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Multilevel Monte Carlo for Reliability Theory

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  • Aslett, Louis J.M.
  • Nagapetyan, Tigran
  • Vollmer, Sebastian J.

Abstract

As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the number of cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) — a simulation approach which is typically used for stochastic differential equation models — can be applied in reliability problems by carefully controlling the bias-variance tradeoff in approximating large system behaviour. In this first exposition of MLMC methods in reliability problems we address the canonical problem of estimating the expectation of a functional of system lifetime for non-repairable and repairable components, demonstrating the computational advantages compared to classical Monte Carlo methods. The difference in computational complexity can be orders of magnitude for very large or complicated system structures, or where the desired precision is lower.

Suggested Citation

  • Aslett, Louis J.M. & Nagapetyan, Tigran & Vollmer, Sebastian J., 2017. "Multilevel Monte Carlo for Reliability Theory," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 188-196.
    • Handle: RePEc:eee:reensy:v:165:y:2017:i:c:p:188-196
    DOI: 10.1016/j.ress.2017.03.003
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    References listed on IDEAS

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    1. Xing, Liudong & Shrestha, Akhilesh & Dai, Yuanshun, 2011. "Exact combinatorial reliability analysis of dynamic systems with sequence-dependent failures," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1375-1385.
    2. Manno, G. & Chiacchio, F. & Compagno, L. & D'Urso, D. & Trapani, N., 2014. "Conception of Repairable Dynamic Fault Trees and resolution by the use of RAATSS, a Matlab® toolbox based on the ATS formalism," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 250-262.
    3. Frank PA Coolen & Tahani Coolen-Maturi & Abdullah H Al-nefaiee, 2014. "Nonparametric predictive inference for system reliability using the survival signature," Journal of Risk and Reliability, , vol. 228(5), pages 437-448, October.
    4. Chiacchio, F. & D’Urso, D. & Manno, G. & Compagno, L., 2016. "Stochastic hybrid automaton model of a multi-state system with aging: Reliability assessment and design consequences," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 1-13.
    5. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
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    Cited by:

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    5. Keshtegar, Behrooz & Chakraborty, Souvik, 2018. "Dynamical accelerated performance measure approach for efficient reliability-based design optimization with highly nonlinear probabilistic constraints," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 69-83.
    6. Huang, Xianzhen & Aslett, Louis J.M. & Coolen, Frank P.A., 2019. "Reliability analysis of general phased mission systems with a new survival signature," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 416-422.
    7. Gascard, Eric & Simeu-Abazi, Zineb, 2018. "Quantitative Analysis of Dynamic Fault Trees by means of Monte Carlo Simulations: Event-Driven Simulation Approach," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 487-504.
    8. Postnikov, Ivan & Stennikov, Valery & Mednikova, Ekaterina & Penkovskii, Andrey, 2018. "Methodology for optimization of component reliability of heat supply systems," Applied Energy, Elsevier, vol. 227(C), pages 365-374.

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