IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v59y2002i3p245-255.html
   My bibliography  Save this article

The rate of occurrence of failures for semi-Markov processes and estimation

Author

Listed:
  • Ouhbi, Brahim
  • Limnios, Nikolaos

Abstract

This paper investigates the rate of occurrence of failures (ROCOF) of finite state semi-Markov systems. Firstly, a formula for evaluating the ROCOF for semi-Markov systems is derived. As a consequence of this result, we derive the ROCOF of Markov systems as well as the ROCOF of the alternating renewal processes and we give their asymptotic values. From the semi-Markov ROCOF formula, we propose a statistical estimator of this function. Finally, the uniform strong consistency and the asymptotic normality of this estimator are obtained.

Suggested Citation

  • Ouhbi, Brahim & Limnios, Nikolaos, 2002. "The rate of occurrence of failures for semi-Markov processes and estimation," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 245-255, October.
    • Handle: RePEc:eee:stapro:v:59:y:2002:i:3:p:245-255
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(02)00139-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Citations

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


    Cited by:

    1. Guglielmo D’Amico, 2015. "Rate of Occurrence of Failures (ROCOF) of Higher-Order for Markov Processes: Analysis, Inference and Application to Financial Credit Ratings," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 929-949, December.
    2. D’Amico, Guglielmo & Petroni, Filippo, 2023. "ROCOF of higher order for semi-Markov processes," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    3. Irene Votsi & Nikolaos Limnios & George Tsaklidis & Eleftheria Papadimitriou, 2012. "Estimation of the Expected Number of Earthquake Occurrences Based on Semi-Markov Models," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 685-703, September.
    4. Gámiz, M.L. & Román, Y., 2008. "Non-parametric estimation of the availability in a general repairable system," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1188-1196.
    5. Márcio das Chagas Moura & Enrique López Droguett, 2010. "Numerical Approach for Assessing System Dynamic Availability Via Continuous Time Homogeneous Semi-Markov Processes," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 431-449, September.
    6. 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.
    7. Nikolaos Limnios, 2012. "Reliability Measures of Semi-Markov Systems with General State Space," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 895-917, December.
    8. Moura, Márcio das Chagas & Droguett, Enrique López, 2009. "Mathematical formulation and numerical treatment based on transition frequency densities and quadrature methods for non-homogeneous semi-Markov processes," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 342-349.
    9. I. Votsi & N. Limnios, 2015. "Estimation of the intensity of the hitting time for semi-Markov chains and hidden Markov renewal chains," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(2), pages 149-166, June.

    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:stapro:v:59:y:2002:i:3:p:245-255. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.