Ideal Value Method

In this method, criteria values are scaled using their ideal values as given in the following  

Note that the scaled criteria values will always be 1, and all the criteria have been changed to maximization. The best value of each criterion is 1, 

Note that the scaled criteria values (r j) will always be 1, and all the criteria have been changed to maximizahon. The best value of each criterion is 1, but the worst value need not necessarily be zero. In the next approach, all criteria values will be scaled between 0 and 1, with 1 for the best value and 0 for the worst. 

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Scaled Criteria Values by the Ideal Value Method (Example 6.5)... 

The scaled criteria values, using the Ideal Value method are computed using Equation 6.5 for TCO and Equation 6.4 for Service and Experience. They are given in Table 6.20. 

Weighted methods for ranking alternatives, such as the rating method and Borda method, require that the criteria values (/jy) are properly scaled so that they are of similar magnitudes. Otherwise, the rankings will be incorrect. There are several methods available for scaling criteria values, such as ideal value method, linear normalization, and vector normalization using Lp norms. 

The ideal values for the three criteria are 65,000, 10, and 9, respectively. Of course, the ideal solution is not achievable. Using the ideal value method, the scaled criteria values are computed using Equation 2.6 for TCO and Equation 2.5 for service and experience. They are given in Table 2.4. 

A visual inspection of a two-sample chart provides an effective means for qualitatively evaluating the results obtained by each analyst and of the capabilities of a proposed standard method. If no random errors are present, then all points will be found on the 45° line. The length of a perpendicular line from any point to the 45° line, therefore, is proportional to the effect of random error on that analyst s results (Figure 14.18). The distance from the intersection of the lines for the mean values of samples X and Y, to the perpendicular projection of a point on the 45° line, is proportional to the analyst s systematic error (Figure 14.18). An ideal standard method is characterized by small random errors and small systematic errors due to the analysts and should show a compact clustering of points that is more circular than elliptical. 

As we shall have occasion to note in dealing with solutions, the composition of the surface phase is very different from that of the bulk liquid. When a liquid interface is newly formed the system is unstable until the surface phase has acquired its correct excess or deficit of solute by diffusion from or into the bulk of the solution. This process of diffusion is by no means instantaneous and, as has been observed in discussing the drop weight method, several minutes may elapse before equilibrium is established. In the ripple method the surfece is not renewed instantaneously but may be regarded as undergoing a series of expansions and contractions, thus we should anticipate that the value of the surface tension of a solution determined by this method would lie between those determined by the static and an ideal dynamic method respectively. 

In order to use Donnelly s (11,12) method, we must convert the observed values of cr and d In c/d(r2) in nonideal solutions to ideal values. Then we can use the ideal value of d In c/d(r2) to calculate MWD s as has been described previously here and elsewhere (11, 12). One must also remember to use Equation 49 for non-sector-shaped centerpieces. 

Figure 6-3 shows a method for setting specihcations. The list of needs gives a first list of specifications. Quantify the specifications with metrics more about these in a moment. Then benchmark compare your ideas with the competition. Finally discuss what the ideal values would be for the metrics, and which would be just acceptable use these values to set the list of specifications. 

There exists a number of chemical and physical (mainly spectrometric) methods for determining the concentration of hydroxyl groups. This data combined with the molecular weights of HTP gives their functionality. The number of OH groups per molecule of HTP often differs from the ideal value 2 and may be higher or lower (cf., e.g., Ref.117)). The existence of side reactions in the initiation and recombination steps is the main reason. 

Atomic-Weight Determinations by the Gas-Density Method. If a sufficiently careful measurement of the density of a gas is made, under conditions such that the gas obeys the perfect-gas law, a good value for the molecular weight of the gas can be obtained, which can be used to find the atomic weight of one of the elements in the gas. The way to determine this ideal value of the density of a gas is to determine the density of the gas at smaller and smaller pressures, and to extrapolate to zero pressure-all gases approach the perfect-gas law in their behavior as the pressure becomes very low. This method of atomic-weight determination has been used extensively in recent vears by the Spanish cheijaist E. Moles. 

Since two liquid phases coexist at equilibrium only in systems that exhibit significant departure from ideality (Chapter 1), the / -values for three-phase equilibrium must be calculated using methods that are capable of predicting this non-ideality. The method based on liquid activity coefficients, described in Chapter 1, is recommended for this purpose ... 

The method was successfully applied to insulin [125] and actinidin [139] and a number of other proteins [126]. For insulin, the final R for 1.5 A resolution was 0.11 for some 1077 atoms and 11 890 reflections. For actinidin, the final R for 10-1.7 A resolution was 0.17 for some 1821 atoms and 23390 reflections. The standard deviation in bond lengths from ideal values was 0.014 A. 

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