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2016/3
Analytical and discrete methods of research of failure intensity in gas transport
Geosciences

Authors: Vladimir N. RUSEV graduated from Lomonosov Moscow State University specializing in probability theory and mathematical statistics in 1997. He is senior lecturer of the Department of Higher Mathematics of Gubkin Russian State University of Oil and Gas (National Research University). The focus of his academic interests is information theory, applied mathematical statistics and theory of reliability. He is author of 15 scientific publications including 3 teaching aids. E-mail: vnrusev@yandex.ru
Alexandr V. SKORIKOV graduated from Rostov State University in 1971. He is Candidate of Physical and Mathematical Sciences, associate professor of the Department of Higher Mathematics of Gubkin Russian State University (National Research University) of Oil and Gas. His scientific interests are fractional derivatives and integrals, operators of potential type and functional spaces, theory of reliability. He has published over 30 works including 5 teaching aids. E-mail: skorikov.a@gubkin.ru

Abstract: Reliability indicators of restorable systems and their components, depending on the statistical characteristics estimations based on real operational data, are studied. It is assumed that the objects entire life cycle is described by the law of WeibullGnedenko distribution. The research technique of reliability indicators of restorable systems and their components is presented. It takes into account the dependence of these indicators on time and is based both on analytical and discrete methods. The advantages of the considered discrete method include its universality, simplicity of algorithms and calculations. This work is focused on further realization of mathematical models and methods as unique informational and analytical software. The so-called moments problem relevant for the solution of reliability problems has been analyzed. Examples of processing of real statistical data on failures of technologically active elements in gas supply system are considered

Index UDK: 519.218.4:622.691.4

Keywords: reliability indicators, failure rate, failure intensity, renewal equation, distribution of Weibull-Gnedenko, finite element method, moments problem

Bibliography:
1. Grigoriev L., Kucheryavy V., Rusev V., Sedyh I. Formation of estimates of reliability indicators for active elements in gas transport systems on the basis of refusals statistics. Journal of Polish Safety and Reliability Association, Summer Safety and Reliability Seminars. Vol. 5, no. 1-2, 2014.
2. Rossiyskaya gazovaya entsiklopediya/Pod red. R. Vyakhireva. M.: Bol’shaya Rossiyskaya entsiklopediya, 2004 (slovarnaya stat’ya Nadezhnost’ sistem gazosnabzheniya” — M.G. Sukharev) (In Russian).
3. Polovko A.M., Gurov S.V. Osnovy teorii nadezhnosti. 2-e izd., pererab. i dop. SPb.: BKhV-Peterburg, 2006, 704 p. (In Russian).
4. Sukharev M.G. Modeli nadezhnosti markovskogo tipa s prilozheniyami k neftegazovomu delu. Uchebnoe posobie. M.: Izdatel’skiy tsentr RGU nefti i gaza imeni I.M. Gubkina, 2012, 131 p. (In Russian).
5. Rusev V.N., Sкоriкоv А.V. Аnаliz elеmеntоv sistеm gаzоsnаbzhеniya s pоmоshch’yu mеtоdа prоizvоdyashchih funкtsiy mоmеntоv. Trudy RGU nefti i gaza imеni I.М. Gubкinа [Proceeding of Gubkin Russian State University of Oil and Gaz], 2016, no. 1 (282), p. 78-88 (In Russian).
6. Bahvalov N.S., Zhidkov N.P., Kobelkov G.M. Chislennye metody. M.: Binom. Laboratoriya znaniy, 2003, 602 p. (In Russian).
7. Strang G., Fix G. An Analysys of the Finite Element Method. Prentice-Hall, INC. Englewood Cliffs, N.J. 1973. (Russ. ed.: Strang G., Fix G. Teoriya metoda konechnyh elementov. M.: Mir, 1977, 351 p.).
8. Strelyaev Y.M., Klimenko M.I. Primenenie metoda konechnyh elementov k resheniyu integral’nyh uravneniy Volterra vtorogo roda. Visnik ZNU. Fiziко-mаtеmаtichni nаuкi, 2011, no. 2, p. 131-135 (In Russian).
9. Russ. ed.: Cox D.R., Smith W.L. Teoriya vosstanovleniya. М: Sоvеtsкое rаdio, 1967, 292 p.
10. Grigor’ev L.I., Mikova E.S., Rusev V.N. Osobennosti postroeniy monitoringovikh system i otsenok pokazateley proizvodstvennykh protsessov dlya avtomatizirovannogo dispetcherskogo upravlenia v neftegazovom komplexe. Avtomatizatsiya, telemehanizatsiya i svyaz’ v neftyanoy promyshlennosti, 2014, no. 9, p. 7–12 (In Russian).
11. Rеvаzоv А.М., Lеоnоvich I.А. Rаzrаbоtка sstеariеv rаzvitiya аvariynyh situаtsiy nа коm-prеssоrnyh stаntsiyah маgistrаl’nyh gаzоprоvоdоv. Trudy RGU nefti i gaza imеni I.М. Gubкinа [Proceeding of Gubkin Russian State University of Oil and Gaz], 2015, no. 4 (281), p. 78-88 (In Russian).

