Confidence

It is estimated that for every two retirees who volunteer, an additional person has the desire but not the confidence to take the first step. If you are in the latter category, visit the organization directly after making a telephone appointment to learn more about opportunities to do volunteer work. 

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When there are sufficient data at different temperatures, the temperature dependence of the parameters is reflected in the confidence ellipses (Bryson and Ho, 1969 Draper and Smith,... 

Figure 4-2. UNIQUAC parameters and their approximate confidence regions for the ethanol-cyclohexane system for three isotherms. Data of Scatchard and Satkiewicz, 1964.

The results shown in Table 2 indicate that UNIQUAC can be used with confidence for multicomponent vapor-liquid equilibria including those that exhibit large deviations from ideality. 

Using the ternary tie-line data and the binary VLE data for the miscible binary pairs, the optimum binary parameters are obtained for each ternary of the type 1-2-i for i = 3. .. m. This results in multiple sets of the parameters for the 1-2 binary, since this binary occurs in each of the ternaries containing two liquid phases. To determine a single set of parameters to represent the 1-2 binary system, the values obtained from initial data reduction of each of the ternary systems are plotted with their approximate confidence ellipses. We choose a single optimum set from the intersection of the confidence ellipses. Finally, with the parameters for the 1-2 binary set at their optimum value, the parameters are adjusted for the remaining miscible binary in each ternary, i.e. the parameters for the 2-i binary system in each ternary of the type 1-2-i for i = 3. .. m. This adjustment is made, again, using the ternary tie-line data and binary VLE data. 

The optimum parameters for furfural-benzene are chosen in the region of the overlapping 39% confidence ellipses. The ternary tie-line data were then refit with the optimum furfural-benzene parameters final values of binary parameters were thus obtained for benzene-cyclohexane and for benzene-2,2,4-trimethyl-pentane. Table 4 gives all optimum binary parameters for this quarternary system. 

Figure 4-21. Parameters obtained for the furfural-benzene binary are different for the two ternary systems. An optimum set of these parameters is chosen from the overlapping confidence regions, capable of representing both ternaries equally well.

The primary purpose for expressing experimental data through model equations is to obtain a representation that can be used confidently for systematic interpolations and extrapolations, especially to multicomponent systems. The confidence placed in the calculations depends on the confidence placed in the data and in the model. Therefore, the method of parameter estimation should also provide measures of reliability for the calculated results. This reliability depends on the uncertainties in the parameters, which, with the statistical method of data reduction used here, are estimated from the parameter variance-covariance matrix. This matrix is obtained as a last step in the iterative calculation of the parameters. 

Figure 6-2. Confidence ellipses for van Laar parameters. Acetone(l)-methanol(2) system at 755 mm Hg (Othmer, 1928).

Large confidence regions are obtained for the parameters because of the random error in the data. For a "correct" model, the regions become vanishingly small as the random error becomes very small or as the number of experimental measurements becomes very large. 

For the acetone-methanol data of Othmer, the correlation coefficient is -0.678, indicating a moderate degree of correlation between the two van Laar parameters. The elongated confidence ellipses shown in Figure 2 further emphasize this correlation. 

If the parameters were to become increasingly correlated, the confidence ellipses would approach a 45 line and it would become impossible to determine a unique set of parameters. As discussed by Fabrics and Renon (1975), strong correlation is common for nearly ideal solutions whenever the two adjustable parameters represent energy differences. 

The maximum temperature cross which can be tolerated is normally set by rules of thumb, e.g., FrSQ,75 °. It is important to ensure that Ft > 0.75, since any violation of the simplifying assumptions used in the approach tends to have a particularly significant effect in areas of the Ft chart where slopes are particularly steep. Any uncertainties or inaccuracies in design data also have a more significant effect when slopes are steep. Consequently, to be confident in a design, those parts of the Ft chart where slopes are steep should be avoided, irrespective of Ft 0.75. 

Different utility options such as furnaces, gas turbines, and different steam levels can be assessed more easily and with greater confidence knowing the capital cost implications for the heat exchanger network. 

The field development plan s prime purpose is to serve as a conceptual project specification for subsurface and surface facilities, and the operational and maintenance philosophy required to support a proposal for the required investments. It should give management and shareholders confidence that all aspects of the project have been... 

