Reliability estimation

The most reliable estimates of the parameters are obtained from multiple measurements, usually a series of vapor-liquid equilibrium data (T, P, x and y). Because the number of data points exceeds the number of parameters to be estimated, the equilibrium equations are not exactly satisfied for all experimental measurements. Exact agreement between the model and experiment is not achieved due to random and systematic errors in the data and due to inadequacies of the model. The optimum parameters should, therefore, be found by satisfaction of some selected statistical criterion, as discussed in Chapter 6. However, regardless of statistical sophistication, there is no substitute for reliable experimental data. 

The volumetries of a field, along with the anticipated recovery factors, control the reserves in the field those hydrocarbons which will be produced in the future. The value of an oil or gas company lies predominantly in its hydrocarbon reserves which are used by shareholders and investors as one indication of the strength of the company, both at present and in the future. A reliable estimate of the reserves of a company is therefore important to the current value as well as the longer term prospects of an oil or gas company. 

This fomuila does not include the charge-dipole interaction between reactants A and B. The correlation between measured rate constants in different solvents and their dielectric parameters in general is of a similar quality as illustrated for neutral reactants. This is not, however, due to the approximate nature of the Bom model itself which, in spite of its simplicity, leads to remarkably accurate values of ion solvation energies, if the ionic radii can be reliably estimated [15],... 

Abstract. A smooth empirical potential is constructed for use in off-lattice protein folding studies. Our potential is a function of the amino acid labels and of the distances between the Ca atoms of a protein. The potential is a sum of smooth surface potential terms that model solvent interactions and of pair potentials that are functions of a distance, with a smooth cutoff at 12 Angstrom. Techniques include the use of a fully automatic and reliable estimator for smooth densities, of cluster analysis to group together amino acid pairs with similar distance distributions, and of quadratic progrmnming to find appropriate weights with which the various terms enter the total potential. For nine small test proteins, the new potential has local minima within 1.3-4.7A of the PDB geometry, with one exception that has an error of S.SA. 

The computation of mesopore size distribution is valid only if the isotherm is of Type IV. In view of the uncertainties inherent in the application of the Kelvin equation and the complexity of most pore systems, little is to be gained by recourse to an elaborate method of computation, and for most practical purposes the Roberts method (or an analogous procedure) is adequate—particularly in comparative studies. The decision as to which branch of the hysteresis loop to use in the calculation remains largely arbitrary. If the desorption branch is adopted (as appears to be favoured by most workers), it needs to be recognized that neither a Type B nor a Type E hysteresis loop is likely to yield a reliable estimate of pore size distribution, even for comparative purposes. 

Infomiation is iaadequate to fomiulate reliable estimates for iadividual republics. Total is rounded. 

Reliability Estimation. Both a point estimate and a confidence interval estimate of product rehabUity can be obtained. Point Estimate. The point estimate of the component rehabUity is given by... 

There are a number of reliable estimating techniques for obtaining pure-component hq uid heat capacity as a function of tem )erature, including Ruzicka and Dolmalsld, Tarakad and Danner, " and Lee and Kesler. These methods are somewhat compheated. The relatively single atomic group contribution approach of Chueh and Swanson for liquid heat capacity at 29.3.15 K is presented here ... 

Qualitative analysis methods should have well-grounded and generally adopted quantitative reliability estimations. At first the problem was formulated by N.P. Komar in 1955. Its actuality increased when test methods and identification software systems (ISS) entered the market. Metrological aspects evolution for qualitative analysis is possible only within the scope of the uncertainty theory. To estimate the result reliability while detecting a substance X it is necessary to calculate both constituents of uncertainty the probability of misidentifications and the probability of unrevealing for an actual X. There are two mutual complementary approaches to evaluate uncertainties in qualitative analysis, just as in quantitative analysis ... 

Furthermore, the situation becomes even worse for an asymmetric potential like that in (3.18), because at low temperature nearly the entire period p is spent on dwelling in the potential well (see appendix A), so that lim -oo < >ins = 0- In other words, unless the potential is strictly symmetric, the transition state position x tends to the minimum of the initial state It is natural to expect that the centroid approximation will work well when x does not deviate too far from x. To summarize, the centroid method is an instructive way to describe in a unique TST-like manner both the high [T > T ) and fairly low [T < T ) temperature regions, but it does not give a reliable estimate for k. ... 

Confidence levels on the reliability estimates from the SSI model can be determined and are useful when the PDFs for stress and strength are based on only small amounts of data or where critical reliability projects are undertaken. However, approaches to determine these confidence levels only strictly apply when stress and strength are characterized by the Normal distribution. Detailed examples can be found in Kececioglu (1972) and Sundararajan and Witt (1995). 

These types of stoichiometric calculations are commonplace and can provide reliable estimates for the material balance. As with any calculation method, one should list the assumptions to qualify the accuracy of the estimate. Limited field measurements can always be done later to verify the estimated emissions. 

