Uncertainty treatment

ANOVA was performed on WTP and ITP using the uncertainty treatment level as the independent variable. The ANOVA results suggest that the subjective estimates on willingness to pay to avoid the online phishing risk and on the scale of intention to purchase online are significantly different across the four treatment levels in the experiment. This shows that variant uncertainty levels have a significant effect on online consumer decisirais. 

Moens, D. Vandepitte, D. 2005. A Survey of Non-Probabilistic uncertainty treatment in Finite Element Analysis, Computer Methods in Applied Mechanics and Engineering, Vol. 194, Nos. 12-16, pp. 1527-1555. 

Fleming, K.N. Lydell, B.O.Y, 2004. Database development and uncertainty treatment for estimating pipe failure rates and rupture frequencies. Reliability Engineering System Safety, 86(3) 227-246. 

The Heisenberg uncertainty principle offers a rigorous treatment of the qualitative picture sketched above. If several measurements of andfi are made for a system in a particular quantum state, then quantitative uncertainties are provided by standard deviations in tlie corresponding measurements. Denoting these as and a, respectively, it can be shown that... 

Because of the uncertainties related to the parametrization of an sp C, this approach is unsuitable for the study of protomeric equilibria for structures 4 through 8. We must lay stress on the fact that this simple treatment does not include (a) medium effects which are known to be important and b) the existence of associated species (see Chapter VII, Section I. LB) whose consequences have been thoroughly studied in pyridone series (1688). 

So what is the total uncertainty when using this pipet to deliver two successive volumes of solution from the previous discussion we know that the total uncertainty is greater than 0.000 mL and less than 0.012 mL. To estimate the cumulative effect of multiple uncertainties, we use a mathematical technique known as the propagation of uncertainty. Our treatment of the propagation of uncertainty is based on a few simple rules that we will not derive. A more thorough treatment can be found elsewhere. ... 

This is a formidable analysis problem. The number and impact of uncertainties makes normal pant-performance analysis difficult. Despite their limitations, however, the measurements must be used to understand the internal process. The measurements have hmited quahty, and they are sparse, suboptimal, and biased. The statistical distributions are unknown. Treatment methods may add bias to the conclusions. The result is the potential for many interpretations to describe the measurements equaUv well. 

The nuclear equipment failure rate database has not changed markedly since the RSS and chemical process data contains information for non-chemical process equipment in a more benign environment. Uncertainty in the database results from the statistical sample, heterogeneity, incompleteness, and unrepresentative environment, operation, and maintenance. Some PSA.s use extensive studies of plant-specific data to augment the generic database by Bayesian methods and others do not. No standard guidance is available for when to use which and the improvement in accuracy that is achieved thereby. Improvements in the database and in the treatment of data requires, uhstaiui.il indu.sinal support but it is expensive. 

Every measured quantity or component in the main equations, Eqs. (12.30) and (12.31), influence the accuracy of the final flow rate. Usually a brief description of the estimation of the confidence limits is included in each standard. The principles more or less follow those presented earlier in Treatment of Measurement Uncertainties. There are also more comprehensive error estimation procedures available.These usually include, beyond the estimation procedure itself, some basics and worked examples. 

Due to difficulties and uncertainties in the experimental separation of the porous media [93], and the inevitability of approximations in the analytical treatment [87,89], the nature of the chain movement in a random environment is still far from being well understood, and theoretical predictions are controversial [87,89]. Thus, on the ground of replica calculations within a variational approach, one predicts three regimes [87] in which the chain gyration radius Rg scales with the number of repeatable units N as rI (X for low, R x N for medium, and R x for high... 

It can be argued that the main advantage of least-squares analysis is not that it provides the best fit to the data, but rather that it provides estimates of the uncertainties of the parameters. Here we sketch the basis of the method by which variances of the parameters are obtained. This is an abbreviated treatment following Bennett and Franklin.We use the normal equations (2-73) as an example. Equation (2-73a) is solved for <2o-... 

In the earlier treatment we reached the conclusion that resonance absorption occurs at the Larmor precessional frequency, a conclusion implying that the absorption line has infinitesimal width. Actually NMR absorption bands have finite widths for several reasons, one of which is spin-lattice relaxation. According to the Heisenberg uncertainty principle, which can be stated... 

Examination of Table 6-1 reveals how the weighting treatment takes into account the reliability of the data. The intermediate point, which has the poorest precision, is severely discounted in the least-squares fit. The most interesting features of Table 6-2 are the large uncertainties in the estimates of A and E. These would be reduced if more data points covering a wider temperature range were available nevertheless it is common to find the uncertainty in to be comparable to RT. The uncertainty of A is a consequence of the extrapolation to 1/7" = 0, which, in effect, is how In A is determined. In this example, the data cover the range 0.003 23 to 0.003 41 in 1/r, and the extrapolation is from 0.003 23 to zero thus about 95% of the line constitutes an extrapolation over unstudied tempertures. Estimates of A and E are correlated, as are their uncertainties. ... 

A further benefit is that this treatment makes the uncertainties more explicit. If the payback time is five years, then it is clear that the calculated benefit hangs on estimates of markets, costs, and prices up to five years ahead the shorter the interval, the less the uncertainty. In troubled economic times, short payback strategies may be deliberately sought. 

Due to the inherent uncertainty of the Langmuir model and difficulties in solving the transcendental equation (41), probably the most accurate treatment in the near-equilibrium cases is a numerical or graphical integration of the expression... 

Chueh s method for calculating partial molar volumes is readily generalized to liquid mixtures containing more than two components. Required parameters are and flb (see Table II), the acentric factor, the critical temperature and critical pressure for each component, and a characteristic binary constant ktj (see Table I) for each possible unlike pair in the mixture. At present, this method is restricted to saturated liquid solutions for very precise work in high-pressure thermodynamics, it is also necessary to know how partial molar volumes vary with pressure at constant temperature and composition. An extension of Chueh s treatment may eventually provide estimates of partial compressibilities, but in view of the many uncertainties in our present knowledge of high-pressure phase equilibria, such an extension is not likely to be of major importance for some time. 

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