Uncertainty analysis

Finally, the MOS should also take into account the uncertainties in the estimated exposure. For predicted exposure estimates, this requires an uncertainty analysis (Section 8.2.3) involving the determination of the uncertainty in the model output value, based on the collective uncertainty of the model input parameters. General sources of variability and uncertainty in exposure assessments are measurement errors, sampling errors, variability in natural systems and human behavior, limitations in model description, limitations in generic or indirect data, and professional judgment. 

The toxicity exposure ratio approach, rather than a more rigid standard setting approach (Section 8.2.2), allows greater room for expert judgment because the size of an overall assessment factor is not fixed. Furthermore, this approach can be readily applied to substances for which limited data are available. The risk assessor can decide how wide the MOS should be in the light of the data available. 

It should be noted that MOS ratios are no absolute measure of risks. Nobody knows the real risks of chemicals where the exposure exceeds the derived no-effect level (DNEL). The risk assessor only knows that the likelihood of adverse effects increases when the DNEL/E ratios decrease or the E/DNEL ratios increase. Thus, such ratios are internationally accepted only as substitutes for risks. 

An alternative approach to the toxicity exposure ratio approach described in the previous section is the standard setting approach. 

the output of the hazard (effects) assessment (e.g., the NOAEL) leads directly to the establishment of a regulatory standard, for example the derivation of an acceptable or tolerable daily intake (ADI/TDI) (Section 5.12) for a chemical in relation to a specific use category such as, e.g., pesticide, biocide, food additive, food contact material, etc. 

The local concentration sensitivity matrix shows the effect of equal perturbations of parameters. This means equal unit perturbation in the units of each parameter for the case of the original sensitivity matrix, and unit fractional (percentage) perturbation in the case of the normed sensitivity matrix. The local sensitivity matrix itself does not carry any information on the uncertainty of parameters. 

The local sensitivities can be used for a rough assessment of the parameter uncertainties on model output. The variance of the model output cr (c, ) can be estimated from the variance of the parameters (r kj) and the local sensitivities, 

The global sensitivity analysis methods address the problem of the precise calculation of the uncertainty of the model output as a result of uncertainties in parameters. These methods can handle any large uncertainty in the input parameters. More refined techniques include the determination of the extent of the uncertainty in output as a result of the uncertainty of each parameter. 

The first widely used global method was the Fourier Amplitude Sensitivity Test (FAST) (for a review see [83]). In the FAST method, all rate parameters were simultaneously perturbed by sine functions with incommensurate frequencies. Fourier analysis of the solution of the model provided the variance crf(t) of concentration i, and also the variance o- (t) of c, arising from the uncertainty in the /th parameter. Their ratio 

All global methods require considerable computer time and these methods have not been applied to combustion problems. It is expected in the near future that they will be applied to the evaluation of spatially homogeneous combustion models. 

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Gordon, R. Pickering, M. Bisson, D. Uncertainty Analysis by the Worst Gase Method, /. Chem. Educ. 1984, 61, 780-781. 

If a heat exchanger is sized usiag the mean values of the design parameters, then the probabiUty, or the confidence level, of the exchanger to meet its design thermal duty is only 50%. Therefore, in order to increase the confidence level of the design, a proper uncertainty analysis must be performed for all principal design parameters. 

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. 

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. 

A common risk evaluation and presentation method is simply to multiply the frequency of each event by consequence of each event and then sum these products for all situations considered in the analysis. In insurance terms, this is the expected loss per year. The results of an uncertainty analysis, if performed, can be presented as a range defined by upper and lower confidence bounds that contain the best estimates. If the total risk represented by the best estimate or by the range estimate is... 

Some advocates of sophisticated data analysis and detailed uncertainty analysis contend that these approaches will engender greater con-... 

Meetings should be held with all parties concerned as to how the test will be conducted and an uncertainty analysis should be performed prior to the test. The overall test uncertainty will vary because of the differences in the scope of supply, fuel(s) used, and driven equipment characteristics. The code establishes a limit for the uncertainty of each measurement required the overall uncertainty is then calculated in accordance with the procedures defined in the code and by ASME PTC 19.1. 

