Radiotekhnika
Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS


Тел.: +7 (495) 625-9241

 

Investigation of semi-Markov models of special equipment operation

DOI 10.18127/j19997493-201901-01

Keywords:

R.Z. Khairullin – Dr.Sc.(Phys.-Math.), National Research Moscow State University of Civil Engineering
E-mail: zrkzrk@list.ru
I.A. Nikitina – Ph.D.(Eng.), Main scientific metrology center Ministry of Defense RF
E-mail: nikitina-irina78@mail.ru


A method for assessing the applicability of stationary semi-Markov models for the problems of efficient operation of special equipment is proposed. The methodology is based on the Euler method of finding the fundamental system of solutions for a system of ordinary differential equations with constant coefficients based on the calculation of all eigenvalues (spectrum) and eigenvectors of the system matrix. It is shown that for the classical 6 order operating model for a typical range of changes in the basic parameters of the model (probability of failure, false failure and undetected failure), the characteristic equation of the system has two invariant eigenvalues and four eigenvalues that are functions of the model parameters. The results obtained allow us to estimate the degree of influence of the parameters of semi-Markov models of operation on the convergence of the solution of the dynamic model to the solution of the stationary model. The results of mathematical modeling are given.

The technique presented in the article is applicable to constructing convergence estimates for systems and mathematical models de-scribed by linear differential equations with constant coefficients of arbitrary order, including operating models of control and measuring equipment used in the construction and housing and utilities sectors.

References:
  1. Arbuzov V.I., Mrochek Zh.A., Panov A.N., Xarton V.L. Osnovy’ sistemy’ menedzhmenta kachestva mashinostroitel’nogo predpriyatiya. M.: Znanie. 2001.
  2. Vasil’ev A.S., Dal’skij A.M., Klimenko S.A., Polonskij L.G., Xejfecz M.L., Yashhericzy’n P.I. Texnologicheskie osnovy’ upravleniya kachestvom mashin. (Biblioteka texnologa). M.: Mashinostroenie. 2003.
  3. Kornev A.S. Voprosy’ metrologicheskogo obespecheniya robotizirovanny’x obrazczov vooruzheniya i voennoj texniki // Trudy’ pervoj voenno-nauchnoj konf. «Robotizacziya Vooruzhenny’x Sil Rossijskoj Federaczii». 2016. S. 111−113.
  4. Daleczkij S.V., Derkach O.Ya., Petrov A.N. E’ffektivnost’ texnicheskoj e’kspluataczii samoletov grazhdanskoj aviaczii. M.: Vozdushny’j transport. 2002.
  5. Volkov L.I. Upravlenie e’kspluatacziej letatel’ny’x apparatov. M.: Vy’sshaya shkola.1981. 368 s.
  6. Khayrullin R.Z., Ivanov P.S. Step-by-step control of target efficiency indices of the control and measuring equipment stock applied in construction and housing and communal services // 2nd International Conference of Material Science and nanotechnology, MATEC Web of Conferences. 2018. V. 170. 01010 [(WOS) 5 p.].
  7. Khayrullin R.Z. Optimal resource allocation of the servicing companies in the field of housing and public utilities on the basis of the theory of multiphase queueing systems // XXVII RSP Seminar «Theoretical Foundation of Civil Engineering», MATEC Web Conferences. 2018. 196, 04002, https://doi.org/10.1051/matecconf/201819604002 SKOPUS.
  8. Sy’chev E.B., Xramenkov V.N., Shkitin A.D. Osnovy’ metrologii voennoj texniki. M.: Voennoe izdatel’stvo. 1993. 400 s.
  9. Korolik V.S., Turbin A.F. Polumarkovskie proczessy’ i ix prilozheniya. Kiev: Naukova dumka. 1976. 236 s.
  10. Xajrullin R.Z., Safonov A.A. Polumarkovskaya model’ e’kspluataczii radioizmeritel’noj texniki s metrologicheskim obespecheniem // Nauchnoe obozrenie. 2017. № 19. S. 167−170.
  11. Ershov D.S., Smagin V.A., Sy’soev D.O. Postanovka zadachi obosnovaniya optimal’noj nomenklatury’ i raczional’nogo kolichestva poverochnogo oborudovaniya metrologicheskix podrazdelenij voinskix chastej // Sovremennaya nauka: Aktual’ny’e problemy’ teorii i praktiki. Ser. «Estestvenny’e i texnicheskie nauki». 2018. № 4. S. 31−34.
  12. Ershov D.S. Metodika obosnovaniya optimal’noj nomenklatury’ i kolichestva poverochnogo oborudovaniya metrologicheskix podrazdelenij operativno-takticheskix voinskix formirovanij s uchetom prognoziruemy’x poter’ sredstv izmerenij voennogo naznacheniya // Estestvenny’e i texnicheskie nauki. 2018. № 4. S. 214−216.
  13. Ershov D.S., Babak A.V., Sy’soev D.O. Matematicheskaya model’ proczessa poverki sredstv izmerenij voennogo naznacheniya metrologicheskimi podrazdeleniyami operativno-takticheskix voinskix formirovanij v xode boevy’x dejstvij // Estestvenny’e i texnicheskie nauki. № 4. M.: 2018. S. 217−220.
  14. Popenkov A.Ya. Teoreticheskie osnovy’ i rezul’taty’ issledovanij metrologicheskogo obespecheniya vojsk (sil) v mirnoe i voennoe vremya // XI Vseros. nauchno-texnich. konf. «Metrologicheskoe obespechenie oborony’ i bezopasnosti v Rossijskoj Federaczii». M.: Povedniki. 1−3 noyabrya 2016. 5 c.
  15. Popenkov A.Ya., Xajrullin R.Z. Novy’j podxod k oczenke vliyaniya metrologicheskogo obespecheniya na dostizhenie czelej e’kspluataczii vooruzheniya, voennoj texniki i voenny’x ob’‘ektov // XII Vseros. nauchno-texnich. konf. «Metrologicheskoe obespechenie oborony’ i bezopasnosti v Rossijskoj Federaczii». M.: Povedniki. 13−15 noyabrya 2018. 5 c.
  16. Xajrullin R.Z., Popenkov A.Ya., Luczkova T.A., Czy’bul’nikova K.A. Raspredelenie ob’‘emov kontrolya po czelyam metrologicheskogo obespecheniya slozhny’x organizaczionno-texnicheskix sistem s ispol’zovaniem polumarkovskix modelej // XI Mezhdunar. konf. «Upravlenie razvitiem krupnomasshtabny’x sistem» (MLSD’2018). M.: 2018. 2 s.
  17. Popenkov A.Ya., Xajrullin R.Z. Primenenie metoda konechny’x e’lementov v zadachax oczenki kachestva metrologicheskogo obespecheniya e’kspluataczii vooruzheniya, voennoj texniki i voenny’x ob’‘ektov // XII Vseros. nauchno-texnich. konf. «Metrologicheskoe obespechenie oborony’ i bezopasnosti v Rossijskoj Federaczii». M.: Povedniki. 13−15 noyabrya 2018. 5 c.

© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio