Ranking the Four Factors

EXERCISE 3.17 Locate the most acidic proton in the following compound  

Now that we have seen each of the four factors individually, we need to consider what order of importance to place them in. In other words, what should we look for first And what should we do if two factors are competing with each other  

In general, the order of importance is the order in which the factors were presented in this chapter. Whenever you need to determine which proton is the most acidic, you need to compare all of the conjugate bases and ask which one is the most stable. To determine stability, here is what you should look for, in this order  

What atom is the charge on (Remember the difference between comparing atoms in the same row and comparing atoms in the same column.) 

Are there any resonance effects making one conjugate base more stable than the others  

Answer It is important to recognize where all of the protons (hydrogen atoms) are. If you cannot do this, then you should review Chapter 1, which covers bond-line drawings. Only one proton can leave behind a negative charge in an sp orbital. All of the other protons would leave behind a negative charge on either sp or sp hybridized orbitals. So the most acidic proton is 

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Using these four factors to evaluate each chosen option will result in each option receiving a score. This score will rank the options from highest to lowest. This will produce an order for further exploring these options. 

Warnings (i) The Tpq do not form a second-rank tensor and so unitary transformations must be carried out using the four-index notation Tijki. (ii) The contraction of TiJki may be accompanied by the introduction of numerical factors, for example when 7(4) is the elastic stiffness (Nye (1957)). 

The rank histogram shows that the sum of ranks does not change evenly, so that we can accept the solution to include the following four factors into the basic design of experiment X3, X1 X2, and X5. A more cautious approach to drawing conclusions suggests a more detailed check of all six factors in an active experiment for screening factors such as, the method of random balance. 

A study about the effect of twelve factors of material preparation with regard to fiber tensile strength was done in the textile industry. Four researchers were asked about the prior ranking of the factors. The rank matrix obtained on the basis of a research poll is shown in Table 2.14. Check the concordance of researchers opinions and choose the significant factors for the next step of experimental research. 

This module evaluates each of the 66 factors, and ranks them according to their impact on plant performance. Factors are classified into one of four categories ... 

The method for finding outliers takes averages around two positions in each auto-correlation and calculates the medians from the distribution of values over the batches. The first position is at zero time-lag where a single, spurious high count distorts the mean squared value. The second position is at two-thirds of the maximum lag where the correlation curve has decayed to its value in the tail and a train of non-zero counts tends to extend the tail. The four median values then are used to form threshold criteria to remove batches that contain auto-correlations that exceed the medians by a factor greater than the ratios of median values to the lowest ranked members. 

Similarly, the spUl numbers and spill amount of the chemicals were ranked by simple numbers. The sum of the ranking for each of the four categories (spill numbers, spill volume, aquatic toxicity, and mammalian toxicity) was simply added to yield an overall value. The vine for spill frequency was added in twice (as a square) to ensure that this factor was rated higher than other factors. These overall values are then directly related to the order of priority, lowest number first. 

For the present context, the hierarchical structure for the AHP is shown in Fig. 3.13. On the top level, the business unit strategy, product characteristics and customer needs are rated against each other with respect to the overall goal. Thereafter, on the next lower level, the different factors are compared with regard to the corresponding factor of the next higher level. For example, the diverse customer needs are ranked. Finally, a pairwise comparison of the four value... 

More than 90 chemicals are considered TICs, and they are grouped as high, medium, and low hazards based on the combination of toxicity, volatility, and amount being produced, stored, and transported annually. Each TIC is ranked according to a hazard index (HI). The HI is the product of four factors, numerically ranked between 1 and 5 according to the ranking scheme in Table 2.6. 

In all areas of risk assessment the confoxmding factor is perception. However rigorously a cost benefit analysis is xmdertaken to reduce the bandwidth of uncertainty, tiie decision to proceed in a chosen direction may be made or will certainly be influenced by how the risk is perceived. An oft-quoted study by Slovic et al. asked four groups of people to rank in order of perceived risk 30 activities and technologies. The results from six of the elements of the study are listed in Table 5.1.3. 

Selection of the risk factor(s) to control, and control measures to try, can be based on numerous criteria. An example of one method involves ranking aU of the ergonomic risk factors and possible controls according to how well they meet these four criteria ... 

Next, the buyer repeats the above procedure to determine the pairwise rankings and the adjusted weights of the suppliers (last row in each table), for each of the four performance factors. These are shown in Tables 4.5, 4.6, 4.7, and 4.8. 

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