DOI: 10.14489/td.2025.08.pp.004-017
Kudryavtseva I. S., Naumenko A. P., Dyshlevsky V. A., Rolgazer V. A. PROBABILISTIC AND STATISTICAL METHODS OF DECISION-MAKING: APPLICATION OF ROC ANALYSIS IN TECHNICAL DIAGNOSTICS (pp. 4-17)
Abstract. The possibilities of using probabilistic and statistical decision-making methods to detect useful information in signals during non-destructive testing and technical diagnostics are considered. The description of ROC analysis as a method of pattern recognition in comparison with classical methods of decision theory is given. A methodology and an example of using ROC analysis and the maximum likelihood method to determine the boundary value of an informative feature of an event, allowing a decision to be made on the validity of the main or alternative hypotheses. The conclusion is made about the mathematical similarity of ROC analysis and the method of maximum likelihood.
Keywords: decision-making, ROC analysis, Yuden index, maximum likelihood method, error of the first and second kind, risk and reliability of decision-making, error matrix, acoustic emission.
I. S. Kudryavtseva, A. P. Naumenko (Federal State Autonomous Educational Institution of Higher Education Omsk State Technical University, Omsk, Russia) E-mail:
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V. A. Dyshlevsky (Federal State Autonomous Educational Institution of Higher Education Omsk State Technical University, Omsk, Russia, VS Engineering LLC, Omsk, Russia) E-mail:
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V. A. Rolgazer (Federal State Autonomous Educational Institution of Higher Education Omsk State Technical University, Omsk, Russia, Federal State Budgetary Educational Institution of Higher Education Omsk State Transport University, Omsk, Russia) E-mail:
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1. Kudryavtseva, I. S., Naumenko, A. P., Demin, A. M., & Odinets, A. I. (2019). Probabilistic-statistical criterion for condition assessment based on vibroacoustic signal parameters. Dinamika Sistem, Mekhanizmov i Mashin, 7(2), 113–122. [in Russian language]. https://doi.org/10.25206/2310-9793-7-2-113-122 2. Kudryavtseva, I. S., Naumenko, A. P., & Demin, A. M. (2019). Criteria for assessing vibration conditions of objects based on signal characteristic function parameters. Omskiy Nauchnyy Vestnik, (4(166)), 97–104. [in Russian language]. https://doi.org/10.25206/1813-8225-2019-166-97-105 3. Demin, A. M., Naumenko, A. P., Odinets, A. I., & Gorchakova, A. A. (2019). Assessment of probabilistic errors in condition monitoring of heat exchange equipment. Dinamika Sistem, Mekhanizmov i Mashin, 7(2), 95–103. [in Russian language]. https://doi.org/10.25206/2310-9793-7-2-95-103 4. GOST R 56233-2014. (2015). Condition monitoring and machine diagnostics. Monitoring of hazardous production equipment. Vibration of stationary piston compressors. Standartinform. URL: https://docs.cntd.ru/document/1200115097 (Retrieved February 2, 2025) [in Russian language]. 5. Aletdinova, A. A., & Kurcheeva, G. I. (2024). Mathematical methods in economics. Novosibirsk State Technical University. ISBN 978-5-7782-5261-5. [in Russian language] 6. Bogolyubskiy, D. D. (2021). Application of Bayesian approach in risk management of energy systems. In Aktual'nye problemy energetiki - 2021: Materialy studencheskoy nauchno-tekhnicheskoy konferentsii (pp. 453–458). Belarusian National Technical University. [in Russian language]. 7. Zolotykh, E. S. (2024). Methodological approach to decision-making in the implementation of network attacks on informatization objects of internal affairs bodies. Vestnik Voronezhskogo Instituta MVD Rossii, (2), 89–97. [in Russian language] 8. Shanov, S. V., Kondratyev, A. Yu., Usov, A. V., & Rogozhin, S. S. (2024). Methodology for assessing the level of comprehensive security of structural divisions of the Ministry of Defense of the Russian Federation operating nuclear and radiation hazardous facilities. Voprosy Oboronnoy Tekhniki. Ser. 16. Tekhnicheskie Sredstva Protivodeystviya Terrorizmu, (1-2(187-188)), 3–13. [in Russian language]. https://doi.org/10.53816/23061456_2024_1-2_3 9. Myasoutov, R. Kh. (2020). Creating a system for recognizing human gender by handwriting. Sovremennaya Nauka: Aktual'nye Problemy Teorii i Praktiki. Ser. Estestvennye i Tekhnicheskie Nauki, (7), 86–90. [in Russian language]. https://doi.org/10.37882/2223-2966.2020.07.23 10. Saubanov, O. M., Valeev, A. R., & Akimov, V. I. (2021). Testing of probabilistic-statistical decision-making method when developing strip norms for hull vibration of gas turbine engines of gas pumping units. Transport i Khranenie Nefteproduktov i Uglevodorodnogo Syr'ya, (4), 5–11. [in Russian language]. https://doi.org/10.24412/0131-4270-2021-4-5-11 11. Shanov, S. V., Chupin, P. G., & Afonin, A. Yu. (2018). Application of Bayesian classifier for text topic determination. Modelirovanie, Optimizatsiya i Informatsionnye Tekhnologii, 6(1(20)), 131–139. [in Russian language]. 