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Optimal Mission Duration for Partially Repairable Systems Operating in a Random Environment

Author

Listed:
  • Maxim Finkelstein

    (University of the Free State
    ITMO University)

  • Gregory Levitin

    (The Israel Electric Corporation)

Abstract

As a system failure during a mission can result in considerable penalties, at some instances it is more cost-effective to terminate operation of a system than to attempt to complete its mission. This paper analyzes the optimal mission duration for systems that operate in a random environment modeled by a Poisson shock process and can be minimally repaired during a mission. Two independent sources of failures are considered and for both cases, the failures are classified as minor or terminal in accordance with the Brown-Proschan model. Under certain assumptions, an optimal time of mission termination is obtained. It is shown that, if for some reason a termination is not technically possible at this optimal time, the mission should be terminated within a specific time interval and, if this is not possible, it should not be terminated beyond this interval. Illustrative examples are presented. The influence of mission and system parameters on the mission termination interval is demonstrated.

Suggested Citation

  • Maxim Finkelstein & Gregory Levitin, 2018. "Optimal Mission Duration for Partially Repairable Systems Operating in a Random Environment," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 505-516, June.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:2:d:10.1007_s11009-017-9571-6
    DOI: 10.1007/s11009-017-9571-6
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    References listed on IDEAS

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    1. Finkelstein, Maxim & Marais, Francois, 2010. "On terminating Poisson processes in some shock models," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 874-879.
    2. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, March.
    3. 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.
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    8. Finkelstein, Maxim, 2007. "Shocks in homogeneous and heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 569-574.
    9. van der Weide, J.A.M. & Pandey, M.D., 2011. "Stochastic analysis of shock process and modeling of condition-based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 96(6), pages 619-626.
    10. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael & del Carmen Segovia, Maria, 2009. "Replacement policy in a system under shocks following a Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 497-502.
    11. Philip J. Boland, 1982. "Periodic replacement when minimal repair costs vary with time," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(4), pages 541-546, December.
    12. 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.
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    Cited by:

    1. 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.
    2. Maxim Finkelstein & Ji Hwan Cha & Amy Langston, 2023. "Termination versus operation extension for degrading systems," Journal of Risk and Reliability, , vol. 237(6), pages 1175-1185, December.
    3. Maxim Finkelstein & Ji Hwan Cha & Shyamal Ghosh, 2021. "Optimal inspection for missions with a possibility of abortion or switching to a lighter regime," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 722-740, October.
    4. Qiu, Qingan & Cui, Lirong, 2019. "Gamma process based optimal mission abort policy," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    5. Cheng, Guoqing & Li, Ling & Shangguan, Chunxia & Yang, Nan & Jiang, Bo & Tao, Ningrong, 2023. "Optimal joint inspection and mission abort policy for a partially observable system," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    6. Maxim Finkelstein & Gregory Levitin, 2020. "On missions’ quality of performance for systems with partially or completely observable degradation," Journal of Risk and Reliability, , vol. 234(5), pages 676-685, October.

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