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Robust counterpart optimization for the redundancy allocation problem in series-parallel systems with component mixing under uncertainty

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  • Soltani, Roya
  • Safari, Jalal
  • Sadjadi, Seyed Jafar

Abstract

In this paper, a robust optimization approach is used to solve the redundancy allocation problem (RAP) in series-parallel systems with component mixing where uncertainty exists in components’ reliabilities. In real world, the reliabilities of components are imprecisely estimated or the reliability of some components may vary due to some realistic factors. Therefore, we may deal with a system where there are many components with uncertain values of reliabilities. To deal with this problem, for the first time a robust optimization approach is applied to RAP with component mixing to produce a robust solution, which is relatively insensitive with respect to uncertainty in reliability of components. In addition, the advantages of the proposed robust technique are illustrated by considering a series-parallel system and finding the suitable redundancy levels and then Monte Carlo simulation is implemented to examine the quality of the robust solutions. The results indicate that applying the proposed robust RAP can be more reliable to determine system reliability in the designing phase of systems.

Suggested Citation

  • Soltani, Roya & Safari, Jalal & Sadjadi, Seyed Jafar, 2015. "Robust counterpart optimization for the redundancy allocation problem in series-parallel systems with component mixing under uncertainty," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 80-88.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:80-88
    DOI: 10.1016/j.amc.2015.08.069
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    References listed on IDEAS

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    1. Roya Soltani & Seyed J Sadjadi & Reza Tavakkoli-Moghaddam, 2014. "Robust cold standby redundancy allocation for nonrepairable series–parallel systems through Min-Max regret formulation and Benders’ decomposition method," Journal of Risk and Reliability, , vol. 228(3), pages 254-264, June.
    2. Safari, Jalal, 2012. "Multi-objective reliability optimization of series-parallel systems with a choice of redundancy strategies," Reliability Engineering and System Safety, Elsevier, vol. 108(C), pages 10-20.
    3. Roya Soltani & Seyed J Sadjadi, 2014. "Reliability optimization through robust redundancy allocation models with choice of component type under fuzziness," Journal of Risk and Reliability, , vol. 228(5), pages 449-459, October.
    4. Tavakkoli-Moghaddam, R. & Safari, J. & Sassani, F., 2008. "Reliability optimization of series-parallel systems with a choice of redundancy strategies using a genetic algorithm," Reliability Engineering and System Safety, Elsevier, vol. 93(4), pages 550-556.
    5. Sadjadi, Seyed Jafar & Soltani, R., 2009. "An efficient heuristic versus a robust hybrid meta-heuristic for general framework of serial–parallel redundancy problem," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1703-1710.
    6. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
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    Cited by:

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    2. Sun, Lu & Xu, Qingshan & Song, Yun, 2022. "Game-theoretic genetic-priced optimization of multiple microgrids under uncertainties," Applied Mathematics and Computation, Elsevier, vol. 426(C).
    3. Kim, Heungseob, 2018. "Maximization of system reliability with the consideration of component sequencing," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 64-72.
    4. Guilani, Pardis Pourkarim & Juybari, Mohammad N. & Ardakan, Mostafa Abouei & Kim, Heungseob, 2020. "Sequence optimization in reliability problems with a mixed strategy and heterogeneous backup scheme," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    5. Jiang, Ling & Cao, Jinde & Xiong, Lianglin, 2019. "Generalized multiobjective robustness and relations to set-valued optimization," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 599-608.
    6. Cao, Ran & Coit, David W. & Hou, Wei & Yang, Yushu, 2020. "Game theory based solution selection for multi-objective redundancy allocation in interval-valued problem parameters," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    7. Mohammad N. Juybari & Pardis Pourkarim Guilani & Mostafa Abouei Ardakan, 2022. "Bi-objective sequence optimization in reliability problems with a matrix-analytic approach," Annals of Operations Research, Springer, vol. 312(1), pages 275-304, May.
    8. Alikar, Najmeh & Mousavi, Seyed Mohsen & Raja Ghazilla, Raja Ariffin & Tavana, Madjid & Olugu, Ezutah Udoncy, 2017. "Application of the NSGA-II algorithm to a multi-period inventory-redundancy allocation problem in a series-parallel system," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 1-10.

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