OBRABOTKAMETALLOV Vol. 28 No. 3 2026 42 TECHNOLOGY References 1. Korsakov V.S. Osnovy proektirovaniya tekhnologicheskikh protsessov mashinostroeniya [Fundamentals of designing mechanical engineering technological processes]. Moscow, Mashinostroenie Publ., 1972, 368 p. 2. Lanetskii B., Lukyanchuk V., Khudov H., Fisun M., Zvieriev O., Terebuha I. Developing the model of reliability of a complex technical system of repeated use with a complex operating mode. Eastern-European Journal of Enterprise Technologies, 2020, vol. 5, no. 4 (107), pp. 55–65. DOI: 10.15587/1729-4061.2020.214995. 3. Wentzell A.D. A course in the theory of stochastic processes. New York,etc., McGraw-Hill, 1981. 304 p. ISBN 0-070-69305-6. 4. Ventsel E.S., Ovcharov L.A. Teoriya sluchainykh protsessov i ee inzhenernye prilozheniya [Theory of Stochastic Processes and Its Engineering Applications]. 2nd ed. Moscow, Vysshaya Shkola Publ., 2000. 383 p. ISBN 5-06-003831-9. Analytical assessment of the processing productivity of complex workpieces based on Markov models Galina Nevar a, *, Stanislav Roshchupkin b, Sergey Bratan c, Alexander Kharchenko d Sevastopol State University, 33 Universitetskaya str., Sevastopol, 299053, Russian Federation a https://orcid.org/0009-0008-2528-881X, GVNevar@sevsu.ru; b https://orcid.org/0000-0003-2040-2560, st.roshchupkin@yandex.ru; c https://orcid.org/0000-0002-9033-1174, serg.bratan@gmail.com; d https://orcid.org/0000-0003-1704-9380, khao@list.ru Obrabotka metallov - Metal Working and Material Science Journal homepage: http://journals.nstu.ru/obrabotka_metallov Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science. 2026 vol. 28 no. 3 pp. 29–43 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2026-28.3-29-43 ART I CLE I NFO Article history: Received: 01 June 2026 Revised: 13 June 2026 Accepted: 27 June 2026 Available online: 15 September 2026 Keywords: Markov processes Transition intensities Productivity Complex workpiece Limit probabilities ABSTRACT Introduction. In multi-product manufacturing, loading, unloading, and auxiliary movements of equipment components contribute signifi cantly to the overall processing cycle time. It is hypothesized that transitioning from the processing of individual simple workpieces to complex workpieces – combining several parts in a single unit – can reduce unproductive time expenditures. However, existing analytical approaches do not provide a quantitative assessment of the productivity gain while accounting for the probabilistic nature of transitions between technological states. Purpose of the work is to develop analytical expressions for evaluating the productivity of a technological system when processing simple and complex workpieces on the basis of Markov models. The research objective is to establish a correspondence between the time parameters of conventional time-and-motion study (technical rating) and the transition intensities in a Markov chain, and to derive a formula for the relative gain. The technological process is represented as a directed graph, with transitions between states specifi ed by intensities. The research methods include mathematical modeling based on the fundamental principles of Markov process theory, numerical simulation in the Maple environment, and the principles of group parts processing theory. Results and discussion. The developed mathematical models enable quantitative estimation of the fractions of time that the technological system spends in the states of loading, processing, auxiliary movements, and unloading. The analytical relationships obtained directly relate productivity to the transition intensities between states. It is shown that the key states determining processing effi ciency are loading, unloading, and auxiliary movements. Numerical simulations performed in the Maple environment confi rmed the validity of the derived formulas. The results obtained demonstrate the potential of the proposed approach for the analytical assessment of the processing productivity of complex workpieces. The derived expressions are valid for a wide range of surface confi gurations and can be used to calculate the gain achieved when combining an arbitrary number of parts. For citation: Nevar G.V., Roshchupkin S.I., Bratan S.M., Kharchenko A.O. Analytical assessment of the processing productivity of complex workpieces based on Markov models. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2026, vol. 28, no. 3, pp. 29–43. DOI: 10.17212/1994-6309-2026-28.3-29-43. (In Russian). ______ * Corresponding author Nevar Galina Valerievna, Senior Lecturer Sevastopol State University, 33 Universitetskaya str., 299053, Sevastopol, Russian Federation Tel.: +7 978 727-32-47, e-mail: gvnevar@sevsu.ru
RkJQdWJsaXNoZXIy MTk0ODM1