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26 calculates the overall ranking of the test methods by multiply- The ranking is determined using pairwise comparisons of ing the priority matrix of the methods by the priority vector the characteristics (level 2) and the test methods (level 3). The of the characteristics and displays it in a separate interface first pairwise comparison is conducted among the character- window (Figure 7b). istics in the second level using the comparison scale given in The program also has features that enable the user to: Table 23 and results are listed in Table 24. The number in each (1) extract the priority vectors and the overall ranking from a cell of the table is a weight that reflects the relative importance text file and (2) examine the influence of changes in the weights of the characteristic in the horizontal list compared with the or importance of one or more of the characteristics without one in the vertical list. If this number is higher than one, it changing the remaining ones (i.e., the software has to be exe- means that the characteristic listed in the row is more impor- cuted several times with just one matrix change) without a tant than the characteristic listed in the column. For example, need to re-enter the unchanged matrices. accuracy is considered three times as important as repeatability and reproducibility and five times as important as all the other characteristics. All other characteristics are considered to be AHP Ranking of Test Methods equal in their importance. The ranking of test methods depends on the desired out- Weights that compare test methods based on each of the comes from the test. This section provides an example of how characteristics are based on the measurements and data pre- the AHP can be used to determine the ranking of test methods sented in Chapter 2; these are listed in Table 25. The compar- ison scale values shown in Table 28 were selected based on the measuring fine aggregate angularity, and texture and shape of importance of each of the desired characteristics as follows: coarse aggregates. The first level in AHP is the overall goal, which is the satis- Repeatability/Reproducibility: Repeatability and reproduc- faction with test methods. The second level consists of the cri- teria elements by which this satisfaction is measured. These ibility are categorized into three main categories as Levels 1, 2, and 3. Levels 1 and 2 can be considered as acceptable scales characteristics are repeatability, reproducibility, accuracy, price, and some of the test methods can move from Level 2 to 1 readiness for implementation, ability to interpret data and with some minor improvements. However, Level 3 is un- results, ease of use by technician, portability, and applicability acceptable because it covers high ranges of coefficient of vari- to measure different aggregate types and sizes. The third level ations. Therefore, the difference between Levels 3 and 2 is less consists of the test methods that are under evaluation. Figure 8 desirable than the difference between Levels 1 and 2. illustrates a basic hierarchy for the ranking process. Accuracy: Accuracy of test methods was assessed based on the correlation between the test method and a reference method. The scale for accuracy was established by dividing Satisfaction with Method (Overall Objective) the R2 values into four categories as shown in Table 26. The ratio between the numbers assigned to each accuracy group is then used to assign the accuracy scale. Price: The price scale is assigned taking into consideration that the lowest price of a test method is about $250, while Reproducibility Interpret Data the highest price is about $45,000 ($250 is taken as the basis Repeatability Applicability Ease of Use Portability Readiness Accuracy for the cost ratio). Price Table 23. Rating scale. Verbal Judgment of Preference Numerical Rating Equally Important or Preferred 1 Weakly More Important 3 Moderately More Important 5 Strongly More Important 7 Absolutely More Important 9 AIMS Method Method Method Weakly Less Important 1/3 1 2 n Moderately Less Important 1/5 Strongly Less Important 1/7 Figure 8. An example of basic analytical hierarchy Absolutely Less Important 1/9 process (AHP).