Hierarchy, analytical

Weighted scoring methods, such as Kepner-Tregoe Decision Analysis and the Analytical Hierarchy Process (AHP)... 

Saaty T.L. (1980) The Analytic Hierarchy Process. McGra.vf-HiR, Hew York. 

Table 8.69 Hierarchy of analytical methods with respect to accuracy...

In general, it is well-known that analytical results can be assessed and how it is done in detail. On the other hand, an assessment of analytical operations, carried out within the hierarchy of analytical techniques, methods, procedures, and SOPs, takes place scarcely according to standardized viewpoints. 

Quantification Precision can be quantified by suitable dispersion characteristics. It is proposed to characterize precision by standard deviation, see Eqs. (4.12)-(4.14) and relative standard deviation, see Eq. (4.15) (Fleming et al. [1996b] Prichard et al. [2001]). Because of some uncertainty, the characterization of analytical proceedings in their hierarchy (see Fig. 7.1) and of analytical results, respectively, will be considered in detail. 

Avoidance of unphysical, analytical pathologies intrinsic to a particular truncation of the hierarchy of sophistication levels in that theory ... 

Whereas the microprocessor controls an individual basic operation, the central computer, which has all the analytical procedures held in its memory, controls the particular analytical procedure required. At the appropriate time, the central computer transmits the relevant set of parameters to the corresponding units and provides the schedule for the sample-transport operation. All units are monitored to ensure proper functioning. If one of the units signals an error, a predetermined action, such as disposing of the sample, is taken. The basic results from the units are transferred to the central computer, the final results are calculated, and the report is passed to the output terminal. These results can also be transmitted to other data processing equipment for administrative or management purposes. The central control is, therefore, the leading element in a hierarchy of... 

Figure 1.2 — Technical hierarchies of analytical information. For details, see text.

Figure 1.3.A shows the scheme for another analytical information hierarchy that is complementary to the previous ones. Thus, gravimetries, titrimetries, classical qualitative analyses and sensors provide onedimensional information of the form F = where x is the signal concerned. On the other hand, instrumental techniques provide two-dimensional information that can be of two types depending on whether the signal (x) is combined with an instrumental parameter (y), time (f) or space (s). Some modem analytical techniques (several of which use hybrid instruments) furnish three-dimensional information by combining signals with one or two instrumental parameters (y, z), time and space. The great...

A typical set-up is shown in Fig. 6. The analytical instruments are coupled to a mainframe computer over a decreasing hierarchy of microcomputers and instrument processors. Figure 7 shows schematically the information flows and storage of a... 

FIGURE 9 Hierarchy of, relationship between, and objectives and requirements for prevalidation [106], validation [62,63, 68], and standardization of analytical methods [62, 63, 67, 68,75,84] RSD = relative standard deviation, CV = coefficient of variation, SOP = standard operating procedure. 

In such a representation of an infinite set of master equations for the distribution functions of the state of the surface and of pairs of surface sites (and so on) will arise. This set of equations cannot be solved analytically. To handle this problem practically, this hierarchy must be truncated at a certain level. In such an approach the numerical part needs only a small amount of computer time compared to direct computer simulations. In spite of very simple theoretical descriptions (for example, mean-field approach for certain aspects) structural aspects of the systems are explicitly taken here into account. This leads to results which are in good agreement with computer simulations. But the stochastic model successfully avoids the main difficulty of computer simulations the tremendous amount of computer time which is needed to obtain good statistics for the results. Therefore more complex systems can be studied in detail which may eventually lead to a better understanding of such systems. 

The linear operators on a vector space forms themselves a vector space, called operator space. In this context, the original vector space is called the carrier space for the operators. The operator space is sometimes normed, but usually not. Since operator products are defined, we have here a vector space where a product of vectors to give a vector is defined. Such a vector space is also called a linear algebra. Operations and functions can be defined in the operator space thus we can define superoperators for which the operator space is the carrier space. The hierarchy is not usually driven any further. Functions are usually named in analogy to their analytical counterparts. To be specific, assume that A has a spectral resolution... 

Chapter 4 covers the site selection and site controlling phase. Consequently, it deals with the assessment of individual production sites based on primarily qualitative criteria. Alternative Multiple Attribute Decision Analysis methods are reviewed and a decision support model employing the Analytic Hierarchy Process, which can be used both for site selection problems and as a controlling tool to perform site portfolio rankings of entire production networks, is proposed. Experiences from application in industry are reported. 

Analytic Hierarchy Process Eigenvector Method (cf. Saaty 1980, pp. 165-197)... 

The objective was to develop a site assessment model based on the Analytic Hierarchy Process that can be used both for site selection and site ranking/controlling purposes. While the different application situations to some extent require different criteria the intention was to develop a model as uniform as possible to achieve consistency in site strategy processes. 

Belton V (1986) A comparison of the analytic hierarchy process and a simple multi-attribute value function. European Journal of Operational Research 26 7-21... 

Dyer JS (1990) Remarks on the Analytic Hierarchy Process. Management Science 36 249-258... 

Fong CO, Srinivasan V (1981) The Multiregion Dynamic Capacity Expansion Problem, Part I. Operations Research 29 787-799 Forman EH (1990) Multi criteria decision making and the analytic hierarchy process. In Bana e Costa CA (ed) Readings in Multiple Criteria Decision Aid. Springer, Berlin et al., pp 295-318 Forman EH, Gass SI (2001) The analytic hierarchy process - an exposition. Operations Research 49 469-486... 

Golden BL, Wasil EA, Levy DE (1989) Applications of the Analytic Hierarchy Process A categorized, annotated bibliography. In Golden BL, Wasil EA, Harker PT (eds) The Analytic Hierarchy Process. Springer, Berlin et al., pp 37-58... 

Haines LM, (1998) Interval Judgements in the Analytic Hierarchy Process A Statistical Perspective. In Stewart TJ, van den Honert RC (eds) Trends in Multicriteria Decision Making. Springer, Berlin et al., pp 87-105... 

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