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A New Method of Reliability Optimization in the Classical Problem Statement

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Abstract

The problem of reliability minimization is considered. One of the available approaches to solving this problem, namely bPOE, is analyzed. The advantages and disadvantages of this approach are determined. It is noted that the results of minimizing the probability of failures in the classical setting and minimizing the bPOE may differ. A new method of reliability optimization in the classical formulation of the problem is proposed. A comparative analysis of the results of reliability minimization using the bPOE and the results obtained by the proposed method is carried out.

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References

  1. T. Rockafellar and J. O. Royset, “On buffered failure probability in design and optimization of structures,” Reliability Engineering and System Safety, Vol. 95, No. 5, 499–510 (2010). https://doi.org/10.1016/j.ress.2010.01.001.

    Article  Google Scholar 

  2. R. T. Rockafellar, “Convexity and reliability in engineering optimization,” in: Proc. 9th Intern. Conf. on Nonlinear Analysis and Convex Analysis (Chiangrai, Thailand) (2015), pp. 1–10. URL: https://sites.math.washington.edu/~rtr/papers/rtr239-Reliability.pdf.

  3. J. R. Davis and S. Uryasev, “Analysis of tropical storm damage using buffered probability of exceedance,” Natural Hazards, Vol. 83, 465–483 (2016). https://doi.org/10.1007/s11069-016-2324-y.

  4. V. A. Pepelyaev, A. N. Golodnikov, and N. A. Golodnikova, “Reliability optimization in plant production,” Cybern. Syst. Analysis, Vol. 58, No. 2, 191–196 (2022). https://doi.org/10.1007/s10559-022-00450-5.

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Mafusalov and S. Uryasev, “Buffered probability of exceedance: Mathematical properties and optimization,” SIAM. J. Optim., Vol. 28, 1077–1103 (2018). https://doi.org/10.1137/15M1042644.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. T. Rockafellar and S. Uryasev, “Optimization of conditional value-at-risk,” The J. of Risk, Vol. 2, No. 3, 21–41 (2000). 10.21314/JOR.2000.038.

  7. R. T. Rockafellar and S. Uryasev, “Conditional value-at-risk for general loss distributions,” J. of Banking & Finance, Vol. 26, No. 7, 1443–1471 (2002). https://doi.org/10.1016/S0378-4266(02)00271-6.

    Article  Google Scholar 

  8. M. Norton and S. Uryasev, “Maximization of AUC and buffered AUC in binary classification,” Mathem. Programming, Ser. A and B, Vol. 174, No. 1–2, 575–612 (2019). https://doi.org/10.1007/s10107-018-1312-2.

    Article  MathSciNet  MATH  Google Scholar 

  9. R. T. Rockafellar and S. Uryasev, “Minimizing buffered probability of exceedance by progressive hedging,” Math. Program., Vol. 181, 453–472 (2020). https://doi.org/10.1007/s10107-019-01462-4.

    Article  MathSciNet  MATH  Google Scholar 

  10. G. M. Zrazhevsky, A. N. Golodnikov, S. P. Uryasev, and A. G. Zrazhevsky, “Application of buffered probability of exceedance in reliability optimization problems,” Cybern. Syst. Analysis, Vol. 56, No. 3, 476–484 (2020). https://doi.org/10.1007/s10559-020-00263-4.

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Golodnikov, V. Kuzmenko, and S. Uryasev, “CVaR regression based on the relation between CVaR and mixed-quantile quadrangles,” J. of Risk and Financial Management, Vol. 12, 107 (2019). https://doi.org/10.3390/jrfm12030107.

    Article  Google Scholar 

  12. V. A. Pepelyaev, A. N. Golodnikov, and N. A. Golodnikova, “Reliability optimization method alternative to bPOE,” Cybern. Syst. Analysis, Vol. 58, No. 4, 598–610 (2022).

    Article  MathSciNet  MATH  Google Scholar 

  13. V. A. Pepelyaev and N. A. Golodnikova, Mathematical methods for crop losses risk evaluation and account for sown areas planning. Cybern. Syst. Analysis, Vol. 50, No. 1, 60–67 (2014). https://doi.org/10.1007/s10559-014-9592-x.

    Article  Google Scholar 

  14. A. N. Golodnikov, P. S. Knopov, and V. A. Pepelyaev, “Estimation of reliability parameters under incomplete primary information,” Theor. Decis., Vol. 57, 331–344 (2004). https://doi.org/10.1007/s11238-005-3217-9.

    Article  MathSciNet  MATH  Google Scholar 

  15. Portfolio Safeguard. URL: http://www.aorda.com/index.php/portfolio-safeguard/.

  16. “Test problems for nonlinear, stochastic, mixed-integer optimization,” URL: http://uryasev.ams.stonybrook.edu/index.php/research/testproblems/.

  17. Omega Portfolio Rebalancing. URL: http://uryasev.ams.stonybrook.edu/index.php/research/testproblems/financial_engineering/omega-portfolio-rebalancing/.

  18. “Classification by maximizing area under ROC curve (AUC).” URL: http://uryasev.ams.stonybrook.edu/index.php/research/testproblems/advanced-statistics/classification-by-maximizing-area-under-curve/.

  19. “Style classification with quantile regression.” URL: http://uryasev.ams.stonybrook.edu//index.php/research/testproblems/financial_engineering/style-classification-with-quantile-regression/.

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Correspondence to V. A. Pepelyaev.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 6, November–December, 2022, pp. 74–79.

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Pepelyaev, V.A., Golodnikov, A.N. & Golodnikova, N.A. A New Method of Reliability Optimization in the Classical Problem Statement. Cybern Syst Anal 58, 917–922 (2022). https://doi.org/10.1007/s10559-023-00525-x

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