On the Probabilities Analytical Assessment of Automated Data Preparation System States for Aircraft Application
Authors: Zhurbin S.A.
Published in issue: #1(169)/2026
Category: Aviation and Rocket-Space Engineering | Chapter: Design, Construction, Production, Testing, and Operation of Aircraft
When designing an automated data preparation system (ADPS) for aircraft application, it becomes necessary to study random processes of failures and recoveries of units (elements) forming the basis of the system technical support. These units can be automated workstations (AWS) of the ADPS, each of which solves the tasks of preparing data for aircraft application. Such researches are conducted, for example, to evaluate the probabilistic and temporal characteristics of the AWS, or to determine the values of the latter ones based on the requirements for more general data preparation systems. In most cases, random processes of failures and recoveries of technical means can be classified as Markov processes, for which the dynamics of system transitions between different states are mathematically described by a system of Kolmogorov differential equations (SDE). The solution of the mentioned SDE for specific values of the intensities of failures and restorations of technical means and for its small dimension is not difficult. The solution of the Kolmogorov SDE of arbitrary order is of practical and theoretical interest when the number of ASPD workstations is not known in advance and is the subject of research. The article presents the solution of the Kolmogorov SDE of arbitrary order under certain assumptions that significantly simplified the SDE. The results presented by the author can be useful in solving research problems, designing organizational and technical systems, and preparing tactical and technical specifications for the development of automated systems.
EDN DERLQV
References
[1] Gnedenko B.V., Belyaev Yu.K., Solovyov A.D. Matematicheskie metody v teorii nadezhnosti [Mathematical methods in reliability theory]. Moscow, Nauka Publ., 1965, 524 p.
[2] Shubinsky I.B. Nadezhnye otkazoustoichivye informatsionnye sistemy. Metody sinteza [Reliable fault-tolerant information systems. Methods of synthesis]. Dependability Journal, 2016, no. 2, 546 p.
[3] Polovko A.M., Gurov S.V. Osnovy teorii nadezhnosti [Fundamentals of reliability theory]. 2nd ed., revised and enlarged. St. Petersburg, BHV–Petersburg Publ., 2006, 704 p.
[4] Ivanov A.K. Design of a Sustainable Automated Control System. Ulyanovsk, Ulyanovsk State Technical University, 2002, 144 p.
[5] GOST 27.002–2015. Nadezhnost v tekhnike. Osnovnye ponyatiya. Terminy i opredeleniya [Dependability in engineering. Basic concepts. Terms and definitions]. Moscow, Interstate Council for Standardization, Metrology and Certification Publ., 2017, 37 p.
[6] RD 50-492–84. Metodika otsenki nauchno-tekhnicheskogo urovnya ASU. Tipovye polozheniya [Methodology for assessing the scientific and technical level of automated control systems. Standard provisions]. Moscow, Standards Publ., 1985, 14 p.
[7] GOST 34.601–90. Avtomatizirovannye sistemy. Stadii sozdaniya. Kompleks standartov na avtomatizirovannye sistemy [Automated systems. Stages of creation. Set of standards for automated systems]. Moscow, State Committee of the USSR for Quality Management and Standards Publ., 1992, 6 p.
[8] Sarvin A.A., Abakulina L.I., Gotshalk O.A. Diagnostika i nadezhnost avtomatizirovannykh sistem [Diagnostics and reliability of automated systems]. St. Petersburg, North-West Technical University Publ., 2003, 69 p.
[9] Volkov I.K., Zuev S.M., Tsvetkova G.M. Sluchaynye protsessy [Random processes]. Moscow, Bauman Moscow State Technical University Publ., 1999, 448 p.
[10] Kazakov V.L. Vvedenie v teoriyu Markovskikh protsessov i nekotorye radiotekhnicheskie zadachi [Introduction to the theory of Markov processes and some radio engineering problems]. Moscow, Sovetskoe Radio Publ., 1973, 232 p.
[11] Ventzel E.S. Teoriya veroyatnostey [Probability theory]. Moscow, Nauka Publ., 1969, 576 p.
[12] Golinkievich T.A. Prikladnaya teoriya nadezhnosti [Applied reliability theory]. Moscow, HSE University Publ., 1977, 160 p. (Transition from Markov chains to processes).
[13] Korn G., Korn T. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov [Mathematical handbook for scientists and engineers]. Moscow, Nauka Publ., 1968720 p.
[14] Bermant A.F., Aramanovich I.G. Kratkiy kurs matematicheskogo analiza [A short course of mathematical analysis]. 4th ed., rev. and enlarged. Moscow, Nauka Publ., Main Editorial Office of Physical and Mathematical Literature, 1966, 735 p.
[15] Kaplan I.A. Prakticheskie zanyatiya po vysshey matematike. Differentsialnoe i integralnoe ischislenie [Practical classes in higher mathematics. Differential and integral calculus]. Kharkov, Kharkov State University Publ., 1968, 250 p.
[16] Fikhtengolts G.M. Kurs differentsialnogo i integralnogo ischisleniya. Vol. 1 [A course of differential and integral calculus]. 5th ed., enlarged. Moscow, State Publishing House of Physical and Mathematical Literature, 1962, 607 p.
[17] Andreev A.G., Zhurbin S.A., Kazakov G.V. Matematicheskaya model’ funktsionirovaniya avtomatizirovannykh sistem kriticheskikh prilozheniy s setevoy strukturoy [Mathematical model of functioning of automated systems of critical applications with a network structure]. In: Sbornik dokladov nauchno-tekhnicheskoy konferentsii [Proceedings of the scientific and technical conference]. 4th Central Research Institute of the Ministry of Defence of the Russian Federation, 2016.
[18] Zhurbin S.A., Kazakov G.V. Podkhod k razrabotke predlozheniy po opredeleniyu kolichestvennogo sostava tekhnicheskikh ob”ektov odnorodnoy vychislitelnoy seti i otsenke trebuemykh znacheniy pokazateley ikh nadezhnosti [An approach to developing proposals for determining the quantitative composition of technical objects of a homogeneous computing network and assessing the required values of their reliability indicators]. In: XLII Academic Space Conference, Dedicated to the Memory of Academician S.P. Korolev and Other Outstanding National Scientists — Pioneers of Space Exploration. Proceedings. Moscow, Bauman Moscow State Technical University Publ., 2017, p. 461.