Objectives 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. 

Lack of representativeness at the step of collecting a sample from an examined material object Uncertainties associated with the applied standards and/or reference materials... 

Introduction and Commercial Application JUe objective of performing appraisal activities on discovered accumulations is to reduce the uncertainty in the description of the hydrocarbon reservoir, and to provide information with which to make a decision on the next action. The next action may be, for example, to undertake more appraisal, to commence development, to stop activities, or to sell the prospect. In any case, the appraisal activity should lead to a decision which yields a greater value than the outcome of a decision made in the absence of the information from the appraisal. The improvement in the value of the action, given the appraisal information, should be greater than the cost of the appraisal activities, otherwise the appraisal effort is not worthwhile. 

The stated objective of appraisal activity is to reduce uncertainty. The impact of appraisal on uncertainty can be shown on an expectation curve, if an outcome is assumed from the appraisal. The following illustrates this process. 

Note that it is not the objective of the appraisal well to find more oil, but to reduce the range of uncertainty in the estimate of STOMP. Well A being dry does not imply that it is an unsuccessful appraisal well. 

Descriptions of Physical Objects, Processes, or Abstract Concepts. Eor example, pumps can be described as devices that move fluids. They have input and output ports, need a source of energy, and may have mechanical components such as impellers or pistons. Similarly, the process of flow can be described as a coherent movement of a Hquid, gas, or coUections of soHd particles. Flow is characterized by direction and rate of movement (flow rate). An example of an abstract concept is chemical reaction, which can be described in terms of reactants and conditions. Descriptions such as these can be viewed as stmctured coUections of atomic facts about some common entity. In cases where the descriptions are known to be partial or incomplete, the representation scheme has to be able to express the associated uncertainty. 

Relationships Between Objects, Processes, and Events. Relationships can be causal, eg, if there is water in the reactor feed, then an explosion can take place. Relationships can also be stmctural, eg, a distiUation tower is a vessel containing trays that have sieves in them or relationships can be taxonomic, eg, a boiler is a type of heat exchanger. Knowledge in the form of relationships connects facts and descriptions that are already represented in some way in a system. Relational knowledge is also subject to uncertainty, especiaUy in the case of causal relationships. The representation scheme has to be able to express this uncertainty in some way. 

Accuracy of Pyrometers Most of the temperature estimation methods for pyrometers assume that the objec t is either a grey body or has known emissivity values. The emissivity of the nonblack body depends on the internal state or the surface geometry of the objects. Also, the medium through which the therm radiation passes is not always transparent. These inherent uncertainties of the emissivity values make the accurate estimation of the temperature of the target objects difficult. Proper selection of the pyrometer and accurate emissivity values can provide a high level of accuracy. 

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. 

The level of effort required for a frequency analysis is a function of the complexity of the system or process being analyzed and the level of detail required to meet the analysis objectives. Frequency analysis can typically require 25% to 50% of the total effort in a large-scale QRA study. If an uncertainty analysis is performed, the effort required for the frequency analysis can be much greater. 

The work required to evaluate risk results will be a function of the objectives of the study. For relative risk studies, this evaluation is usually not very time-consuming. For absolute risk studies, in which many uncertainty and sensitivity cases may have been produced, the risk evaluation step may account for to 35% of the total effort of a large-scale QRA. Chapter 4 discusses the problems associated with interpreting risk results. 

The. statement goes on to acknowledge the contribution of the Reactor Safety Study (WASH-1400) to risk quantification but points out that safety goals were not the study objectives and that the uncertainties make it unsuitable for such a purpose. After pointing out that the death I f any individual is not "acceptable," it states two quantitative objectives ... 

The assembly process (Figure 10-1) brings together all of the assessment tasks to provide the risk, its significance, how it was found, its sensitivity to uncertainties, confidence limits, and how it may be reduced by system improvements. Not all PSAs use fault trees and event trees. This is especially true of chemical PSAs that may rely on HAZOP or FMEA/FMECAs. Nevertheless the objectives are the same accident identification, analysis and evaluation. Figure 10-1 assumes fault tree and event tree techniques which should be replaced by the equivalent methods that are used. 

Radiation effects from a flash fire are now fully determined if vapor cloud composition, as well as the geometry of the flame front (dependent on time), is known. Vapor cloud composition is, of course, place- and time-dependent, and the shape of flame front will greatly depend on cloud shape and ignition site within the cloud. The total radiation intercepted by an object equals the surmnation of contributions by all successive flame positions during flame propagation. This is an impossible value to compute with the simplified approach just described. Because there are many uncertainties (e.g., cloud composition, location of ignition site) which greatly influence the final result, a conservative approach is recommended for practical applications ... 

