Error analysis, model

Confirmatory Factor Measurement Error Analysis Models Models... 

In the process of risk and human reliability assessment, there are various methods to be used, such as Cognitive Reliability and Error Analysis Model (CREAM), A Technique for Human Error Analysis (ATHENA), and Technique for Human Error Rate Prediction (THERP). 

In addition, the chapter will provide an overview of htunan reliability quantification techniques, and the relationship between these techniques and qualitative modeling. The chapter will also describe how human reliability is integrated into chemical process quantitative risk assessment (CPQRA). Both qualitative and quantitative techniques will be integrated within a framework called SPEAR (System for Predictive Error Analysis and Reduction). 

Halfon, E. 1984. Error analysis and simulation of mirex behaviour in Lake Ontario. Ecolog. Model. 22 213-252. 

G. Vivo-Truyols, J.R. Torres-Lapasio and M.C. Garcia-Alvarez-Coque, Error analysis and performance of different retention models in the transference of data from/to isocratic/gradi-ent elution. J. Chromatogr.A 1018 (2003) 169-181. 

In Figures 8 and 9 are shown the data for the dependence of the characteristic film buildup time t on Apg and U. In accord with the model, t is found to be independent of U, with only a very weak dependence on Apg indicated. This latter result could in part be a function of experimental inaccuracy. The data reduction for t introduces no assumptions beyond that needed to draw the exponential flux decline curves such as those shown in Figures 2 and 3. However, an error analysis shows that the maximum errors relative to the exponential curve fits occur at the earlier times of the experiment. This is seen in the typical error curve plotted in Figure 10. The error analysis indicates that during the early fouling stage the relatively crude experimental procedure used is not sufficiently accurate or possibly that the assumed flux decline behavior is not exponential at the early times. In any case, it follows that the accuracy of the determination of 6f is greater than that for t. 

First-order error analysis is a method for propagating uncertainty in the random parameters of a model into the model predictions using a fixed-form equation. This method is not a simulation like Monte Carlo but uses statistical theory to develop an equation that can easily be solved on a calculator. The method works well for linear models, but the accuracy of the method decreases as the model becomes more nonlinear. As a general rule, linear models that can be written down on a piece of paper work well with Ist-order error analysis. Complicated models that consist of a large number of pieced equations (like large exposure models) cannot be evaluated using Ist-order analysis. To use the technique, each partial differential equation of each random parameter with respect to the model must be solvable. 

As an example, in the following derivation the Ist-order error analysis equation for a simple model with both constants and random variables is found. The random terms ate X and Z, with constants a, b, and c. The model is... 

With simple linear models, try several uncertainty methods, like Ist-order error analysis, and Judge whether the results are consistent. 

O Neill RV. 1973. Error analysis of ecological models. In NeLson DJ, editor, Conf. 710501, Radionuclides in ecosystems. Springfield (VA) National Technological Information Service. 

Error Analysis and Quantification of Uncertainty. The error associated with paleolimnological inferences must be understood. Two sources of error worthy of special attention are the predictive models (transfer functions) developed to infer chemistry and inferences generated by using those equations with fossil samples in sediment strata. Much of the following discussion is based on the pioneering work reviewed by Sachs et al. (35) and by Birks et al. (17, 22), among others. We emphasize error analysis here because it is not covered in detail in most of the general review articles cited earlier. 

Optimal Data Collection Site Individual calibration models based on cross-validation can be established for several candidate sites such as forearm, fingernail, and so on, and the results can be compared. The minimum detection error analysis can also be employed to evaluate different sites. 

Problem 2.9 Error Analysis for Simple Response Modelling... 

Analysis of the Deviations. The axial variation of the errors of models I-T and II-T calculated according to Equation 10 are represented in Figure 1. Values of the parameters shown in Table II remain constant in all the analyzed cases while the values of the remaining parameters are shown in each figure. 

Access to powerful computers and to commercial partial-differential-equation (PDE) solvers has facilitated modeling of the impedance response of electrodes exhibiting distributions of reactivity. Use of these tools, coupled with development of localized impedance measurements, has introduced a renewed emphasis on the study of heterogenous surfaces. This coupling provides a nice example for the integration of experiment, modeling, and error analysis described in Chapter 23. 

A distinction is drawn in equation (21.1) between stochastic errors that are randomly distributed about a mean value of zero, errors caused by the lack of fit of a model, and experimental bias errors that are propagated through the model. The problem of interpretation of impedance data is therefore defined to consist of two parts one of identification of experimental errors, which includes assessment of consistency with the Kramers-Kronig relations (see Chapter 22), and one of fitting (see Chapter 19), which entails model identification, selection of weighting strategies, and examination of residual errors. The error analysis provides information that can be incorporated into regression of process models. The experimental bias errors, as referred to here, may be caused by nonstationary processes or by instrumental artifacts. 

It should be noted that the error analysis methods using measurement models are sensitive to data outliers. Occasionally, outliers can be attributed to external influences. Most often, outliers appear near the line frequency and at the beginning of an impedance measurement. Data collected within 5 Hz of the line frequency and its first harmonic (e.g., 50 and 100 Hz in Europe or 60 and 120 Hz in the United States) should be deleted. Startup transients cause some systems to exhibit a detectable artifact at the first frequency measured. This point, too, should be deleted. 

Remember 21.3 The error analysis methods using measurement models are sensitive to data outliers. 

Remember 23.1 The philosophical approach of this textbook integrates experimental observation, model development, and error analysis. 

Figure 23.1 Schematic flowchart showing the relationship between impedance measurements, error analysis, supporting observations, model development, and weighted regression analysis. (Taken from Orazem and Tribollet and reproduced with permission of Elsevier, Inc.)...

Example 23.2 demonstrates the utility of the error analysis for determining consistency with the Kramers-Kronig relations. In this case, the low-frequency inductive loops were foimd to be consistent with the Kramers-Kronig relations at frequencies as low as 0.001 Hz so long as the system had reached a steady-state operation. The mathematical models that were proposed to account for the low-frequency features were based on plausible physical and chemical hypotheses. Nevertheless, the models are ambiguous and require additional measurements and observations to identify the most appropriate for the system under study. 

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