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Safety Margin Prediction Algorithms Based on Linear Regression Analysis Estimates

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  • Gurami Tsitsiashvili

    (Institute for Applied Mathematics, Far Eastern Branch of Russian Academy of Sciences, 690041 Vladivostok, Russia
    Current address: IAM FEB RAS, Radio Str. 7, 690041 Vladivostok, Russia.)

  • Alexandr Losev

    (Institute for Applied Mathematics, Far Eastern Branch of Russian Academy of Sciences, 690041 Vladivostok, Russia)

Abstract

In this paper, we consider the problem of approximating the safety margin of a single instance of a technical system based on inaccurate observations at specified time points. The solution to this problem is based on the selection of a certain set of reference points in time, in a small neighbourhood of which a sufficiently large number of inaccurate measurements are carried out. Analogously with the failure rate, it is assumed that the rate of decrease in the safety margin over time is represented by a polynomial of the fourth degree, and the safety margin itself is a polynomial of the fifth degree. A system of linear algebraic equations is constructed that determine the coefficients of this polynomial through its values and the values of its derivative at reference points in time. These values themselves are estimated by the method of linear regression analysis based on numerous observations in a small neighbourhood of reference points in time. A detailed computational experiment is carried out to verify the accuracy of the approximation of a fifth-degree polynomial and alternative ways of estimating it are constructed in the vicinity of points where the quality of approximation is insufficient.

Suggested Citation

  • Gurami Tsitsiashvili & Alexandr Losev, 2022. "Safety Margin Prediction Algorithms Based on Linear Regression Analysis Estimates," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2008-:d:836089
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    References listed on IDEAS

    as
    1. Ahmad, Abd EL-Baset A. & Ghazal, M.G.M., 2020. "Exponentiated additive Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    2. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, March.
    3. Shakhatreh, Mohammed K. & Lemonte, Artur J. & Moreno–Arenas, Germán, 2019. "The log-normal modified Weibull distribution and its reliability implications," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 6-22.
    4. Almalki, Saad J. & Yuan, Jingsong, 2013. "A new modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 164-170.
    5. Gurami Tsitsiashvili & Marina Osipova & Yury Kharchenko, 2022. "Estimating the Coefficients of a System of Ordinary Differential Equations Based on Inaccurate Observations," Mathematics, MDPI, vol. 10(3), pages 1-9, February.
    Full references (including those not matched with items on IDEAS)

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