Uncertainty Bounds

FIGURE 15. An illustration of the problem of QRA reproducibility. (Note The bars in the figure represent uncertainty bounds.)... 

The uncertainties in human error rates may be within the stated uncertainty bounds, but such is not demonstrated from sparse experiments. Both the qualitative description of the human interaction logic and the quantitative assessment of those actions rely on the virtually untested judgment of experts. 

Computerized Aggregate of Reliability Parameters (CARP) A computer code developed by SAIC to aggregate data sets into a single generic set determine uncertainty bounds (5th and 95th percentiles) fit raw data to statistical distributions and print reports documenting determinations made. 

The second part of the work involves implementing a robust controller. The key issue in the controller design is the treatment of system dynamics uncertainties and rejection of exogenous disturbances, while optimizing the flow responses and control inputs. Parameter uncertainties in the wave equation and time delays associated with the distributed control process are formally included. Finally, a series of numerical simulations of the entire system are carried out to examine the performance of the proposed controller design. The relationships among the uncertainty bound of system dynamics, the response of flow oscillation, and controller performance are investigated systematically. 

Based on Eqs. (22.18), (22.21), and (22.25), a sufficient condition for the existence of a robust controller which stabilizes all perturbed plants with desired performance, subject to some uncertainty bound, can be obtained as follows ... 

The affordable uncertainty bound I/7 is insensitive to the disturbance weightings a and / ... 

There is a trade-off between the affordable model uncertainty bound 1/7 and the maximum time delay 6t Fig. 22.5 shows this relationship. 

Practitioners of ecological risk assessments will frequently experience large uncertainty bounds on the estimates of risk. Unfortunately, characterizing and/or reducing uncertainty can be very costly. However, these costs must be balanced with the need to conduct sufficient analysis to make an informed decision. 

FIGURE 8.1 The risk curve lines shown represent thresholds between different types of decisions (based on ECOFRAM 1999a and 1999b). These thresholds would be determined by decision makers and may move location subject to other factors that affect the decision (e.g., pesticide benefits). The bottom graph shows an example risk curve with uncertainty bounds. The curve clearly fits within the acceptable risk category however the upper uncertainty bound does not, indicating a need for risk mitigation or further refinement of the risk assessment. 

To provide the most realistic representation of risk, all forms of uncertainty arc considered. Rather than assuming the existence of some representative condition prior to the accident scenario, a study models the full range of conditions and other uncertainties that can affect the scenario. Results include uncertainties in the frequency and consequences of each scenario. The upper uncertainty bound shown for the QRA risk estimates is a measure of the analysts confidence in the results. There is a 95 percent chance that the risk is less than the upper bound. 

If the estimated uncertainty bounds are considered, the value from Nair and Nancollas overlaps with those from the conductance studies. Using the weighted average of the conductance and emf data ((228.1 + 15.5) and (173 80), respectively, weighted according to their uncertainties), the selected value of AT°((V.88), 298.15 K) is ... 

K, the formation constant was recalculated to be (173 64). However, if the value for log,/f°(A.16) was changed from 1.98 to 1.96, well within the assessed uncertainty bound, the value became (140 72). The uncertainties here are merely the 2ct uncertainties in the set of seven values recalculated from [59NA1/NAN], and do not include uncertainties in the auxiliary data. Even though the solute concentrations are low (/ < 0.05), and the overall changes to the activity coefficients from the SIT interaction terms are small, the calculated value of log, AT (A.15) increases from (173 64) to (201 35) if all the e values are set to zero (but the maximum change in from the interaction terms is 0.004). 

A chemical mechanism is evaluated by comparing its predictions to laboratory or field data. Both the measurements and the predictions have uncertainties associated with them since the agreement between measurements and predictions is never perfect, the question then arises as to whether the differences exhibited are significant. When dealing with an atmospheric chemical mechanism, it is desirable to place uncertainty bounds on simulations. There have been a number of such studies for stratospheric chemical mechanisms (Stolarski et al., 1978 Falls et al., 1979 Ehhalt et al., 1979 Tilden et al., 1981 Tilden and Seinfeld, 1982 Stolarski and Douglass, 1986). 

In his earlier paper, Currie considered only the random error component. Later, Currie and DeVoe (1 ) considered the effect of systematic errors (bias) on detection limits (and by implication determination limits). At these levels, random error introduces a sizable component into the presumably stable bias component. Therefore, in order to detect a systematic error of magnitude comparable to the standard deviation, one needs at least 15 observations. If the systematic error is not constant, these authors point out that it becomes impossible to generate meaningful uncertainty bounds for experimental data. 

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