Appendix HI, of WASH-1400 presents a database from 52 references that were used in the study. It includes raw data, notes on test and maintenance time and frequency, human-reliability estimates, aircraft-crash probabilities, frequency of initiating events, and information on common-cause failures. Using this information, it assesses the range for each failure rate. 

Comer, M. K. et al, enerating Human Reliability Estimates using Expert Judgment. SNL, November 1984. 

Bloom, E.D., 1981, A Technique to Reliability Estimate Earthquake Recurrence Intervals, EPRI... 

The precondition for the use of the normal distribution in estimating the random error is that adequate reliable estimates are available for the parame-rcrs ju. and cr. In case of a repeated measurement, the estimates are calculated using Eqs. (12.1) and (12,3). When the sample size iiicrease.s, the estimates m and s approach the parameters /c and cr. A rule of rhumb is that when s 30. the normal distribution can be osecl,... 

Documentation of data origin is essential. Each completed data collection form needs to contain a file reference number or code to connect it to the documentation sources. This provides an essential trail to audit data quality, to confirm risk or reliability estimates or to investigate data values that appear questionable. Procedures to control data during handling, processing, recording, and reviewing are also necessary to prevent loss of data and to assure that opportunities are not lost to check the content of a form, by... 

Shinha, S. K. and B. K. Kale Life Testing and Reliability Estimation. John Wiley Sons (Halsted), New York, 1980. 

Solutes in Methanol Solution. In Table 23 we have seen that for four solutes in methanol the viscosity //-coefficients are positive. This is the case even for KC1 and KBr, for which the coefficients are negative in aqueous solution. In Sec. 88 it was pointed out that it would be of interest to see whether this inversion is likewise accompanied by a change in sign for the ionic entropy. Although no accurate values for the entropy of solution of salts in methanol arc available, reliable estimates have been made for KC1, KBr, and NaCl.1 Since the /1-coefficients of KC1 and KBr have been determined both in methanol and in water, all the required data are available for these two solutes. The values of A/S" given in Table 29 have been taken from Table 34 in Chapter 12, where the method of derivation is explained. The cratie term included in each of these values is 14 cal/deg, as already mentioned in Sec. 90. 

The mean of several readings (x) will make a more reliable estimate of the true mean (yu) than is given by one observation. The greater the number of measurements (n), the closer will the sample average approach the true mean. The standard error of the mean sx is given by ... 

Another set of terms considered by Eyring, et al. consisted of structures having a double bond between carbons. These should be expected to be involved to some small extent—small because they have one less real bond. This is essentially invoking hyperconjugation. These authors did not reach a definite conclusion regarding the importance of these structures and decided that they probably would stabilize the eclipsed configuration, which was not known at that time to be the incorrect one. It is still not simple to make a reliable estimate of the importance of this contribution. 

Referring to the ionic effects, measuring of swelling in solutions which closely model real ones can provide reliable estimates. The papers [58, 132] can serve as examples of such an approach. In choosing a type of SAH suitable for some particular soil it is necessary to take into account the acid-base properties of the gel and the soil because otherwise collapse phenomena are likely to result from common counterions and the sorption on solid surfaces. 

The data in the validation set are used to challenge the calibration. We treat the validation samples as if they are unknowns. We use the calibration developed with the training set to predict (or estimate) the concentrations of the components in the validation samples. We then compare these predicted concentrations to the actual concentrations as determined by an independent referee method (these are also called the expected concentrations). In this way, we can assess the expected performance of the calibration on actual unknowns. To the extent that the validation samples are a good representation of all the unknown samples we will encounter, this validation step will provide a reliable estimate of the calibration s performance on the unknowns. But if we encounter unknowns that are significantly different from the validation samples, we are likely to be surprised by the actual performance of the calibration (and such surprises are seldom pleasant). 

Die Tg can be determined readily only by observing the temperature at which a significant change takes place in a specific electric, mechanical, or physical property. Moreover, the observed temperature can vary significantly, depending on the specific property chosen for observation and on details of the experimental technique (for example, the rate of heating, or frequency). Therefore, the observed Tg should be considered to be only an estimate. The most reliable estimates are normally obtained from the loss peak observed in dynamic mechanical tests or from dilatometric data (ASTM D-20). 

As indicated above, absorption effects can generally be predicted and satisfactorily estimated when only monochromatic x-rays are involved. When a polychromatic beam is used for excitation, the filtering of the beam by the sample complicates the situation and modifies the absorption effects. Even then, fairly reliable estimates of the effects can be made. 

The renal clearance can be under estimated in the case of renal drug metabolism. The total drug clearance depends on bioavailability. Therefore, the most reliable estimate for the fraction eliminated by the renal route (fren) is given by the normal clearance (Clnorm) and drug clearance in case of acute and/ or chronic renal failure (Clfail), or from half-lives (Tl/2norm) and (Tl/2fail). 

Slightly removed from this in rigor is the use of a substituent to make a pure exchange into a net chemical reaction. No isotopic label is then needed. For example, the first reliable estimate of the rate constant for the exchange of ferrocenium ions and ferrocene was made on the basis of kinetic data for processes such as... 

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