In addition, the separator temperature and pressure of the surface facilities are typically outside the two-phase envelope, so that no liquids form during separation. This makes the prediction of the produced fluids during development very simple, and gas sales contracts can be agreed with the confidence that the fluid composition will remain constant during field life in the case of a dry gas. 

From the probability distributions for each of the variables on the right hand side, the values of K, p, o can be calculated. Assuming that the variables are independent, they can now be combined using the above rules to calculate K, p, o for ultimate recovery. Assuming the distribution for UR is Log-Normal, the value of UR for any confidence level can be calculated. This whole process can be performed on paper, or quickly written on a spreadsheet. The results are often within 10% of those generated by Monte Carlo simulation. 

The basic condition of the Standard application - the availability of stable coupled probabilistic or the multiple probabilistic relations between then controlled quality indexes and magnetic characteristics of steel. All the probabilistic estimates, used in the Standard, are applied at confidence level not less than 0,95. General requirements to the means of control and procedure of its performance are also stipulated. Engineers of standard development endeavoured take into consideration the existed practice of technical control performance and test at the enterprises that is why the preparation of object control for the performance of nondestructive test can be done during the process of ordinary acceptance test. It is suggested that every enterprise is operated in correspondence with direct and non-destructive tests, obtained exactly at it, for detailed process chart and definite product type, however the tests have long since been performed after development of the Standard displayed that process gives way to unification. 

As the safety and quality of industrial components, equipments and constructions is correlated with the inspection sensitivity and this is influenced in radiography by the film system class, a continuous supervision of the film systems on the market seems to be urgently necessary. To support the confidence of the film users in the film properties specified by the film manufacturers such a system for quality assurance for industrial x-ray films is proposed by some manufacturers and BAM. This system will be open to all manufacturers, distributers and users of x-ray films. It will deal with all film systems inclusive those which are not specified by a manufacturer as for instance mixed systems. The system for quality assurance will be based... 

We are confident that any user of this combined evaluation technique, as well as the development of future test standards for manual ultrasonic testing will benefit from this result, because it allows a greater flexibility in the applicable method without loosing reliability. Often an expensive production of a reference block can be avoided and therefore testing costs are reduced. Since all calculations are performed by a PC, the operator can fully concentrate on his most important duty scanning the workpiece and observing the A-scan. Additional time will be saved for the test documentation, since all testing results are stored in the instrument s memory (the PC s hard drive) with full link to the Software World (Microsoft Word, Excel, etc.). 

However this is not sufficient to give the customer confidence that a satisfactory quality of NDT will be provided. It is necessary to have a system of quality management and to confirm the effectiveness of its functioning. 

Radiography provides the only means of reliably detecting voids in pre-stressed cable ducts or of detecting loss of section or fracture of eables inside the duets. The maximum thiekness of eonerete whieh ean be radiographed for confident loeation of voids inside ducts is of course dependant on a number of variables, e g. amount of reinforcing bars, size of void in duet etc... 

Fig. X-7. Advancing and receding contact angles of octane on mica coated with a fluo-ropolymer FC 722 (3M) versus the duration of the solid-liquid contact. The solid lines represent the initial advancing and infinite time advancing and receding contact lines and the dashed lines are 95% confidence limits. (From Ref. 75.)...

Eurthemiore, the actual Hamiltonians obtained very closely match tliose obtained via the empirical fitting of spectra This consistency lends great confidence that both approaches are complementary, mutually consistent ways of apprehendmg real infomiation on molecules and their internal dynamics. 

The potential fiinctions for the mteractions between pairs of rare-gas atoms are known to a high degree of accuracy [125]. Flowever, many of them use ad hoc fiinctional fonns parametrized to give the best possible fit to a wide range of experimental data. They will not be considered because it is more instmctive to consider representations that are more finnly rooted in theory and could be used for a wide range of interactions with confidence. 

But decision making in the real world isn t that simple. Statistical decisions are not absolute. No matter which choice we make, there is a probability of being wrong. The converse probability, that we are right, is called the confidence level. If the probability for error is expressed as a percentage, 100 — (% probability for error) = % confidence level. 

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