IDEAS home Printed from https://ideas.repec.org/a/sae/risrel/v227y2013i5p523-533.html
   My bibliography  Save this article

Affine arithmetic for assessing the uncertainty propagation on steady-state probabilities of Markov models owing to uncertainties in transition rates

Author

Listed:
  • Claudio M Rocco S

Abstract

This article proposes the use of affine arithmetic as an alternative approach for assessing the effects of uncertainties of transition rates on the steady-state probabilities for each possible state of a system represented by a Markov model. Affine arithmetic is an extension of interval arithmetic, able to track “the dependency between variables throughout calculations†and to provide strict bounds. Several examples illustrate the proposed approach. Results are compared with other approaches, such as interval arithmetic, Monte Carlo simulation or solving linear systems of simultaneous equations.

Suggested Citation

  • Claudio M Rocco S, 2013. "Affine arithmetic for assessing the uncertainty propagation on steady-state probabilities of Markov models owing to uncertainties in transition rates," Journal of Risk and Reliability, , vol. 227(5), pages 523-533, October.
    • Handle: RePEc:sae:risrel:v:227:y:2013:i:5:p:523-533
    DOI: 10.1177/1748006X13485189
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/1748006X13485189
    Download Restriction: no
    File URL: https://libkey.io/10.1177/1748006X13485189?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Do Van, Phuc & Barros, Anne & Bérenguer, Christophe, 2010. "From differential to difference importance measures for Markov reliability models," European Journal of Operational Research, Elsevier, vol. 204(3), pages 513-521, August.
    2. Do Van, Phuc & Barros, Anne & Bérenguer, Christophe, 2008. "Reliability importance analysis of Markovian systems at steady state using perturbation analysis," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1605-1615.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lin, Yan-Hui & Yam, Richard C.M., 2017. "Uncertainty importance measures of dependent transition rates for transient and steady state probabilities," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 402-409.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shumin Li & Shubin Si & Liudong Xing & Shudong Sun, 2014. "Integrated importance of multi-state fault tree based on multi-state multi-valued decision diagram," Journal of Risk and Reliability, , vol. 228(2), pages 200-208, April.
    2. Zhu, Xiaoyan & Boushaba, Mahmoud & Coit, David W. & Benyahia, Azzeddine, 2017. "Reliability and importance measures for m-consecutive-k, l-out-of-n system with non-homogeneous Markov-dependent components," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 1-9.
    3. C M Rocco S, 2012. "Effects of the transition rate uncertainty on the steady state probabilities of Markov models using interval arithmetic," Journal of Risk and Reliability, , vol. 226(2), pages 234-245, April.
    4. Rocco S., Claudio M. & Emmanuel Ramirez-Marquez, José, 2015. "Assessment of the transition-rates importance of Markovian systems at steady state using the unscented transformation," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 212-220.
    5. Aizpurua, J.I. & Catterson, V.M. & Papadopoulos, Y. & Chiacchio, F. & D'Urso, D., 2017. "Supporting group maintenance through prognostics-enhanced dynamic dependability prediction," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 171-188.
    6. Zhai, Qingqing & Yang, Jun & Xie, Min & Zhao, Yu, 2014. "Generalized moment-independent importance measures based on Minkowski distance," European Journal of Operational Research, Elsevier, vol. 239(2), pages 449-455.
    7. Tyrväinen, T., 2013. "Risk importance measures in the dynamic flowgraph methodology," Reliability Engineering and System Safety, Elsevier, vol. 118(C), pages 35-50.
    8. Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.
    9. Wu, Shaomin & Coolen, Frank P.A., 2013. "A cost-based importance measure for system components: An extension of the Birnbaum importance," European Journal of Operational Research, Elsevier, vol. 225(1), pages 189-195.
    10. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    11. Do Van, Phuc & Barros, Anne & Bérenguer, Christophe, 2010. "From differential to difference importance measures for Markov reliability models," European Journal of Operational Research, Elsevier, vol. 204(3), pages 513-521, August.
    12. Do, Phuc & Bérenguer, Christophe, 2020. "Conditional reliability-based importance measures," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    13. Mario Hellmich & Heinz-Peter Berg, 2013. "On the construction of component importance measures for semi-Markov systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 15-32, February.
    14. P Do Van & A Barros & C Berenguer, 2008. "Importance measure on finite time horizon and application to Markovian multistate production systems," Journal of Risk and Reliability, , vol. 222(3), pages 449-461, September.
    15. Borgonovo, E. & Smith, C.L., 2012. "Composite multilinearity, epistemic uncertainty and risk achievement worth," European Journal of Operational Research, Elsevier, vol. 222(2), pages 301-311.
    16. Borgonovo, E., 2010. "The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions," European Journal of Operational Research, Elsevier, vol. 204(3), pages 485-495, August.
    17. E. Borgonovo & C. L. Smith, 2011. "A Study of Interactions in the Risk Assessment of Complex Engineering Systems: An Application to Space PSA," Operations Research, INFORMS, vol. 59(6), pages 1461-1476, December.
    18. Borgonovo, Emanuele & Aliee, Hananeh & Glaß, Michael & Teich, Jürgen, 2016. "A new time-independent reliability importance measure," European Journal of Operational Research, Elsevier, vol. 254(2), pages 427-442.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:risrel:v:227:y:2013:i:5:p:523-533. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.