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Selection of risk reduction portfolios under interval-valued probabilities

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  • Toppila, Antti
  • Salo, Ahti

Abstract

A central problem in risk management is that of identifying the optimal combination (or portfolio) of improvements that enhance the reliability of the system most through reducing failure event probabilities, subject to the availability of resources. This optimal portfolio can be sensitive with regard to epistemic uncertainties about the failure events' probabilities. In this paper, we develop an optimization model to support the allocation of resources to improvements that mitigate risks in coherent systems in which interval-valued probabilities defined by lower and upper bounds are employed to capture epistemic uncertainties. Decision recommendations are based on portfolio dominance: a resource allocation portfolio is dominated if there exists another portfolio that improves system reliability (i) at least as much for all feasible failure probabilities and (ii) strictly more for some feasible probabilities. Based on non-dominated portfolios, recommendations about improvements to implement are derived by inspecting in how many non-dominated portfolios a given improvement is contained. We present an exact method for computing the non-dominated portfolios. We also present an approximate method that simplifies the reliability function using total order interactions so that larger problem instances can be solved with reasonable computational effort.

Suggested Citation

  • Toppila, Antti & Salo, Ahti, 2017. "Selection of risk reduction portfolios under interval-valued probabilities," Reliability Engineering and System Safety, Elsevier, vol. 163(C), pages 69-78.
    • Handle: RePEc:eee:reensy:v:163:y:2017:i:c:p:69-78
    DOI: 10.1016/j.ress.2017.02.005
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    References listed on IDEAS

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    1. Enrico Zio, 2011. "Risk Importance Measures," Springer Series in Reliability Engineering, in: Hoang Pham (ed.), Safety and Risk Modeling and Its Applications, pages 151-196, Springer.
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    8. Eeva Vilkkumaa & Ahti Salo & Juuso Liesiö, 2014. "Multicriteria Portfolio Modeling for the Development of Shared Action Agendas," Group Decision and Negotiation, Springer, vol. 23(1), pages 49-70, January.
    9. Caserta, Marco & Voß, Stefan, 2015. "An exact algorithm for the reliability redundancy allocation problem," European Journal of Operational Research, Elsevier, vol. 244(1), pages 110-116.
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    Cited by:

    1. Edoardo Tosoni & Ahti Salo & Enrico Zio, 2018. "Scenario Analysis for the Safety Assessment of Nuclear Waste Repositories: A Critical Review," Risk Analysis, John Wiley & Sons, vol. 38(4), pages 755-776, April.
    2. Chemweno, Peter & Pintelon, Liliane & Muchiri, Peter Nganga & Van Horenbeek, Adriaan, 2018. "Risk assessment methodologies in maintenance decision making: A review of dependability modelling approaches," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 64-77.
    3. Mancuso, A. & Compare, M. & Salo, A. & Zio, E., 2017. "Portfolio optimization of safety measures for reducing risks in nuclear systems," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 20-29.

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