Deterministic considerations

In the following, both experience data (from the Three Mile Island accident) and deterministic considerations justified by the existing knowledge are shown. At least a picture of the important factors for the decrease of the vessel damage probability and indications on the still necessary research will be obtained. In particular, the importance of the prevention of severe accidents will be clearly demonstrated. 

Based on this consideration, the German nuclear power plants have been designed to withstand the impact of external hazards according to the regulations in effect at the time of their construction (BMU 2007). In general, this design was based on deterministic considerations. 

Use of expert judgement. Deterministic consideration should be given to the total effect on the safe operation of the plant of all unresolved shortcomings and all corrective actions and/or safety improvements and strengths identified in the PSR, to ensure that the overall level of plant safety is adequate. 

It is very important to make classification of dynamic models and choose an appropriate one to provide similarity between model behavior and real characteristics of the material. The following general classification of the models is proposed for consideration deterministic, stochastic or their combination, linear, nonlinear, stationary or non-stationary, ergodic or non-ergodic. 

The WATS model is formulated in deterministic terms. However, an extension to include simple Monte-Carlo stochastic simulation is possible, taking into consideration a measured variability of the process parameters. 

Up to this point, it is assumed that prices are deterministic, which is true for contract demand and procurement but is not necessarily true for spot demand and procurement prices. Therefore, an important value chain planning requirement is the consideration of uncertain prices and price scenarios. Now, uncertain spot demand prices are under consideration and it is illustrated how price uncertainty can be integrated into the model in order to reach robust planning solutions. 

Functional Model The functional model will in general describe the deterministic properties of the physical situation or event under consideration. 

As with all statistical methods, the mean-field estimate will have statistical error due to the finite sample size (X ), and deterministic errors due to the finite grid size (S ) and feedback of error in the coefficients of the SDEs Ui,p). Since error control is an important consideration in transported PDF simulations, we will now consider a simple example to illustrate the tradeoffs that must be made to minimize statistical error and bias. The example that we will use corresponds to (6.198), where the exact solution141 to the SDEs has the form ... 

Measurement of dietary exposure to pesticides has historically relied upon deterministic methods that assign finite values to both the pesticide residue level and the food consumption estimates to yield a point estimate of exposure. The calculations are relatively simple, but consideration needs to be given to the accuracy of the assumptions concerning residue level and food consumption. 

The realization of the need and importance of petrochemical planning has inspired a great deal of research in order to devise different models to account for the overall system optimization. Optimization models include continuous and mixed-integer programming under deterministic or parameter uncertainty considerations. Related literature is reviewed at a later stage in this book, based on the chapter topic. 

The results of the model considered in this Chapter under uncertainty and with risk consideration, as one can intuitively anticipate, yielded different petrochemical network configurations and plant capacities when compared to the deterministic model results. The concepts of EVPI and VSS were introduced and numerically illustrated. The stochastic model provided good results as the objective function value was not too far from the results obtained using the wait-and-see approach. Furthermore, the results in this Chapter showed that the final petrochemical network was more sensitive to variations in product prices than to variation in market demand and process yields when the values of 0i and 02 were selected to maintain the final petrochemical structure. 

In the following two sections, deterministic (prescribed diffusion and FACSIMILE) and stochastic (random flights and IRT) approaches for the modeling of radiation chemical kinetics will be described. Then representative calculations for simple aqueous systems will be shown The stochastic approach to modeling radiolysis kinetics is more physically realistic than the primitive deterministic models however, it is also more conceptually advanced, requiring a more detailed (fuller) knowledge of the system under consideration. 

Negligible risks or doses used to classify exempt waste could be established based on a variety of considerations, consistent with the different approaches to risk management for radionuclides and hazardous chemicals described in Section 1.5.3. For noncarcinogenic hazardous chemicals, NCRP recommends that a negligible dose should be set at a small fraction (e.g., 10 percent) of a nominal threshold for deterministic responses in humans the recommended approach to estimating this threshold is described in Section I.5.5.3. For radionuclides, NCRP has recommended that an annual effective... 

