Matching errors

If there are no false matches and no false non-match errors for the tested database, we define the separation margin s as the difference between the worst (the lowest) between-class comparison score and the worst (the highest) within-class comparison score. 

Figure 8. Comparison scores for iris data in NASK BioBase. 180 (N) genuine and 32220 (N(N-l)) comparisons impostor transactions were used. The average genuine transaction score 0.22, the average impostor transaction score 0.48, the minimal impostor transaction score 0.37, maximal genuine transaction score 0.32, Threshold = 0.35 results in no sample false match and no sample false non-match errors.

Each of the aforementioned features, spatial and spectral, can be independently employed for explosive detection. No detection method is foolproof, but the combination of the two reduces identification uncertainty and matching error. Two approaches to THz image analysis are discussed in Sections 6.1. and 6.2. 

These matching errors are less alarming than they might appear, because all known price information is built into the real yield formula as soon as it is published. Two things really matter, in terms of the achieved real yield relative to the quoted real yield at purchase firstly, the difference between future inflation over the life of the bond and the 3% inflation assumption used in the market convention for calculating yields, and secondly (as with any coupon bond) reinvestment risk. However, we are getting ahead of ourselves—the next section handles the market s yield conventions. 

This discussion may well leave one wondering what role reality plays in computation chemistry. Only some things are known exactly. For example, the quantum mechanical description of the hydrogen atom matches the observed spectrum as accurately as any experiment ever done. If an approximation is used, one must ask how accurate an answer should be. Computations of the energetics of molecules and reactions often attempt to attain what is called chemical accuracy, meaning an error of less than about 1 kcal/mol. This is suf-hcient to describe van der Waals interactions, the weakest interaction considered to affect most chemistry. Most chemists have no use for answers more accurate than this. 

The method of standard additions can be used to check the validity of an external standardization when matrix matching is not feasible. To do this, a normal calibration curve of Sjtand versus Cs is constructed, and the value of k is determined from its slope. A standard additions calibration curve is then constructed using equation 5.6, plotting the data as shown in Figure 5.7(b). The slope of this standard additions calibration curve gives an independent determination of k. If the two values of k are identical, then any difference between the sample s matrix and that of the external standards can be ignored. When the values of k are different, a proportional determinate error is introduced if the normal calibration curve is used. 

Next, by trial and error, we try to find a value for y such that sinh" y matches one of the 17/17 fractions in Table 2.2, say 17/17 = 0.80. This is easily done using either tables of sinh functions or the equation given in Table 2.1. The following results show that it is possible to place y within a range and then narrow that range without much difficulty. Remember, it is the inverse sinh values we are examining ... 

Experienced color matchers can achieve a good color match by trial and error without using any instmmentation. In some cases, however, this technique can be a lengthy process, and should the desired match be outside the color space defined by the available color standards, the technician might spend too much time just to determine that the match is not possible. To get the most cost-effective match using a low metamerism in the shortest possible time, the use of a computet color matching system is preferable. 

Errors due to nonspectral interferences can be reduced via matrix matching, the method of standard additions (and its multivariant extensions), and the use of internal standards. ... 

The corrective action requirements fail to stipulate when corrective action should be taken except to say that they shall be to a degree appropriate to the risks encountered. There is no compulsion for the supplier to correct nonconformities before repeat production or shipment of subsequent product. However, immediate correction is not always practical. You should base the timing of your corrective action on the severity of the nonconformities. All nonconformities are costly to the business, but correction also adds to the cost and should be matched to the benefits it will accrue (see later under Risks). Any action taken to eliminate a nonconformity before the customer receives the product or service could be considered a preventive action. By this definition, final inspection is a preventive action because it should prevent the supply of nonconforming product to the customer. However, an error becomes a nonconformity when detected at any acceptance stage in the process, as indicated in clause 4.12 of the standard. Therefore an action taken to eliminate a potential nonconformity prior to an acceptance stage is a preventive action. This rules out any inspection stages as being preventive action measures - they are detection measures only. 

From the traditional HF/E perspective, error is seen as a consequence of a mismatch between the demands of a task and the physical and mental capabilities of an individual or an operating team. An extended version of this perspective was described in Chapter 1, Section 1.7. The basic approach of HF/E is to reduce the likelihood of error by the application of design principles and standards to match human capabilities and task demands. These encompass the physical environment (e.g., heat, lighting, vibration), and the design of the workplace together with display and control elements of the human-machine interface. Examples of the approach are given in Wilson and Corlett (1990) and Salvendy (1987). 

Another TSK combination (precolumn -I- PWM -I 6000 -I 5000 -I- 4000 -I-3000) was tested on differences in separation performance between individual narrow distributed samples and mixtures of several narrow distributed samples. The result is summarized in Eig. 16.31 within experimental error the summed chromatograms (theory) of four narrow distributed glucans (dextran) match perfectly with the experimentally determined chromatogram of the mixture. The (theory/experimental) ratio, plotted for quantification of the match, in-... 

This is also a trial and error solution following the pattern of (A), except capacities are assumed and the pressure drops are calculated to find a match for the given conditions of inlet pressure, calculating back from the outlet pressure. 

This is greater than the selected pressure of 110 psia, therefore, for a binary the results will work out without a trial-and-error solution. But, for the case of other mixtures of 3 or more components, the trial-and-error assumption of the temperature for the vapor pressure will require a new temperature, redetermination of the component s vapor pressure, and repetition of the process until a closer match with the pressure is obtained. 

A trial-and-error calculation is necessary to solve for W until a value is found from the In Wj/W equation above that matches the xq avg which represents the required overhead distillate composition. By material balance ... 

A. Standard series method (Section 17.4). The test solution contained in a Nessler tube is diluted to a definite volume, thoroughly mixed, and its colour compared with a series of standards similarly prepared. The concentration of the unknown is then, of course, equal to that of the known solution whose colour it matches exactly. The accuracy of the method will depend upon the concentrations of the standard series the probable error is of the order of + 3 per cent, but may be as high as + 8 per cent. 

It is desirable for the record to have an objective statement of the nature and degree of color deterioration. The simplest, but least desirable, method is comparison of sample color with color charts or plates such as those used in the Munsell system, Ridgeway s color standards, or the Maerz and Paul dictionary of color. Such a method is limited in value because of the difficulty of obtaining true color matches, and because of variations due to human error. The use of color charts or plates may be much improved in the Munsell system by employing a disk colorimeter (29). Kramer and Smith (21) have pointed out that the results obtained in its application to foods are sometimes difficult to explain and compare, and that the method requires special training of the operator and is tedious and cumbersome. 

There have been few discussions of the specific problems inherent in the application of methods of curve matching to solid state reactions. It is probable that a degree of subjectivity frequently enters many decisions concerning identification of a best fit . It is not known, for example, (i) the accuracy with which data must be measured to enable a clear distinction to be made between obedience to alternative rate equations, (ii) the range of a within which results provide the most sensitive tests of possible equations, (iii) the form of test, i.e. f(a)—time, reduced time, etc. plots, which is most appropriate for confirmation of probable kinetic obediences and (iv) the minimum time intervals at which measurements must be made for use in kinetic analyses, the number of (a, t) values required. It is also important to know the influence of experimental errors in oto, t0, particle size distributions, temperature variations, etc., on kinetic analyses and distinguishability. A critical survey of quantitative aspects of curve fitting, concerned particularly with the reactions of solids, has not yet been provided [490]. 

The first example is the 4-m class William Herschel telescope, at la Pakna, whose optical specifications, drafted by D. Brown, were expressed in terms of allowable wavefront error as a function of spatial frequencies matching those of atmospheric turbulence. 

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