Mathematical apparatus of quality assessment of complex systems operation: methods and algorithms

Kamil Z. Biliatdinov

Abstract


The article proposes new methods of assessment of quality and effectiveness of functioning of complex systems. The methods are developed for the purpose of evaluation and recording of the specificity of functioning of different systems, moreover, for conducting assessment in the conditions of increasing volume of various sources of information together with stochastic character of dynamics of structured and unstructured data about complex systems. The article also presents a model and formulas of control algorithms in complex systems, where managerial decisions are made on the basis of quality assessment of functioning of complex systems and (or) their subsystems (elements) and taking into consideration influence of external environment. The modified DEA method used for assessment of systems effectiveness presents a combination of a classical DEA method, calculation of correlation of dependence of indices’ values and application of veto coefficient. The article presents the directions of improvement of methods for calculating the probabilistic characteristics of complex systems of various physical nature based on the application of the methodology for assessing the probability of failure of a given number of elements of a complex system, depending on the probability of failure one element in its composition, and methods for assessing the probability of achieving the goal of functioning of a complex system, depending on time characteristics and the number of failures that occur during operation. In each technique, on the basis of a systematic approach, a sequence for assessing the corresponding probabilistic characteristics has been developed for rational implementation in computer programs. Methods of calculation of complex quality indices include basic formulas and formulated conditions of their application. The proposed variant of presenting methods and algorithms allows to maximum rationally use them in software for assessment of effectiveness and quality of complex systems.


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References


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