No matter what the objectives and operations are, neither the functioning of an operation nor the choice of objectives is always decisively perfect at the start. There are situations in which uncertainty and lack of information are factors to reckon with. Sometimes it is necessary to make extrapolations and predictions without being able to study the actual environment of the operation. 

The uncertainty principle has negligible practical consequences for macroscopic objects, but it is of profound importance for subatomic particles such as the electrons in atoms and for a scientific understanding of the nature of the world. 

STRATEGY We expect the uncertainty in the position of an object as heavy as a marble to be very small but the uncertainty in the speed of an electron, which has a very small mass and is confined to a small region, to be very large, (a) The uncertainty Ap is equal to mAv, where Av is the uncertainty in the speed we use Eq. 8 to estimate the minimum uncertainty in position, Ax, along the direction of the travel of the marble from ApAx = fi (the minimum value of the product of uncertainties), (b) We assume Ax to be the diameter of the atom and use Eq. 8 to estimate Ap by using the mass of the electron inside the back cover, we find Av from Ap = mAv. ... 

The uncertainty principle is negligible for macroscopic objects. Electronic devices, however, are being manufactured on a smaller and smaller scale, and the properties of nanoparticles, particles with sizes that range from a few to several hundred nanometers, may be different from those of larger particles as a result of quantum mechanical phenomena, (a) Calculate the minimum uncertainty in the speed of an electron confined in a nanoparticle of diameter 200. nm and compare that uncertainty with the uncertainty in speed of an electron confined to a wire of length 1.00 mm. (b) Calculate the minimum uncertainty in the speed of a I.i+ ion confined in a nanoparticle that has a diameter of 200. nm and is composed of a lithium compound through which the lithium ions can move at elevated temperatures (ionic conductor), (c) Which could be measured more accurately in a nanoparticle, the speed of an electron or the speed of a Li+ ion ... 

By making use of the spatial information, the velocity field of an extended, structured object can be obtained unambiguously without errors caused by uncertainty in the position of a feature within the slit. 

This paper discusses the role that statistics can play In environmental sampling. The primary difference between an Investigation based on statistical considerations and one that Is not Is the degree of objectivity that can be Incorporated Into the evaluation of the quality and uncertainty of the study results. Statistical methods In the planning stage can also aid In optimizing allocation of resources. 

Uncertainties in amounts of products to be manufactured Qi, processing times %, and size factors Sij will influence the production time tp, whose uncertainty reflects the individual uncertainties that can be presented as probability distributions. The distributions for shortterm uncertainties (processing times and size factors) can be evaluated based on knowledge of probability distributions for the uncertain parameters, i.e. kinetic parameters and other variables used for the design of equipment units. The probability of not being able to meet the total demand is the probability that the production time is larger than the available production time H. Hence, the objective function used for deterministic design takes the form ... 

In essence, the earlier components of this overall assessment process are mainly deterministic in character (albeit with some probabilistic elements), whereas the later stages are mainly probabilistic. Not all elements of the process are quantifiable (with any degree of confidence), however and the socicii-political-cultural context of any downstream decision-making process may be intensely uncertain. Such uncertainties make the process of risk communication and debate a complex and sometimes unpredictable undertaking. It is essential therefore that those elements of the risk management process that cein be objectively einalysed and evaluated (either qualitatively or quantitatively, as appropriate) are so assessed. 

At this point is worthwhile commenting on the computer standard estimation errors of the parameters also shown in Table 16.24. As seen in the last four estimation runs we are at the minimum of the LS objective function. The parameter estimates in the run where we optimized four only parameters (K2, kt, K k3) have the smallest standard error of estimate. This is due to the fact that in the computation of the standard errors, it is assumed that all other parameters are known precisely. In all subsequent runs by introducing additional parameters the overall uncertainty increases and as a result the standard error of all the parameters increases too. 

With the revised zonation the LS objective function was reduced to 0.00392. The final match is shown in Figures 18.26 and 18.27. The estimated parameters and their standard deviation are shown in Table 18.5. As seen, the estimated permeability for layer 7 has the lowest standard error. This is simply due to the fact that the well is completed in layers 7 and 8. It is interesting to note that contrary to expectation, the estimated permeability corresponding to layer 5 has a higher uncertainty compared to zones even further away from it. The true permeability of layer 5 is low and most likely its effects have been missed in the timing of the 16 observations taken. 

It is reasonable to assume that the most probable values of the parameters have normal distributions with means equal to the values that were obtained from well test and core data analyses. These are the prior estimates. Each one of these most probable parameter values (kBj, j=l,...,p) also has a corresponding standard deviation parameter estimate. As already discussed in Chapter 8 (Section 8.5) using maximum likelihood arguments the prior information is introduced by augmenting the LS objective function to include... 

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