Ensuring functional stability of the information system with limited initial information about determining random values

Abstract

Ensuring functional stability, reliability and effective management in information systems is a complex and complex scientific task. At the stage of design and construction of information systems, reliability indicators are interpreted as characteristics of the created probabilistic mathematical models of objects, and at the stage of experimental development, testing and operation, the role of reliability indicators is performed by statistical assessments of the corresponding probabilistic characteristics. When assessing the reliability indicators of information systems, the necessary initial data for a priori probabilistic calculations are often lacking, and the statistical assessment is hampered by a small volume of tests, according to which it is possible to determine only the estimates of the moments of determining random variables of the process of functioning of information systems or its components (mathematical expectations and variances of mean time between failures, recovery time, standby time, etc.). However, in such a situation, it is necessary to substantiate some characteristics of the information system, for example, a reserve of time, guaranteed exact boundaries of the probability of system uptime and the availability factor. When obtaining specific estimates, the minimum a priori information is used, which corresponds to a large number of real situations when assessing the reliability of information systems with time redundancy in the process of design, testing and operation. This article highlights various types of functionals that characterize the efficiency of an information system, under conditions of incomplete a priori information about the distribution function of determining random variables, through which the main indicators of the reliability of information systems are expressed, an analytical method is proposed and substantiated for finding distribution functions that deliver the greatest or least linear value. or linear fractional functionals under moment constraints on variable distribution functions. The method is based on identifying the limiting distribution functions, constructing the corresponding limiting polynomials, and solving special inequalities.