12. Trukhanov, V. M., & Lazarev, V. V. (2019). Planning tests of expensive objects using fixed-volume method. Vestnik Mashinostroeniya, (11), 3–8. [in Russian language]. 13. Prokhorov, Yu. V. (Ed.). (1999). Probability and mathematical statistics: Encyclopedia. Bolshaya Rossiyskaya Entsiklopediya. ISBN 5-85270-265-X. [in Russian language]. 14. GOST R 50779.10-2000. (2005). Statistical methods. Probability and fundamentals of statistics. Terms and definitions. Gosstandart Rossii. URL: https://docs.cntd.ru/document/1200017686 (Retrieved October 23, 2024) [in Russian language]. 15. Stehman, S. V. (1997). Selecting and interpreting measures of thematic classification accuracy. Remote Sensing of Environment, *62*(1), 77–89. https://doi.org/10.1016/S0034-4257(97)00083-7 16. Birger, I. A. (2018). Technical diagnostics (2nd ed.). Lenand. ISBN 978-5-9710-6012-3. [in Russian language]. 17. Naumenko, A. P., Kudryavtseva, I. S., & Odinets, A. I. (2018). Probabilistic-statistical decision-making methods: Theory, examples, problems. Omsk State Technical University. ISBN 978-5-8149-2720-0. [in Russian language]. 18. Kharkevich, A. A. (2018). Fighting interference (5th ed.). Librokom. [in Russian language]. 19. Burlakov, M. E. (2016). Application of optimized naive Bayesian classifier in SMS message classification task. Izvestiya Samarskogo Nauchnogo Tsentra RAN, *18*(4-4), 705–709. [in Russian language]. 20. Wald, A. (1960). Sequential analysis. Fizmatgiz. [in Russian language]. 21. Shiryaev, A. N. (2014). Probabilistic-statistical methods in decision theory (2nd ed.). MTSNMO. ISBN 978-5-4439-0247-0. [in Russian language]. 22. Lloyd, D., & Lipov, M. (1964). Reliability. Sovetskoye Radio. [in Russian language]. 23. Klyuev, V. V. (Ed.). (2003). Mechanical engineering: Encyclopedia. Vol. IV-3. Machine reliability. Mashinostroenie. [in Russian language]. 24. Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics. John Wiley and Sons Inc. ISBN 0-471-32420-5. 25. Yudina, E. V., & Ziganshina, L. E. (2024). ROC-curve. Nauchno-obrazovatel'nyy portal «Bol'shaya rossiyskaya entsiklopediya», (5). [in Russian language]. https://doi.org/10.54972/00000001_2024_5_34 26. Hajian-Tilaki, K. (2013). Receiver Operating Characteristic (ROC) Curve Analysis for Medical Diagnostic Test Evaluation. Caspian Journal of Internal Medicine, 4(2), 627–635. 27. Swets, J. A. (1986). Indices of discrimination or diagnostic accuracy: their ROCs and implied models. Psychological Bulletin, 99(1), 100–117. 28. Zweig, M. H., & Campbell, G. (1993). Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. Clinical Chemistry, 39(8), 561–577. 29. Lusted, L. B. (1960). Logical analysis in roentgen diagnosis. Radiology, 74(2), 178–193. 30. Dorfman, D. D., & Alf, E. (1968). Maximum like-lihood estimation of parameters of signal detection theory a direct solution. Psychometrika, 33(1), 117–124. 31. Tharwat, A. (2021). Classification assessment methods. Applied Computing and Informatics, 17(1), 168–192. 32. Choi, S. S., Cha, S. H., & Tappert, C. C. (2010). A survey of binary similarity and distance measures. Journal of Systemics, Cybernetics and Informatics, 8(1), 43–48. 33. Canbek, G., Sagiroglu, S., Temizel, T. T., & Baykal, N. (2017). Binary classification performance measures/metrics: A comprehensive visualized roadmap to gain new insights. In International Conference on Computer Science and Engineering (pp. 821–826). 34. Youden, W. J. (1950). Index for rating diagnostic tests. Cancer, 3(1), 32–35. URL: https://acsjournals.online library.wiley.com/doi/10.1002/1097-0142(1950)3:1%3C32::AID-CNCR2820030106%3E3.0.CO;2-3 (Retrieved January 15, 2025). 35. Starovoitov, V. V., & Golub, Yu. I. (2020). Comparative analysis of binary classification quality metrics. Informatika, 17(1), 87–101. [in Russian language]. https://doi.org/10.37661/1816-0301-2020-17-1-87-101 36. Korneenkov, A. A., Lilenko, S. V., Lilenko, A. S., et al. (2018). Possibilities of ROC-analysis for variable categorization in outcome prediction model for surgical treatment of patients with Meniere's disease. Rossiyskaya Otorinolaringologiya, (4(95)), 62–68. [in Russian language]. https://doi.org/10.18692/1810-4800-2018-4-62-68 37. Barat, V. A. (2020). Development of acoustic emission method through data processing automation, noise immunity improvement and reliability enhancement of crack-like defect detection in metal structures [Doctoral dissertation, Moscow Power Engineering Institute]. [in Russian language]. 38. Rastegaev, I. A. (2022). Methods and means for detecting noise-like signals of tribological and hydrodynamic acoustic emission sources based on hierarchical threshold-free spectral-temporal analysis [Doctoral dissertation, Togliatti State University]. [in Russian language]. 39. Naumenko, A. P., Burda, E. A., Dyshlevskiy, V. A., et al. (2024). New approaches to acoustic emission signal detection. In P. K. Lange (Ed.), Informatsionno-izmeritel'nye i upravlyayushchie sistemy: mezhvuz. sb. nauch. st. (Vol. 1(22), pp. 98–125). Samara State Technical University. [in Russian language].
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