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Mission reliability of semi-Markov systems under generalized operational time requirements

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  • Wu, Xiaoyue
  • Hillston, Jane

Abstract

Mission reliability of a system depends on specific criteria for mission success. To evaluate the mission reliability of some mission systems that do not need to work normally for the whole mission time, two types of mission reliability for such systems are studied. The first type corresponds to the mission requirement that the system must remain operational continuously for a minimum time within the given mission time interval, while the second corresponds to the mission requirement that the total operational time of the system within the mission time window must be greater than a given value. Based on Markov renewal properties, matrix integral equations are derived for semi-Markov systems. Numerical algorithms and a simulation procedure are provided for both types of mission reliability. Two examples are used for illustration purposes. One is a one-unit repairable Markov system, and the other is a cold standby semi-Markov system consisting of two components. By the proposed approaches, the mission reliability of systems with time redundancy can be more precisely estimated to avoid possible unnecessary redundancy of system resources.

Suggested Citation

  • Wu, Xiaoyue & Hillston, Jane, 2015. "Mission reliability of semi-Markov systems under generalized operational time requirements," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 122-129.
    • Handle: RePEc:eee:reensy:v:140:y:2015:i:c:p:122-129
    DOI: 10.1016/j.ress.2015.04.002
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    Cited by:

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    4. Yu, Haiyue & Wu, Xinyang & Wu, Xiaoyue, 2020. "An extended object-oriented petri net model for mission reliability evaluation of phased-mission system with time redundancy," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    5. Cheng, Chen & Yang, Jun & Li, Lei, 2021. "Reliability evaluation of a k-out-of-n(G)-subsystem based multi-state phased mission system with common bus performance sharing subjected to common cause failures," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    6. Wu, Xinyang & Yu, Haiyue & Balakrishnan, Narayanaswamy, 2022. "Modular model and algebraic phase algorithm for reliability modelling and evaluation of phased-mission systems with conflicting phase redundancy," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    7. Zhao, Xian & Fan, Yu & Qiu, Qingan & Chen, Ke, 2021. "Multi-criteria mission abort policy for systems subject to two-stage degradation process," European Journal of Operational Research, Elsevier, vol. 295(1), pages 233-245.
    8. Ke Chen & Xian Zhao & Qingan Qiu, 2022. "Optimal Task Abort and Maintenance Policies Considering Time Redundancy," Mathematics, MDPI, vol. 10(9), pages 1-16, April.
    9. Yihai He & Changchao Gu & Zhaoxiang Chen & Xiao Han, 2017. "Integrated predictive maintenance strategy for manufacturing systems by combining quality control and mission reliability analysis," International Journal of Production Research, Taylor & Francis Journals, vol. 55(19), pages 5841-5862, October.
    10. Qiu, Qingan & Cui, Lirong, 2019. "Gamma process based optimal mission abort policy," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    11. Li, Yan & Cui, Lirong & Lin, Cong, 2017. "Modeling and analysis for multi-state systems with discrete-time Markov regime-switching," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 41-49.
    12. Li, Xiang-Yu & Huang, Hong-Zhong & Li, Yan-Feng & Xiong, Xiaoyan, 2021. "A Markov regenerative process model for phased mission systems under internal degradation and external shocks," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    13. He Yi & Lirong Cui & Narayanaswamy Balakrishnan & Jingyuan Shen, 2022. "Multi-Point and Multi-Interval Bounded-Covering Availability Measures for Aggregated Markovian Repairable Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2427-2453, December.
    14. Fang, Chen & Cui, Lirong, 2021. "Reliability evaluation for balanced systems with auto-balancing mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    15. Zhao, Jiangbin & Si, Shubin & Cai, Zhiqiang & Guo, Peng & Zhu, Wenjin, 2020. "Mission success probability optimization for phased-mission systems with repairable component modules," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    16. Wu, Shengnan & Zhang, Laibin & Zheng, Wenpei & Liu, Yiliu & Lundteigen, Mary Ann, 2019. "Reliability modeling of subsea SISs partial testing subject to delayed restoration," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    17. Xiaoyu Cui & Shaoping Wang & Tongyang Li & Jian Shi, 2019. "System Reliability Assessment Based on Energy Dissipation: Modeling and Application in Electro-Hydrostatic Actuation System," Energies, MDPI, vol. 12(18), pages 1-22, September.
    18. Zhao, Xian & Sun, Jinglei & Qiu, Qingan & Chen, Ke, 2021. "Optimal inspection and mission abort policies for systems subject to degradation," European Journal of Operational Research, Elsevier, vol. 292(2), pages 610-621.
    19. Dhulipala, Somayajulu L.N. & Flint, Madeleine M., 2020. "Series of semi-Markov processes to model infrastructure resilience under multihazards," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    20. Yi, He & Cui, Lirong & Shen, Jingyuan & Li, Yan, 2018. "Stochastic properties and reliability measures of discrete-time semi-Markovian systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 162-173.
    21. Yan, Rui & Zhu, Xiaoping & Zhu, Xiaoning & Peng, Rui, 2023. "Joint optimisation of task abortions and routes of truck-and-drone systems under random attacks," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    22. 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.
    23. Yi, He & Cui, Lirong & Balakrishnan, Narayanaswamy, 2021. "New reliability indices for first- and second-order discrete-time aggregated semi-Markov systems with an application to TT&C system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    24. Qiu, Qingan & Cui, Lirong & Wu, Bei, 2020. "Dynamic mission abort policy for systems operating in a controllable environment with self-healing mechanism," Reliability Engineering and System Safety, Elsevier, vol. 203(C).

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