Intended model

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. 

First, the scope for the use of RBRK models in a particular risk assessment has to be clearly identified since it essentially determines the intended model complexity, model capability, and Ihe extent of model evaluation. Here, the goal is really to specify the purpose for which the RBRK model would be used in a cancer risk... 

Only when sufficient understanding of the system has been achieved can we develop the conceptual model which represents our understanding of the features and processes of interest. It is an abstraction of reality which need only include those relationships needed to describe the system for the intended model application. Ideally, the relationships are stated in terms of testable hypotheses. For performance assessment, the relationships of the conceptual model are represented quantitatively in a calculational model. The calculational model may be as simple as a closed-form analytic solution or so complex that only computer solutions are possible. 

Shapiro s idea has also been picked up by [Drabent et al 88] they define four kinds of assertions that may be added to a specification by examples. These assertions describe approximate knowledge about the intended model of the specified program. These assertions are used for partly mechanizing the oracle of Shapiro s MIS. They constitute a possible instantiation of our notion of properties. 

Several thousand, spatially homogeneous simulations are carried out with a series of initial concentrations and/or temperatures, which are typical for the circumstances of applications of the final intended model. 

The newest model of the INTROS, MDK-21 is intended to inspect round ropes of 6.. .64 mm. in diameter as like as flat ropes up to 233 mm width and 38 mm thickness. 

At the start of the development, it had been intended use an expert system shell to implement this tool, however, after careful consideration, it was concluded that this was not the optimum strategy. An examination procedure can be considered as consisting of two parts fixed documentary information and variable parameters. For the fixed documentary information, a hypertext-like browser can be incorporated to provide point-and-click navigation through the standard. For the variable parameters, such as probe scanning paths, the decisions involved are too complex to be easily specified in a set of rules. Therefore a software module was developed to perfonn calculations on 3D geometric models, created fi om templates scaled by the user. 

Finally, the standard draft provides a detailed model of the acquisition data, which intends to describe all the possible shapes which can be taken by NDE data OD (scalar or complex), ID (sampled - cf ultrasonics A-scans - or unsampled - ef ultrasonics time/amplitude data), 2D (images) or 3D (volumes). 

In this section, we intend to show that for a certain type of models the above imposed restrictions become the ordinary well-known Bohr-Sommerfeld quantization conditions [82]. For this purpose, we consider the following non-adiabatic coupling matrix x ... 

D descriptors), the 3D structure, or the molecular surface (3D descriptors) of a structure. Which kind of descriptors should or can be used is primarily dependent on the si2e of the data set to be studied and the required accuracy for example, if a QSPR model is intended to be used for hundreds of thousands of compounds, a somehow reduced accuracy will probably be acceptable for the benefit of short processing times. Chapter 8 gives a detailed introduction to the calculation methods for molecular descriptors. 

We envision a potential energy surface with minima near the equilibrium positions of the atoms comprising the molecule. The MM model is intended to mimic the many-dimensional potential energy surface of real polyatomic molecules. (MM is little used for very small molecules like diatomies.) Once the potential energy surface iias been established for an MM model by specifying the force constants for all forces operative within the molecule, the calculation can proceed. 

This Introductory Section was intended to provide the reader with an overview of the structure of quantum mechanics and to illustrate its application to several exactly solvable model problems. The model problems analyzed play especially important roles in chemistry because they form the basis upon which more sophisticated descriptions of the electronic structure and rotational-vibrational motions of molecules are built. The variational method and perturbation theory constitute the tools needed to make use of solutions of... 

Computational chemistry is used in a number of different ways. One particularly important way is to model a molecular system prior to synthesizing that molecule in the laboratory. Although computational models may not be perfect, they are often good enough to rule out 90% of possible compounds as being unsuitable for their intended use. This is very useful information because syn-... 

It is sometimes desirable to include the effect of the rest of the system, outside of the QM and MM regions. One way to do this is using periodic boundary conditions, as is done in liquid-state simulations. Some researchers have defined a potential that is intended to reproduce the effect of the bulk solvent. This solvent potential may be defined just for this type of calculation, or it may be a continuum solvation model as described in the next chapter. For solids, a set of point charges, called a Madelung potential, is often used. 

SpartanView models are intended to give you a molecule s eye view of chemi cal processes and to help you solve certain text problems The text uses the following icon to alert you to corresponding models on the CD... 

