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On systems with shared resources and optimal switching strategies

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  • Finkelstein, Maxim

Abstract

Simple series systems of identical components with spare parts are considered. It is shown that the cumulative distribution function of a system failure time tends to be a step function as the number of components increases and resources can be shared. An example of ‘continuous resources’ is also described. The time-sharing strategy for standby systems is investigated. It is proved that an optimal rule for a system of standby components with increasing failure rates is the single switching performed at a=t/2, where t is the mission time.

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  • Finkelstein, Maxim, 2009. "On systems with shared resources and optimal switching strategies," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1358-1362.
    • Handle: RePEc:eee:reensy:v:94:y:2009:i:8:p:1358-1362
    DOI: 10.1016/j.ress.2009.02.006
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    References listed on IDEAS

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    1. Samuel Kotz & Nozer D. Singpurwalla, 1999. "On a Bivariate Distribution with Exponential Marginals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 451-464, September.
    2. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, February.
    3. Anatoli Yashin & Ivan Iachine & Alexander Begun, 2000. "Mortality modeling: A review," Mathematical Population Studies, Taylor & Francis Journals, vol. 8(4), pages 305-332.
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    Citations

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    Cited by:

    1. Wang, Wenbin, 2011. "A joint spare part and maintenance inspection optimisation model using the Delay-Time concept," Reliability Engineering and System Safety, Elsevier, vol. 96(11), pages 1535-1541.
    2. Farhadi, Mohammad & Shahrokhi, Mahmoud & Rahmati, Seyed Habib A, 2022. "Developing a supplier selection model based on Markov chain and probability tree for a k-out-of-N system with different quality of spare parts," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    3. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2021. "Optimization of cyclic preventive replacement in homogeneous warm-standby system with reusable elements exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    4. Finkelstein, Maxim & Cha, Ji Hwan & Langston, Amy, 2022. "Optimal preventive switching of components in degrading systems," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    5. van Jaarsveld, Willem & Dekker, Rommert, 2011. "Spare parts stock control for redundant systems using reliability centered maintenance data," Reliability Engineering and System Safety, Elsevier, vol. 96(11), pages 1576-1586.
    6. Rezapour, Shabnam & Allen, Janet K. & Mistree, Farrokh, 2016. "Reliable flow in forward and after-sales supply chains considering propagated uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 409-436.
    7. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Optimal preventive replacement policy for homogeneous cold standby systems with reusable elements," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    8. Bjarnason, Erik T.S. & Taghipour, Sharareh & Banjevic, Dragan, 2014. "Joint optimal inspection and inventory for a k-out-of-n system," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 203-215.
    9. Maxim Finkelstein & Mahmood Shafiee, 2017. "Preventive maintenance for systems with repairable minor failures," Journal of Risk and Reliability, , vol. 231(2), pages 101-108, April.
    10. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2021. "Optimal shock-driven switching strategies with elements reuse in heterogeneous warm-standby systems," Reliability Engineering and System Safety, Elsevier, vol. 210(C).

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