The PTC 22 establishes a limit of uncertainty of each measurement required the overall uncertainty must then be calculated in accordance with the procedures defined in ASME PTC 19.1 Measurement Uncertainty. The code requires that the typical uncertainties be within a 1.1% for the Power Output, and 0.9% in the heat rate calculations. It is very important that the post-test uncertainty analysis should be also performed to assure the parties that the actual test has met the requirement of the code. 

Uncertainty analysis can be performed with the same model. 

Define Constants - specify file locations, archive information, uncertainty analysis settings, cutset generation, transformations, quantification constants, and set default values for the graphical editors. 

The Systems Module constructs and displays fault trees using EASYFLOW which aic read automatically to generate minimal cutsets that can be transferred, for solution, to SETS. CAFT A. or IRRAS and then transferred to RISKMAN for point estimates and uncertainty analysi,s using Monte Carlo simulations or Latin hypercube. Uncertainty analysis is performed on the systems lev el using a probability quantification model and using Monte Carlo simulations from unavailability distributions. 

IMPORTANCE - Accepts the output from BUILD and calculates importance measures (Section 2.8) and provides input for the uncertainty analysis. 

MONTE - Performs a Monte Carlo uncertainty analysis using the uncertainties in the data to estimate the uncertainty in the calculation of the system and subsystem failure probabilities. 

Uncertainty Analysis determines the effects on the overall results from uncertaintic.s in the database, assumptions in modeling, and the completeness of the analysis. Sensitivity analyses determine the robustness of the results importance calculations are useful for identifying and prioritizing plant improvements. 

Also, presented are the level-1 uncertainty analysis, results. The MLO mean core damage frequency from internal events is about an order of magnitude lower than that of full power operation. The mean core damage frequency due... 

Fault tree or equivalent analysis is key to PSA. Small logical structures may be evaluated by hand using the iciples of Chapter 2 but at some point computer support eeded. Even for simple structures, uncertainty analysis VIonte Carlo methods requires a computer. However, t of the codes are proprietary or a fee is charged for their... 

Perform sensitivity and uncertainty analysis. Calculation of life-cycle costs and net benefits assumes that cash-flow profiles and the value of MARR are reasonably accurate. In most cases, uncertain assumptions and estimates are made in developing cash flow profile forecasts. Sensitivity analysis can be performed by testing how the outcome changes as the assumptions and input values change. 

Matthies M, Berding V, Beyer A (2004) Probabilistic uncertainty analysis of the European union system for the evaluation of substances multimedia regional distribution model. Environ Toxicol Chem 3(10) 2494—2502... 

Blower SM, Dowlatabadi H. Sensitivity and uncertainty analysis of complex models of disease transmission an HIV model, as an example. Int Statistical Rev 1994 62 229-43. 

Geisler, G., Hellweg, S., Hungerbuhler, K. (2005) Uncertainty Analysis in Life Cycle Assessment (LCA) Case Study on Plant-Protection Products and Implications for Decision Making. International Journal of Life Cycle Assessment, 10, 184-192. 

Ponce RA, BarteU SM, Kavanagh TJ, Woods JS, Griffith WC, Lee RC, Takaro TK, Faustman EM. 1998. Uncertainty analysis methods for comparing predictive models and biomarkers a case study of dietary methyl mercury exposure. Regulatory Toxicol Pharmacol 28 96-105. 

Carroll J, Harms IH. 1999. Uncertainty analysis of partition coefficients in a radionuclide transport model. Water Res 33(11) 2617-2626. 

Khan MS, Coulibaly P, Dibike Y (2006) Uncertainty analysis of statistical downscaling methods. J Hydrol 319 357-382... 

The uncertainty analysis that is a part of formal EcoRA methodology is designed to ensure adequate estimation of ecological effects based on a state-of-the-art scientific basis. Moreover, if applied on a local scale for site-specific assessments, with the use of empirical input data as biogeochemical parameters, the CLL approach is likely to provide results with a higher degree of confidence than the formal EcoRA model. 

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