Uncertainty specification

Handling of uncertainties is another important area that requires careful thinking. Measurements without uncertainty considerations lose most of their utility, and if a format does not provide a mechanism for their lossless capture, its usage is problematic. Some languages have an element or attribute for a basic uncertainty specification, but ThermoML is the only language that deals with uncertainty seriously. 

The uncertainties through the product life cycle begin from the design intent to the inspection activity. In the ISO TS 17450 Part 2 (Humienny 2009), the notion of the uncertainty is generalized to the specification and the verification. The transition between the functional requirements and their inspection is ensured by some models and tools. The total uncertainty of this transition is divided into correlation uncertainty, specification uncertainty, and measurement uncertainty. Correlation uncertainty characterizes the fact that the intended functionality and the controlled characteristics may not be perfectly correlated. The specification uncertainty characterizes the ambiguity in the specification expression. And the measurement uncertainty is however the best known type of uncertainties. It is considered by the metrologists and well described in GUM. 

Only uncertainties specific to the event and required period of service should be used. The use of different uncertainty components for the same segment may be appropriate for different events. 

In this section, we look at how the temporary organization operates (particularly collectively) and we aim at highlighting the characteristics that make it different from the permanent organization, in order to understand the risks and uncertainties specific to this type of structure. 

One feature of this inequality warrants special attention. In the previous paragraph it was shown that the precise measurement of A made possible when v is an eigenfiinction of A necessarily results in some uncertainty in a simultaneous measurement of B when the operators /land fido not conmuite. However, the mathematical statement of the uncertainty principle tells us that measurement of B is in fact completely uncertain one can say nothing at all about B apart from the fact that any and all values of B are equally probable A specific example is provided by associating A and B with the position and momentum of a particle moving along the v-axis. It is rather easy to demonstrate that [p, x]=- ih, so that If... 

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. 

Although a torsion test is simple to carry out, it is not commonly accepted as an integral part of a material specification furthermore, few torsion data exist in handbooks. If, as is usually the case, the design needs to be based on tensile data, then a criterion of elastic failure has to be invoked, and this introduces some uncertainty in the calculated yield pressure (8). 

Because they are weak acids or bases, the iadicators may affect the pH of the sample, especially ia the case of a poorly buffered solution. Variations in the ionic strength or solvent composition, or both, also can produce large uncertainties in pH measurements, presumably caused by changes in the equihbria of the indicator species. Specific chemical reactions also may occur between solutes in the sample and the indicator species to produce appreciable pH errors. Examples of such interferences include binding of the indicator forms by proteins and colloidal substances and direct reaction with sample components, eg, oxidising agents and heavy-metal ions. 

Scale-Up Principles. Key factors affecting scale-up of reactor performance are nature of reaction zones, specific reaction rates, and mass- and heat-transport rates to and from reaction sites. Where considerable uncertainties exist or large quantities of products are needed for market evaluations, intermediate-sized demonstration units between pilot and industrial plants are usehil. Matching overall fluid flow characteristics within the reactor might determine the operative criteria. Ideally, the smaller reactor acts as a volume segment of the larger one. Elow distributions are not markedly influenced by... 

The summation term is the mass broken into size interval / from all size intervals between j and /, and S is the mass broken from size internal i. Thus for a given feed material the product size distribution after a given time in a mill may be deterrnined. In practice however, both S and b are dependent on particle size, material, and the machine utilized. It is also expected that specific rate of breakage should decrease with decreasing particle size, and this is found to be tme. Such an approach has been shown to give reasonably accurate predictions when all conditions are known however, in practical appHcations severe limitations are met owing to inadequate data and scale-up uncertainties. Hence it is stiH the usual practice to carry out tests on equipment to be sure of predictions. 

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. 

The certainty factor approach has been among the more popular rule-based approaches to uncertainty. However, although it is easy to apply given the individual CFs, acquiring the raw CFs from the experts is often quite difficult. Further, although the formulas for CF combination are mathematically appealing, they often have no relation to the ways in which experts combine evidence to arrive at conclusions. Some of the task-specific approaches discussed later address uncertainty combination in a more intuitive way (35). 

Calvert et al. []. Air Pollut. Control Assoc., 22, 529 (1972)] obtained an explicit equation by making some simplifying assumptions and incorporating an empirical constant that must be evaluated experimentally the constant may absorb some of the deficiencies in the model. Although other models avoid direct incorporation of empirical constants, use of empirical relationships is necessary to obtain specific-estimates of scrubber collec tion efficiency. One of the areas of greatest uncertainty is the estimation of droplet size. 

QRA is fundamentally different from many other chemical engineering activities (e.g., chemistry, heat transfer, reaction kinetics) whose basic property data are theoretically deterministic. For example, the physical properties of a substance for a specific application can often be established experimentally. But some of the basic property data used to calculate risk estimates are probabilistic variables with no fixed values. Some of the key elements of risk, such as the statistically expected frequency of an accident and the statistically expected consequences of exposure to a toxic gas, must be determined using these probabilistic variables. QRA is an approach for estimating the risk of chemical operations using the probabilistic information. And it is a fundamentally different approach from those used in many other engineering activities because interpreting the results of a QRA requires an increased sensitivity to uncertainties that arise primarily from the probabilistic character of the data. 

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. 

If there is a lack of specific, appropriate data for a process facility, there can be considerable uncertainty in a frequency estimate like the one above. When study objectives require absolute risk estimates, it is customary for engineers to want to express their lack of confidence in an estimate by reporting a range estimate (e.g., 90% confidence limits of 8 X 10 per year to 1 X 10 per year) rather than a single-point estimate (e.g., 2 X 10per year). For this reason alone it may be necessary for you to require that an uncertainty analysis be performed. 

Both individual and societal risks may be presented on an absolute basis compared to a specific risk target or criterion. Or, they may be presented on a relative basis to avoid arguments regarding the adequacy of the absolute numbers while preserving the salient differences between alternatives. The end results of the risk presentation may be a single number (or a range of numbers if an uncertainty analysis was performed) or one or more graphs. 

AccuracyAJncertainty The lack of specific data on component failure characteristics, chemical and physical properties, and phenomena severely limit accuracy and can produce large uncertainties. 

The nuclear equipment failure rate database has not changed markedly since the RSS and chemical process data contains information for non-chemical process equipment in a more benign environment. Uncertainty in the database results from the statistical sample, heterogeneity, incompleteness, and unrepresentative environment, operation, and maintenance. Some PSA.s use extensive studies of plant-specific data to augment the generic database by Bayesian methods and others do not. No standard guidance is available for when to use which and the improvement in accuracy that is achieved thereby. Improvements in the database and in the treatment of data requires, uhstaiui.il indu.sinal support but it is expensive. 

Specific measuring range The range of concentration values for w hich the overall uncertainty of a measurement procedure is intended to lie within specific limits. 

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