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Optimal allocation of units in sequential probability series systems

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  • Qiu, Qingan
  • Cui, Lirong
  • Gao, Hongda
  • Yi, He

Abstract

A concept of Sequential Probability Series System (SPSS) is developed in this paper, which widely exists in many practical sectors such as power plants, inventory management and security management. In SPSS the failure states of each unit are divided into two classes according to their consequences: dangerous failure and safe failure, where the former results in system failure while the latter has no impact on the system. Suppose that when a failure unit appears in SPSS, the system fails with probability p while the other units in SPSS can continue working with probability 1−p. This paper treats the problem of achieving optimal allocation of units in SPSSs that maximizes expected total working time of all units. Three optimal allocation models are formulated. We derive the analytical expressions for the optimal allocation solutions under certain assumptions. A genetic algorithm and a Monte Carlo method are provided to solve the allocation problems whose analytical solutions are difficult to obtain. An application can be found in Remote Power Feeding System (RPFS). Numerical examples for a RPFS are presented to demonstrate the application of the developed approach in each model.

Suggested Citation

  • Qiu, Qingan & Cui, Lirong & Gao, Hongda & Yi, He, 2018. "Optimal allocation of units in sequential probability series systems," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 351-363.
    • Handle: RePEc:eee:reensy:v:169:y:2018:i:c:p:351-363
    DOI: 10.1016/j.ress.2017.09.011
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    7. Qiu, Qingan & Cui, Lirong, 2019. "Optimal mission abort policy for systems subject to random shocks based on virtual age process," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 11-20.
    8. Qingan Qiu & Lirong Cui & Dejing Kong, 2019. "Availability and maintenance modeling for a two-component system with dependent failures over a finite time horizon," Journal of Risk and Reliability, , vol. 233(2), pages 200-210, April.
    9. Andreas C. Georgiou & Konstantinos Kaparis & Eleni-Maria Vretta & Kyriakos Bitsis & George Paltayian, 2024. "A Bilevel DEA Model for Efficiency Evaluation and Target Setting with Stochastic Conditions," Mathematics, MDPI, vol. 12(4), pages 1-21, February.
    10. Zhao, Xian & Chai, Xiaofei & Sun, Jinglei & Qiu, Qingan, 2021. "Joint optimization of mission abort and component switching policies for multistate warm standby systems," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    11. Ling, Xiaoliang & Wei, Yinzhao & Si, Shubin, 2019. "Reliability optimization of k-out-of-n system with random selection of allocative components," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 186-193.
    12. Zhao, Qian Qian & Yun, Won Young, 2019. "Storage availability of one-shot system under periodic inspection considering inspection error," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 120-133.
    13. Yang, Li & Zhao, Yu & Peng, Rui & Ma, Xiaobing, 2018. "Hybrid preventive maintenance of competing failures under random environment," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 130-140.
    14. Eslami Baladeh, Aliakbar & Taghipour, Sharareh, 2022. "Reliability optimization of dynamic k-out-of-n systems with competing failure modes," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    15. Zhao, Xian & Liu, Haoran & Wu, Yaguang & Qiu, Qingan, 2023. "Joint optimization of mission abort and system structure considering dynamic tasks," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    16. Wang, Jinhe & Zhang, Xiaohong & Zeng, Jianchao & Zhang, Yunzheng, 2020. "Joint external and internal opportunistic optimisation for wind turbine considering wind velocity," Renewable Energy, Elsevier, vol. 159(C), pages 380-398.
    17. Liu, Baoliang & Wen, Yanqing & Qiu, Qingan & Shi, Haiyan & Chen, Jianhui, 2022. "Reliability analysis for multi-state systems under K-mixed redundancy strategy considering switching failure," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    18. Xiaofei Chai & Boyu Chen & Xian Zhao, 2023. "Optimal Mission Abort Decisions for Multi-Component Systems Considering Multiple Abort Criteria," Mathematics, MDPI, vol. 11(24), pages 1-12, December.
    19. Zhihua Chen & Xuchen Xu & Hongbo Liu, 2023. "The Successive Approximation Genetic Algorithm (SAGA) for Optimization Problems with Single Constraint," Mathematics, MDPI, vol. 11(8), pages 1-26, April.

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