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On buffered failure probability in design and optimization of structures

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  • Rockafellar, R.T.
  • Royset, J.O.

Abstract

In reliability engineering focused on the design and optimization of structures, the typical measure of reliability is the probability of failure of the structure or its individual components relative to specific limit states. However, the failure probability has troublesome properties that raise several theoretical, practical, and computational issues. This paper explains the seriousness of these issues in the context of design optimization and goes on to propose a new alternative measure, the buffered failure probability, which offers significant advantages. The buffered failure probability is handled with relative ease in design optimization problems, accounts for the degree of violation of a performance threshold, and is more conservative than the failure probability.

Suggested Citation

  • Rockafellar, R.T. & Royset, J.O., 2010. "On buffered failure probability in design and optimization of structures," Reliability Engineering and System Safety, Elsevier, vol. 95(5), pages 499-510.
    • Handle: RePEc:eee:reensy:v:95:y:2010:i:5:p:499-510
    DOI: 10.1016/j.ress.2010.01.001
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    References listed on IDEAS

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    1. J. O. Royset & E. Polak, 2004. "Implementable Algorithm for Stochastic Optimization Using Sample Average Approximations," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 157-184, July.
    2. Kurt Marti, 2005. "Stochastic Optimization Methods," Springer Books, Springer, number 978-3-540-26848-2, December.
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    4. E. Polak & J. O. Royset & R. S. Womersley, 2003. "Algorithms with Adaptive Smoothing for Finite Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 459-484, December.
    5. J. O. Royset & E. Polak, 2007. "Extensions of Stochastic Optimization Results to Problems with System Failure Probability Functions," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 1-18, April.
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    Cited by:

    1. Massimiliano Amarante, 2016. "A representation of risk measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(1), pages 95-103, April.
    2. Chang, Kuo-Hao & Cuckler, Robert & Lee, Song-Lin & Lee, Loo Hay, 2022. "Discrete conditional-expectation-based simulation optimization: Methodology and applications," European Journal of Operational Research, Elsevier, vol. 298(1), pages 213-228.
    3. Byun, Ji-Eun & de Oliveira, Welington & Royset, Johannes O., 2023. "S-BORM: Reliability-based optimization of general systems using buffered optimization and reliability method," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    4. L. Jeff Hong & Zhaolin Hu & Liwei Zhang, 2014. "Conditional Value-at-Risk Approximation to Value-at-Risk Constrained Programs: A Remedy via Monte Carlo," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 385-400, May.
    5. Justin R. Davis & Stan Uryasev, 2016. "Analysis of tropical storm damage using buffered probability of exceedance," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 83(1), pages 465-483, August.
    6. Ruiz Mora, Carlos & Alcántara Mata, Antonio, 2022. "On data-driven chance constraint learning for mixed-integer optimization problems," DES - Working Papers. Statistics and Econometrics. WS 35425, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Villanueva, D. & Haftka, R.T. & Sankar, B.V., 2014. "Accounting for future redesign to balance performance and development costs," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 56-67.
    8. Rocchetta, Roberto & Crespo, Luis G., 2021. "A scenario optimization approach to reliability-based and risk-based design: Soft-constrained modulation of failure probability bounds," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    9. Pertaia, Giorgi & Prokhorov, Artem & Uryasev, Stan, 2022. "A new approach to credit ratings," Journal of Banking & Finance, Elsevier, vol. 140(C).
    10. Matthew Norton & Valentyn Khokhlov & Stan Uryasev, 2021. "Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation," Annals of Operations Research, Springer, vol. 299(1), pages 1281-1315, April.
    11. Abate, Arega Getaneh & Riccardi, Rossana & Ruiz, Carlos, 2021. "Contracts in electricity markets under EU ETS: A stochastic programming approach," Energy Economics, Elsevier, vol. 99(C).
    12. R. Tyrrell Rockafellar & Johannes O. Royset, 2018. "Superquantile/CVaR risk measures: second-order theory," Annals of Operations Research, Springer, vol. 262(1), pages 3-28, March.
    13. Jakeman, John D. & Kouri, Drew P. & Huerta, J. Gabriel, 2022. "Surrogate modeling for efficiently, accurately and conservatively estimating measures of risk," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    14. Danjue Shang & Victor Kuzmenko & Stan Uryasev, 2018. "Cash flow matching with risks controlled by buffered probability of exceedance and conditional value-at-risk," Annals of Operations Research, Springer, vol. 260(1), pages 501-514, January.
    15. Guo, Tiexin & Wang, Hongji & Li, Jinglai & Wang, Hongqiao, 2024. "Sampling-based adaptive design strategy for failure probability estimation," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    16. Chaudhuri, Anirban & Kramer, Boris & Willcox, Karen E., 2020. "Information Reuse for Importance Sampling in Reliability-Based Design Optimization," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    17. Mafusalov, Alexander & Uryasev, Stan, 2016. "CVaR (superquantile) norm: Stochastic case," European Journal of Operational Research, Elsevier, vol. 249(1), pages 200-208.
    18. Tan, Caixia & Wang, Jing & Geng, Shiping & Pu, Lei & Tan, Zhongfu, 2021. "Three-level market optimization model of virtual power plant with carbon capture equipment considering copula–CVaR theory," Energy, Elsevier, vol. 237(C).
    19. Xiaojiao Tong & Hailin Sun & Xiao Luo & Quanguo Zheng, 2018. "Distributionally robust chance constrained optimization for economic dispatch in renewable energy integrated systems," Journal of Global Optimization, Springer, vol. 70(1), pages 131-158, January.
    20. Rockafellar, R.T. & Royset, J.O. & Miranda, S.I., 2014. "Superquantile regression with applications to buffered reliability, uncertainty quantification, and conditional value-at-risk," European Journal of Operational Research, Elsevier, vol. 234(1), pages 140-154.
    21. Mikhail Zhitlukhin, 2018. "Monotone Sharpe ratios and related measures of investment performance," Papers 1809.10193, arXiv.org, revised May 2021.
    22. Amarjit Budhiraja & Shu Lu & Yang Yu & Quoc Tran-Dinh, 2021. "Minimization of a class of rare event probabilities and buffered probabilities of exceedance," Annals of Operations Research, Springer, vol. 302(1), pages 49-83, July.
    23. Thilini V. Mahanama & Abootaleb Shirvani & Svetlozar Rachev, 2023. "The Financial Market of Indices of Socioeconomic Wellbeing," Papers 2303.05654, arXiv.org.
    24. Franco Peschiera & Robert Dell & Johannes Royset & Alain Haït & Nicolas Dupin & Olga Battaïa, 2021. "A novel solution approach with ML-based pseudo-cuts for the Flight and Maintenance Planning problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 635-664, September.
    25. Johannes O. Royset & Roberto Szechtman, 2013. "Optimal Budget Allocation for Sample Average Approximation," Operations Research, INFORMS, vol. 61(3), pages 762-776, June.

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