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Optimal work distribution and backup frequency for two non-identical work sharing elements

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  • Levitin, Gregory
  • Xing, Liudong
  • Dai, Yuanshun

Abstract

Motivated by abundant real-world applications where system elements process different work portions in parallel to accomplish a specified mission task, this paper models and optimizes two-element work-sharing systems. When one of the two elements fails, the remaining element takes over the work of the failed element upon completing its own part. Incremental backups are used to reduce the amount of work that should be redone in the case of failures. System elements can be characterized by different processing speeds, different time-to-failure distributions, and different numbers of backup actions. Mission success probability and expected mission completion time are first derived. Based on the proposed evaluation procedure, unconstrained and constrained optimization problems are formulated and solved, which find optimal work distribution and backup frequencies of the two elements maximizing mission success probability. Influence of element reliability, processing speed, deceleration factor as well as data backup and retrieval complexity on the optimal solutions is further investigated through examples. Results of this work can facilitate the optimal decision on work distribution and backup policies of heterogeneous work-sharing systems.

Suggested Citation

  • Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2018. "Optimal work distribution and backup frequency for two non-identical work sharing elements," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 127-136.
    • Handle: RePEc:eee:reensy:v:170:y:2018:i:c:p:127-136
    DOI: 10.1016/j.ress.2017.10.016
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    References listed on IDEAS

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    1. Paul H. Kvam & Edsel A. Pena, 2005. "Estimating Load-Sharing Properties in a Dynamic Reliability System," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 262-272, March.
    2. Singh, Bhupendra & Gupta, Puneet Kumar, 2012. "Load-sharing system model and its application to the real data set," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1615-1629.
    3. Zhang, Tieling & Xie, Min & Horigome, Michio, 2006. "Availability and reliability of k-out-of-(M+N):G warm standby systems," Reliability Engineering and System Safety, Elsevier, vol. 91(4), pages 381-387.
    4. Levitin, Gregory & Xing, Liudong & Amari, Suprasad V. & Dai, Yuanshun, 2013. "Reliability of non-repairable phased-mission systems with propagated failures," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 218-228.
    5. Levitin, Gregory & Dai, Yuan-Shun, 2008. "Optimal service task partition and distribution in grid system with star topology," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 152-159.
    6. Singh, Bhupendra & Sharma, K.K. & Kumar, Anuj, 2008. "A classical and Bayesian estimation of a k-components load-sharing parallel system," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5175-5185, August.
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    Cited by:

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    2. Franco, Manuel & Vivo, Juana-Maria & Kundu, Debasis, 2020. "A generalized Freund bivariate model for a two-component load sharing system," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    3. Bora Çekyay, 2021. "Reliability of mission-based k-out-of-n systems with exponential phase durations and component lifetimes," Journal of Risk and Reliability, , vol. 235(3), pages 446-457, June.

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