2016/1
Аnalysis of elements of gas supply systems by method of moment generating functions
Geosciences

Authors: Vladimir N. RUSEV graduated from Moscow State University in the field of probability theory and mathematical statistics in 1997. He is senior lecturer of the Department of Higher Mathematics of Gubkin Russian State University (National Research University) of Oil and Gas. The focus of his academic interests is information theory, applied mathematical statistics and theory of reliability. He is author of more than 10 scientific publications including 3 teaching aids. E-mail: vnrusev@yandex.ru
Alexandr V. SKORIKOV graduated from Rostov State University in 1971. He is Candidate of Physical and Mathematical Sciences, associate professor of the Department of Higher Mathematics of Gubkin Russian State University (National Research University) of Oil and Gas. His scientific interests are fractional derivatives and integrals, operators of potential type and functional spaces, theory of reliability. He has published over 30 works including 5 teaching aids. E-mail: skorikov.a@gubkin.ru

Abstract: The relationship between indicators of reliability of non-renewable and recove-rable elements and systems is studied. Technologically active elements of the gas supply system are considered from the perspective of both repairable and non-repairable elements. It is assumed that the entire life cycle of the facilities is described by the power-law distribution of Weibull-Gnedenko. Using this distribution semi-dependences have been obtained. These can be used for engineering calculations on the basis of failures statistics. An example of the processing of real operational data on failures is considered

Index UDK: УДК 519.873+622.691.4.07

Keywords: reliability, failure rate, failure flow parameter, moment-generating function, Weibull-Gnedenko distribution

Bibliography:
1. Grigor’ev L.I., Kalinin V.V., Rusev V.N., Sedykh I.A. Matematicheskoe obespechenie podsistemy otsenki i monitoringa nadezhnosti ASDU v transporte gaza. Avtomatizatsiya v promyshlennosti, 2010, no. 12, p. 11-15. (In Russian).
2. Rusev V.N. Primenenie raspredeleniya Veybulla—Gnedenko dlya opisaniya etapov zhiznennogo tsikla gazoperekachivayushchikh agregatov pri upravlenii tekhnicheskim sostoyaniem gazotransportnykh system. Promyshlennyy servis, 2013, no. 1, p. 17-22 (In Russian).
3. Polovko A.M., Gurov S.V. Osnovy teorii nadezhnosti. 2-e izd., pererab. i dop. SPb., BKhV-Peterburg, 2006, 704 p. (In Russian).
4. Krasnov M.L. Integral’nye uravneniya: Vvedenie v teoriyu, Moscow, Editorial URSS, 2010, 304 p. (In Russian).
5. Rossiyskaya gazovaya entsiklopediya. Pod red. R.I. Vyakhireva. M.: Bol’shaya Rossiyskaya entsiklopediya, 2004 (slovarnaya stat’ya „Nadezhnost’ sistem gazosnabzheniya”, M.G. Sukharev) (In Russian).
6. Lavrent’ev M.A., Shabat B.V. Metody teorii funktsiy kompleksnogo peremennogo, Moscow, Nauka, 1987, 688 p. (In Russian).
7. Sukharev M.G. Modeli nadezhnosti markovskogo tipa s prilozheniyami k neftegazovomu delu. Uchebnoe posobie, Moscow, Izdatel’skiy tsentr RGU nefti i gaza imeni I.M. Gubkina, 2012, 131 p. (In Russian).
8. Kendall M.A., Stuart A. The Advanced Theory of Statistics. Volume 1. Distribution Theory. 2 th ed. London, Charles Griffin &Company Limited, 1961. (Russ.ed.: Kendall M., Stuart A. Teoriy raspredeleniy. Moscow, Nauka, 1966, 588 p.)
9. Rusev V.N. Aktual’nost’ teoreticheskogo issledovaniya raspredeleniya Veybulla—Gnedenko dlya rascheta otsenok tekhnologicheskoy nadezhnosti neftegazovogo oborudovaniya, Avtomatizatsiya, telemekhanizatsiya i svyaz’ v neftyanoy promyshlennosti, 2013, no. 11, p. 46-49. (In Russian).
10. Gradshteyn I.S., Ryzhik I.M. Table of Integrals, Series, and Products. 7 th ed. Oxford, Elsevier Inc, 2007. (Russ.ed.: Gradshteyn I.S., Ryzhik I.M. Tablitsy integralov, summ, ryadov i proizvedeniy. SPb, BKhV-Peterburg, 2011, 1232 p.)
11. Beichelt F., Franken P. Reliability and Maintenance. Mathematical Method. Berlin, Veb Verlag Technik, 1983. (Russ. ed. Beichelt F., Franken P. Nadejnost’ i tehnicheskoe obslujivanie. Matematicheskiy podhod. Moscow, Radio i svyaz’, 1988, 392 p.)