The model describing interaction between two bodies, one of which is a deformed solid and the other is a rigid one, we call a contact problem. After the deformation, the rigid body (called also punch or obstacle) remains invariable, and the solid must not penetrate into the punch. Meanwhile, it is assumed that the contact area (i.e. the set where the boundary of the deformed solid coincides with the obstacle surface) is unknown a priori. This condition is physically acceptable and is called a nonpenetration condition. We intend to give a mathematical description of nonpenetration conditions to diversified models of solids for contact and crack problems. Indeed, as one will see, the nonpenetration of crack surfaces is similar to contact problems. In this subsection, the contact problems for two-dimensional problems characterizing constraints imposed inside a domain are considered. 

This recommended practice is intended to apply to faciUties that (/) handle or store flammable or explosive substances in such a manner that a release of ca 5 t of gas or vapor could occur in a few minutes and (2) handle toxic substances. The threshold quantity for the toxic materials would be determined using engineering judgment and dispersion modeling, based on a potential for serious danger as a result of exposures of <1 h. 

Pesticide Runoff Modeling. Obtaining the field data necessary to understand the potential mnoff of pesticides under a variety of conditions and sods would be an expensive and time-consuming process. As a result, a variety of simulation models that vary in their conceptual approach and degree of complexity have been developed. Models are influenced by their intended purpose, the biases of the developer, and the scale at which they are used. 

Erythrocyte Entrapment of Enzymes. Erythrocytes have been used as carriers for therapeutic enzymes in the treatment of inborn errors (249). Exogenous enzymes encapsulated in erythrocytes may be useful both for dehvery of a given enzyme to the site of its intended function and for the degradation of pathologically elevated, diffusible substances in the plasma. In the use of this approach, it is important to determine that the enzyme is completely internalized without adsorption to the erythrocyte membrane. Since exposed protein on the erythrocyte surface may ehcit an immune response following repeated sensitization with enzyme loaded erythrocytes, an immunologic assessment of each potential system in animal models is required prior to human trials (250). 

Limited Data First, plant data are limited. Unfortunately, those easiest to obtain are not necessarily the most useful. In many cases, the measurements that are absolutely required for accurate model development are unavailable. For those that are available, the sensitivity of the parameter estimate, model evaluation, and/or subsequent conclusion to a particiilar measurement may be very low. Design or control engineers seldom look at model development as the primaiy reason for placing sensors. Further, because equipment is frequently not operated in the intended region, the sensitive locations in space and time have shifted. Finally, because the cost-effectiveness of measurements can be difficult to justify, many plants are underinstru-mented. 

Systematic Operating Errors Fifth, systematic operating errors may be unknown at the time of measurements. Wriile not intended as part of daily operations, leaky or open valves frequently result in bypasses, leaks, and alternative feeds that will add hidden bias. Consequently, constraints assumed to hold and used to reconcile the data, identify systematic errors, estimate parameters, and build models are in error. The constraint bias propagates to the resultant models. 

Because the technical barriers previously outhned increase uncertainty in the data, plant-performance analysts must approach the data analysis with an unprejudiced eye. Significant technical judgment is required to evaluate each measurement and its uncertainty with respec t to the intended purpose, the model development, and the conclusions. If there is any bias on the analysts part, it is likely that this bias will be built into the subsequent model and parameter estimates. Since engineers rely upon the model to extrapolate from current operation, the bias can be amplified and lead to decisions that are inaccurate, unwarranted, and potentially dangerous. 

Intended Use The intended use of the model sets the sophistication required. Relational models are adequate for control within narrow bands of setpoints. Physical models are reqiiired for fault detection and design. Even when relational models are used, they are frequently developed bv repeated simulations using physical models. Further, artificial neural-network models used in analysis of plant performance including gross error detection are in their infancy. Readers are referred to the work of Himmelblau for these developments. [For example, see Terry and Himmelblau (1993) cited in the reference list.] Process simulators are in wide use and readily available to engineers. Consequently, the emphasis of this section is to develop a pre-liminaiy physical model representing the unit. 

Once the model parameters have been estimated, analysts should perform a sensitivity analysis to establish the uniqueness of the parameters and the model. Figure 30-9 presents a procedure for performing this sensitivity analysis. If the model will ultimately be used for exploration of other operating conditions, analysts should use the results of the sensitivity analysis to estabhsh the error in extrapolation that will result from database/model interactions, database uncertainties, plant fluctuations, and alternative models. These sensitivity analyses and subsequent extrapolations will assist analysts in determining whether the results of the unit test will lead to results suitable for the intended purpose. 

Fault detection is a monitoring procedure intended to identify deteriorating unit performance. The unit can be monitored by focusing on values of important unit measurements or on values of model parameters. Step changes or drift in these values are used to identify that a fault (deteriorated performance in unit functioning or effectiveness) has occurred in the unit. Fault detection should be an ongoing procedure for unit monitoring. However, it is also used to compare performance from one formal unit test to another. 

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