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Optimal abort rules for additive multi-attempt missions

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  • Levitin, Gregory
  • Finkelstein, Maxim
  • Xiang, Yanping

Abstract

Mission aborts can be executed in many real-world systems when the specified malfunction/deterioration conditions are met and, therefore, a risk of a system's loss in the case of mission continuation becomes too high. After mission aborting, a rescue or recovery procedure is usually initiated. Previous results reported in the literature dealt with the setting when only one attempt to complete a mission is allowed. However, missions with a possibility of multiple attempts can occur in different real-world settings when accomplishing a mission is really important and the cost-related and the time-wise restrictions for this are not very severe. In this paper, we consider the case when a part of the mission task that was accomplished in the earlier attempts can be saved (additively) and not discarded. The probabilistic model for this case is developed and the tradeoff between the overall mission success probability and the system loss probability is studied. The problem of achieving the maximal mission success probability for the given level of system survivability is solved. A detailed example illustrating application of the suggested model is presented. It is shown that, unlike the single attempt case, aborting the mission when multiple attempts are allowed, can be beneficial even when the mission completion is the only concern and no constraint is imposed on the system survival probability.

Suggested Citation

  • Levitin, Gregory & Finkelstein, Maxim & Xiang, Yanping, 2021. "Optimal abort rules for additive multi-attempt missions," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    • Handle: RePEc:eee:reensy:v:205:y:2021:i:c:s0951832020307456
    DOI: 10.1016/j.ress.2020.107245
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    References listed on IDEAS

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    1. Toshio Nakagawa, 2007. "Shock and Damage Models in Reliability Theory," Springer Series in Reliability Engineering, Springer, number 978-1-84628-442-7, January.
    2. Levitin, Gregory & Finkelstein, Maxim & Xiang, Yanping, 2020. "Optimal multi-attempt missions with cumulative effect," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    3. Tanwar, Monika & Rai, Rajiv N. & Bolia, Nomesh, 2014. "Imperfect repair modeling using Kijima type generalized renewal process," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 24-31.
    4. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "State-based mission abort policies for multistate systems," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    5. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Mission abort policy balancing the uncompleted mission penalty and system loss risk," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 194-201.
    6. Peng, Rui, 2018. "Joint routing and aborting optimization of cooperative unmanned aerial vehicles," Reliability Engineering and System Safety, Elsevier, vol. 177(C), pages 131-137.
    7. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, January.
    8. Zhu, Xiaoning & Yan, Rui & Peng, Rui & Zhang, Zhongxin, 2020. "Optimal routing, loading and aborting of UAVs executing both visiting tasks and transportation tasks," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    9. Maxim Finkelstein & Ji Hwan Cha, 2013. "Burn-in for Heterogeneous Populations," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 261-312, Springer.
    10. Levitin, Gregory & Finkelstein, Maxim & Xiang, Yanping, 2020. "Optimal abort rules and subtask distribution in missions performed by multiple independent heterogeneous units," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    11. Qiu, Qingan & Cui, Lirong, 2019. "Gamma process based optimal mission abort policy," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    12. Gut, Allan & Hüsler, Jürg, 2005. "Realistic variation of shock models," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 187-204, September.
    13. Gregory Levitin & Maxim Finkelstein, 2018. "Optimal Mission Abort Policy for Systems Operating in a Random Environment," Risk Analysis, John Wiley & Sons, vol. 38(4), pages 795-803, April.
    14. 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.
    15. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort policy optimization for series systems with overlapping primary and rescue subsystems operating in a random environment," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    16. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort and rescue for multistate systems operating under the Poisson process of shocks," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    17. Levitin, Gregory & Finkelstein, Maxim & Xiang, Yanping, 2020. "Optimal aborting rule in multi-attempt missions performed by multicomponent systems," European Journal of Operational Research, Elsevier, vol. 283(1), pages 244-252.
    18. 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).
    19. Maxim Finkelstein & Ji Hwan Cha, 2013. "Shocks as Burn-in," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 313-361, Springer.
    20. Gregory Levitin & Maxim Finkelstein & Hong‐Zhong Huang, 2019. "Optimal Abort Rules for Multiattempt Missions," Risk Analysis, John Wiley & Sons, vol. 39(12), pages 2732-2743, December.
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    Cited by:

    1. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2023. "Optimal aborting policy for shock exposed missions with random rescue time," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    2. Levitin, Gregory & Xing, Liudong & Dai, Yanshun, 2021. "Joint optimal mission aborting and replacement and maintenance scheduling in dual-unit standby systems," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    3. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2024. "Optimal task aborting and sequencing in time constrained multi-task multi-attempt missions," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    4. 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).
    5. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2022. "Using kamikaze components in multi-attempt missions with abort option," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    6. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2022. "Mission aborting and system rescue for multi-state systems with arbitrary structure," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    7. Zhao, Xian & Lv, Zuheng & Qiu, Qingan & Wu, Yaguang, 2023. "Designing two-level rescue depot location and dynamic rescue policies for unmanned vehicles," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    8. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2023. "Optimal task sequencing and aborting in multi-attempt multi-task missions with a limited number of attempts," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    9. Zhao, Xian & Dai, Ying & Qiu, Qingan & Wu, Yaguang, 2022. "Joint optimization of mission aborts and allocation of standby components considering mission loss," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    10. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2021. "Dynamic task distribution balancing primary mission work and damage reduction work in parallel systems exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    11. Levitin, Gregory & Finkelstein, Maxim & Xiang, Yanping, 2021. "Optimal mission abort policies for repairable multistate systems performing multi-attempt mission," Reliability Engineering and System Safety, Elsevier, vol. 209(C).

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