The risk index for any hazardous substance in Equation 1.1 or 1.2 (see Section 1.5.1) is calculated based on assumed exposure scenarios for hypothetical inadvertent intruders at near-surface waste disposal sites and a specified negligible risk or dose in the case of exempt waste or acceptable (barely tolerable) risk or dose in the case of low-hazard waste. Calculation of the risk index also requires consideration of the appropriate measure of risk (health-effect endpoint), especially for carcinogens, and the appropriate approaches to estimating the probability of a stochastic response per unit dose for carcinogens and the thresholds for deterministic responses for noncarcinogens. Given a calculated risk index for each hazardous substance in a particular waste, the waste then would be classified using Equation 1.3. 

Based on these differences, the use of RfDs for hazardous chemicals that induce deterministic effects to define acceptable exposures of the public often may be considerably more conservative (provide a substantially larger margin of safety) than the dose limits for radiation induced deterministic effects. The likely degree of conservatism embodied in RfDs has important implications for establishing limits on allowable exposures to substances causing deterministic effects for the purpose of developing a risk-based waste classification system. Dose limits for deterministic effects for radiation should not be important in classifying waste (see Section 3.2.2.1). 

In setting limits on exposure intended to prevent the occurrence of deterministic responses, the safety and uncertainty factors that are applied to the assumed thresholds for hazardous chemicals that cause deterministic effects usually are considerably larger (by at least a factor of 10) than the safety factor normally applied to the thresholds for deterministic responses from exposure to radiation. Furthermore, the assumed threshold usually is more conservative for hazardous chemicals than for radiation (i.e., a lower confidence limit of the threshold often is used for... 

Measures of Response for Substances Causing Deterministic Responses. For purposes of health protection in routine exposure situations, incidence has been the primary measure of deterministic response for both radionuclides and hazardous chemicals. Fatalities also are of concern for substances that cause deterministic responses, but only at doses substantially above the thresholds for nonfatal responses. Given that the objective of standards for health protection is to prevent the occurrence of deterministic responses, incidence is not modified by any subjective factors that take into account, for example, the relative severity of different nonfatal responses with respect to a diminished quality of life. Judgments about the importance of deterministic responses are applied only in deciding which responses are sufficiently adverse to warrant consideration in setting protection standards. 

Formulation of the risk index for mixtures of substances that cause deterministic effects is considerably more complex than in the case of substances that cause stochastic effects discussed in the previous section. The added complexity arises from the threshold dose-response relationship for these substances and the need to keep track of the dose in each organ or tissue at risk in evaluating whether the dose in each organ is less than the allowable dose in that organ. For substances that cause deterministic responses, the index T can refer not only to a specific organ or tissue (e.g., the liver or skin) but also to a body system that may be affected by a particular chemical, such as the immune or central nervous system. 

Similar considerations should apply to waste that contains small amounts of hazardous chemicals that might be sent to a disposal facility for nonhazardous waste. Allowable doses could correspond to a negligible lifetime risk of about 10 5 in the case of substances that induce stochastic effects or an intake at an RfD (Section 3.2.1.2) in the case of substances that induce deterministic effects. The considerations of exposure scenarios should be the same as in the case of radioactive wastes. 

The results in Table 7.8 indicate that the organ- and endpoint-specific risk indexes are about 0.7 to 0.8 in all cases, due mainly to intakes of lead. The maximum risk index for any organ or endpoint is about 0.8. Truncating this result using the INTEGER function, as indicated in Equation 6.5, gives a risk index for all deterministic hazardous chemicals in the waste of zero. This result means that the calculated dose in all organs and for all endpoints due to exposure to all deterministic substances that cause deterministic responses in the waste is less than the assumed acceptable dose of 10 times RfDs. Therefore, based only on consideration of substances that... 

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