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Elements of mathematical reliability theory

ДВС.3.06.03.02

Вибіркова дисципліна для ОП

First

2022/2023

8 Semester

3

PLO21.3. Understand the fundamental areas of mathematics and computer science, to the extent necessary for learning mathematical disciplines, applied disciplines and using their methods in a chosen profession. PLO22.3. Understand the main areas of mathematical logic, theory of algorithms and computational theory, programming theory, probability theory and mathematical statistics. PLO23.3. Be able to use professional knowledge, skills and abilities in the field of fundamental sections of mathematics and computer science for research of real processes of different nature. PLO24.3. Be able to independently analyze the relevant subject area, be able to develop mathematical and structural algorithmic models.

To successfully learn the discipline “Elements of mathematical reliability theory” the student should satisfy the following requirements. They know (a) fundamentals of mathematical methods for construction, verification and investigation of qualitative characteristics of deterministic and stochastic mathematical models; (b) classical methods of Calculus, Algebra and Probability Theory. They can (a) investigate qualitative characteristics of available mathematical models; (b) apply classical methods for solving applied problems in deterministic and stochastic models. They should be able to (a) apply classical methods of Calculus and Probability Theory; (b) seek information in open sources and properly analyze it.

Poisson flow. Characteristic property of exponential distribution. The main characteristics of reliability. Recovery processes and their application in reliability theory. Alternating processes. Statistical estimates for reliability test plans of type [N, B, R], [N, B, T]. Method of simulation modeling in reliability theory. Reliability of systems with independent elements. Scheme of death and reproduction and its application in the theory of reliability. Backup systems without recovery. Duplicate with recovery. General redundant system with recovery.

1. Gnedenko B.V.,Ushakov I.A. Probabilistic mеtods in reliability, New York, Wiley, 1995. - 515 p. 2. Gnedenko B. V., Belyayev Yu. K., Solovyev A. D., Mathematical Methods of Reliability Theory, Academic Press, 1969. -471 p. 3. Barlow R.E., Proschan F., Stistical theory of Reliabiluty and life testing probability models, Holt, Rinehart and Winston, Inc., 2008. -328 p. 4. Томаschevsky V.М. Моdelyuvanya system. Кyiv: BHV, 2005. . -352 p. 5. Law A.M., Kelton W.D. Simulation modeling and analysis, Osborne, 2001. - 848 p.

Lectures, seminars, consultations, test works, independent work.

Intermediate assesement: Maximum number of points that can be obtained by a student: 100 points: 1. Test No1: 30/18 points. 2. Test No 2: 30/18 points. 3. Test No 3: 40/24 points. Final assessment (in the form of test): Not provided

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