IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v93y2008i12p1801-1808.html
   My bibliography  Save this article

Modelling and estimating the reliability of stochastic dynamical systems with Markovian switching

Author

Listed:
  • Chiquet, Julien
  • Eid, Mohamed
  • Limnios, Nikolaos

Abstract

In this paper, a general framework for the modelling of physical phenomena with stochastic dynamical systems switched by jump Markov processes is given. A methodology of the associated estimation procedures is provided. A particular attention is paid to the estimation of the underlying jump process, which is not observable.

Suggested Citation

  • Chiquet, Julien & Eid, Mohamed & Limnios, Nikolaos, 2008. "Modelling and estimating the reliability of stochastic dynamical systems with Markovian switching," Reliability Engineering and System Safety, Elsevier, vol. 93(12), pages 1801-1808.
    • Handle: RePEc:eee:reensy:v:93:y:2008:i:12:p:1801-1808
    DOI: 10.1016/j.ress.2008.03.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832008001014
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2008.03.016?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard & Langrognet, Florent, 2006. "Model-based cluster and discriminant analysis with the MIXMOD software," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 587-600, November.
    2. Julien Chiquet & Nikolaos Limnios, 2006. "Estimating Stochastic Dynamical Systems Driven by a Continuous-Time Jump Markov Process," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 431-447, December.
    3. Myötyri, E. & Pulkkinen, U. & Simola, K., 2006. "Application of stochastic filtering for lifetime prediction," Reliability Engineering and System Safety, Elsevier, vol. 91(2), pages 200-208.
    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. Moghaddass, Ramin & Zuo, Ming J., 2014. "An integrated framework for online diagnostic and prognostic health monitoring using a multistate deterioration process," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 92-104.
    2. Jiang, Shan & Li, Yan-Fu, 2021. "Dynamic Reliability Assessment of Multi-cracked Structure under Fatigue Loading via Multi-State Physics Model," Reliability Engineering and System Safety, Elsevier, vol. 213(C).

    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. Lebret, Rémi & Iovleff, Serge & Langrognet, Florent & Biernacki, Christophe & Celeux, Gilles & Govaert, Gérard, 2015. "Rmixmod: The R Package of the Model-Based Unsupervised, Supervised, and Semi-Supervised Classification Mixmod Library," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(i06).
    2. Maugis, C. & Celeux, G. & Martin-Magniette, M.-L., 2011. "Variable selection in model-based discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1374-1387, November.
    3. Scrucca, Luca, 2011. "Model-based SIR for dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3010-3026, November.
    4. Jeffrey Andrews & Paul McNicholas, 2014. "Variable Selection for Clustering and Classification," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 136-153, July.
    5. Galimberti, Giuliano & Soffritti, Gabriele, 2014. "A multivariate linear regression analysis using finite mixtures of t distributions," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 138-150.
    6. Hai-Kun Wang & Yan-Feng Li & Yu Liu & Yuan-Jian Yang & Hong-Zhong Huang, 2015. "Remaining useful life estimation under degradation and shock damage," Journal of Risk and Reliability, , vol. 229(3), pages 200-208, June.
    7. Ying Liao & Yisha Xiang & Min Wang, 2021. "Health assessment and prognostics based on higher‐order hidden semi‐Markov models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(2), pages 259-276, March.
    8. Zio, Enrico & Compare, Michele, 2013. "Evaluating maintenance policies by quantitative modeling and analysis," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 53-65.
    9. Nazif Çalış & Hamza Erol, 2012. "A new per-field classification method using mixture discriminant analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(10), pages 2129-2140, June.
    10. Carlo Cavicchia & Maurizio Vichi & Giorgia Zaccaria, 2022. "Gaussian mixture model with an extended ultrametric covariance structure," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 399-427, June.
    11. Hu, Chao & Youn, Byeng D. & Wang, Pingfeng & Taek Yoon, Joung, 2012. "Ensemble of data-driven prognostic algorithms for robust prediction of remaining useful life," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 120-135.
    12. Guglielmo D’Amico & Philippe Regnault, 2018. "Dynamic Measurement of Poverty: Modeling and Estimation," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 305-340, November.
    13. Gallopin Mélina & Celeux Gilles & Jaffrézic Florence & Rau Andrea, 2015. "A model selection criterion for model-based clustering of annotated gene expression data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(5), pages 413-428, November.
    14. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    15. Zio, Enrico & Peloni, Giovanni, 2011. "Particle filtering prognostic estimation of the remaining useful life of nonlinear components," Reliability Engineering and System Safety, Elsevier, vol. 96(3), pages 403-409.
    16. Vlad Stefan Barbu & Nicolas Vergne, 2019. "Reliability and Survival Analysis for Drifting Markov Models: Modeling and Estimation," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1407-1429, December.
    17. Pedregal, Diego J. & Carmen Carnero, Ma., 2009. "Vibration analysis diagnostics by continuous-time models: A case study," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 244-253.
    18. Chiquet, Julien & Limnios, Nikolaos, 2008. "A method to compute the transition function of a piecewise deterministic Markov process with application to reliability," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1397-1403, September.
    19. Ryan Browne & Paul McNicholas, 2014. "Estimating common principal components in high dimensions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 217-226, June.
    20. Bouveyron, Charles & Brunet-Saumard, Camille, 2014. "Model-based clustering of high-dimensional data: A review," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 52-78.

    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:eee:reensy:v:93:y:2008:i:12:p:1801-1808. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.