exception. Legitimate questions can be raised with respect to the extent to which observations made on a particular system permit generalization to other systems. Even for the specific systems studied points of detail arise, and choices have to be made where alternatives are possible. Every such choice introduces an element of uncertainty and imposes a limitation on the extent to which the reaction mechanism is, in fact, known. 

The considerations presented above were based on the specific assumption that the catalytic reaction of the serine proteases involves mechanism a of Fig. 7.2. However, one can argue that the relevant mechanism is mechanism b (the so-called charge-relay mechanism ). In principle the proper procedure, in case of uncertainty about the actual mechanism, is to perform the calculations for the different alternative mechanisms and to find out which of the calculated activation barriers reproduces the observed one. This procedure, however, can be used with confidence only if the calculations are sufficiently reliable. Fortunately, in many cases one can judge the feasibility of different mechanisms without fully quantitative calculations by a simple conceptual consideration based on the EVB philosophy. To see this point let us consider the feasibility of the charge-relay mechanism (mechanism b) as an alternative to mechanism a. Starting from Fig. 7.2 we note that the energetics of route b can be obtained from the difference between the activation barriers of route b and route a by... 

In general, the result of measurement is only an approximation or estimate of the value of the specific quantity subject to measurement, and thus the result is complete only when accompanied by a quantitative statement of its uncertainty. Because the reliability of evaluations of components of uncertainty depends on the quality of the information available, it is recommended that all parameters upon which the measurand depends be varied to the fullest extent practicable so that the evaluations are based as much as possible on observed data. 

The results of activation analysis are subject to well known and common analytical sources of uncertainty, as well as method specific uncertainties, e.g. summarized by Greenberg (1997), and also in Section 2.2. In order for INAA experiments to measure differences in induced activity, i.e. differences due to heterogeneity in the amount of analyte in a given test portion, the experimental procedure is designed to allow only the following uncertainties to be part of the result ... 

Various compilations of densities for organic compounds have been published. The early Landolt-Bomstein compilation [23-ano] contained recommended values at specific temperatures. International Critical Tables [28-ano-l] provided recommended densities at 0 °C and values of constants for either a second or third order polynomial equation to represent densities as a function of temperature. This compilation also gave the range of validity of the equation and the limits of uncertainty, references used in the evaluation and those not considered. This compilation is one of the most comprehensive ever published. Timmermans [50-tim, 65-tim], Dreisbach [55-die, 59-die, 61-dre] and Landolt-Bomstein [71-ano] published additional compilations, primarily of experimental data. These compilations contained experimental data along with reference sources but no estimates of uncertainty for the data nor recommended values. 

The feed composition and flowrate to the distillation are usually specified. Also, the specifications of the products are usually known, although there may be some uncertainty in product specifications. The product specifications may be expressed in terms of product purities or recoveries of certain components. The operating parameters to be selected by the designer include ... 

The implications of the analysis have to be considered before taking the sample or devising a sampling scheme. It is the responsibility of the analytical chemist, through discussion with the customer, to establish the real nature of the problem. How much cadmium is there in this sample is not sufficiently specific. You must always ask why the information is required. The answer affects both the sampling plan and the choice of analytical method. These will depend on the acceptable level of uncertainty in the final result. 

The errors that are solely attributed to sampling, specifically in the instance of heterogeneous solids, usually give rise to the most important source of uncertainty in carrying out analysis of pharmaceutical substances. 

F. D. Rossini, W. E. Deming. The Assignment of Uncertainties to the Data of Chemistry and Physics, with Specific Recommendations for Thermochemistry. J. Wash. Acad. Sci. 1939, 29, 416-441. 

With an appropriate specification of the system performance weighting and objective function, a generalized plant dynamics is established, as shown in Fig. 22.2. The feedback controller processes the measured signal y to determine the injection rate of the control fuel rhin based on a regulated relationship between variables w and z, where w is associated with disturbance and uncertainty, and 2 with the objectives of system performance and stability. 

The specific long-term environmental effects of increased trace element loading of the atmosphere continue to be difficult to assess. Specific areas of uncertainty requiring further investigation include the following 1) the mechanisms of particle formation and dispersion in the environment, 2) the chemical transformations and reactivity of the particles in various environmental compartments, 3) the physicochemical characteristics of individual particles, and 4) the specific interactions of the particles with living organisms (11). 

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