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Method of Expansion of Mathematical Tools of the Reliability Theory Due to the Properties of Stochastic Theory of Similarity

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Cyber-Physical Systems and Control II (CPS&C 2021)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 460))

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Abstract

An original approach to the development of mathematical tools of the reliability theory and expanding the range of its capabilities by using the properties of the stochastic theory of similarity are proposed and justified in the article. Such an approach to creating mathematical “symbiosis” of two large theories is aimed at improving the efficiency of solving the problem of identification of the quality indicators (reliability) of complex technical systems during its life cycles: from creation, active usage, and to subsequent disposal. The stochastic similarity is based on the elementary lemma and a metric in the form of a ratio of distribution functions of a random variable. The elementary lemma is also the basis of the probability integral transformation, which is used in the modeling of random variables. Useful properties of the lemma and the integral transformation are given in the study dedicated to the capabilities of the stochastic theory of similarity. In the course of assessing the applicability of the stochastic theory of similarity to the problems of comparing reliability indicators, two alternative methods of solution are presented: the first method is based on the construction of models using the principle of maximum entropy, and the second method is using stochastic similarity.

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Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, Politechnicheskaya St. 29, 195251, St. Petersburg, Russia

    Sergei Efimenko, Anatolii Smetankin & Igor Chernorutsky

  2. Saint-Petersburg State University of Aerospace Instrumentation, Bolshaya Morskaya St. 67, 190000, St. Petersburg, Russia

    Aleksandr Liashenko

  3. The Admiral Makarov State University of Maritime and Inland Shipping, Dvinskaya St. 5/7, 198035, St. Petersburg, Russia

    Melania Arutiunian & Sergei Kolesnichenko

Authors
  1. Sergei Efimenko
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  2. Anatolii Smetankin
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  3. Aleksandr Liashenko
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  4. Melania Arutiunian
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  5. Igor Chernorutsky
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  6. Sergei Kolesnichenko
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Corresponding author

Correspondence to Anatolii Smetankin .

Editor information

Editors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    Dmitry G. Arseniev

  2. School of Science and Technology, City, University of London, London, UK

    Nabil Aouf

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Efimenko, S., Smetankin, A., Liashenko, A., Arutiunian, M., Chernorutsky, I., Kolesnichenko, S. (2023). Method of Expansion of Mathematical Tools of the Reliability Theory Due to the Properties of Stochastic Theory of Similarity. In: Arseniev, D.G., Aouf, N. (eds) Cyber-Physical Systems and Control II. CPS&C 2021. Lecture Notes in Networks and Systems, vol 460. Springer, Cham. https://doi.org/10.1007/978-3-031-20875-1_4

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  • DOI: https://doi.org/10.1007/978-3-031-20875-1_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-20874-4

  • Online ISBN: 978-3-031-20875-1

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