IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v134y2015icp126-133.html
   My bibliography  Save this article

Failure modeling of an electrical N-component framework by the non-stationary Markovian arrival process

Author

Listed:
  • Rodríguez, Joanna
  • Lillo, Rosa E.
  • Ramírez-Cobo, Pepa

Abstract

This paper considers the non-stationary version of the Markovian arrival process to model the failures of N electrical components that are considered to be identically distributed, but for which it is not reasonable to assume that the operational times related to each component are independent or identically distributed. We propose a moment matching estimation approach to fit the data via a non-stationary Markovian arrival process. A simulated and a real data set provided by the Spanish electrical group Iberdrola are presented to illustrate the approach.

Suggested Citation

  • Rodríguez, Joanna & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2015. "Failure modeling of an electrical N-component framework by the non-stationary Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 126-133.
    • Handle: RePEc:eee:reensy:v:134:y:2015:i:c:p:126-133
    DOI: 10.1016/j.ress.2014.10.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832014002610
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2014.10.020?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. Der Kiureghian, Armen & Song, Junho, 2008. "Multi-scale reliability analysis and updating of complex systems by use of linear programming," Reliability Engineering and System Safety, Elsevier, vol. 93(2), pages 288-297.
    2. Bodrog, L. & Heindl, A. & Horváth, G. & Telek, M., 2008. "A Markovian canonical form of second-order matrix-exponential processes," European Journal of Operational Research, Elsevier, vol. 190(2), pages 459-477, October.
    3. Chakravarthy, Srinivas R., 2012. "Maintenance of a deteriorating single server system with Markovian arrivals and random shocks," European Journal of Operational Research, Elsevier, vol. 222(3), pages 508-522.
    4. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2012. "A shock and wear system under environmental conditions subject to internal failures, repair, and replacement," Reliability Engineering and System Safety, Elsevier, vol. 99(C), pages 55-61.
    5. Finkelstein, Maxim & Marais, Francois, 2010. "On terminating Poisson processes in some shock models," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 874-879.
    6. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2014. "Matrix stochastic analysis of the maintainability of a machine under shocks," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 11-17.
    7. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael & del Carmen Segovia, Maria, 2009. "Replacement policy in a system under shocks following a Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 497-502.
    8. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2014. "Optimal component loading in 1-out-of-N cold standby systems," Reliability Engineering and System Safety, Elsevier, vol. 127(C), pages 58-64.
    9. Pepa Ramírez-Cobo & Rosa Lillo & Michael Wiper, 2014. "Identifiability of the MAP 2 /G/1 queueing system," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 274-289, April.
    10. Der Kiureghian, Armen & Ditlevsen, Ove D. & Song, Junho, 2007. "Availability, reliability and downtime of systems with repairable components," Reliability Engineering and System Safety, Elsevier, vol. 92(2), pages 231-242.
    11. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2014. "A redundant n-system under shocks and repairs following Markovian arrival processes," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 69-75.
    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. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2016. "A warmstandby system under shocks and repair governed by MAPs," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 331-338.
    2. Ramírez-Cobo, Pepa, 2017. "Findings about the two-state BMMPP for modeling point processes in reliability and queueing systems," DES - Working Papers. Statistics and Econometrics. WS 24622, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Ramírez-Cobo, Pepa & Carrizosa, Emilio & Lillo, Rosa E., 2021. "Analysis of an aggregate loss model in a Markov renewal regime," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    4. Belén García-Mora & Cristina Santamaría & Gregorio Rubio, 2020. "A Phase-Type Distribution for the Sum of Two Concatenated Markov Processes Application to the Analysis Survival in Bladder Cancer," Mathematics, MDPI, vol. 8(12), pages 1-15, November.
    5. Rodríguez, Joanna & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2016. "Dependence patterns for modeling simultaneous events," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 19-30.
    6. Yera, Yoel G. & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2019. "Fitting procedure for the two-state Batch Markov modulated Poisson process," European Journal of Operational Research, Elsevier, vol. 279(1), pages 79-92.
    7. Yera, Yoel G. & Lillo, Rosa E. & Nielsen, Bo F. & Ramírez-Cobo, Pepa & Ruggeri, Fabrizio, 2021. "A bivariate two-state Markov modulated Poisson process for failure modeling," Reliability Engineering and System Safety, Elsevier, vol. 208(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. Rodríguez, Joanna & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2016. "Dependence patterns for modeling simultaneous events," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 19-30.
    2. Maxim Finkelstein & Gregory Levitin, 2018. "Optimal mission duration for systems subject to shocks and internal failures," Journal of Risk and Reliability, , vol. 232(1), pages 82-91, February.
    3. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "On some properties of shock processes in a ‘natural’ scale," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 104-110.
    4. Ji Hwan Cha & Maxim Finkelstein, 2020. "On optimal life extension for degrading systems," Journal of Risk and Reliability, , vol. 234(3), pages 487-495, June.
    5. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2014. "A reliability system under different types of shock governed by a Markovian arrival process and maintenance policy K," European Journal of Operational Research, Elsevier, vol. 235(3), pages 636-642.
    6. Pepa Ramírez-Cobo & Rosa E. Lillo, 2012. "New Results About Weakly Equivalent MAP 2 and MAP 3 Processes," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 421-444, September.
    7. Levitin, Gregory & Finkelstein, Maxim, 2019. "Optimal loading of elements in series systems exposed to external shocks," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    8. Juan Eloy Ruiz-Castro, 2015. "A preventive maintenance policy for a standby system subject to internal failures and external shocks with loss of units," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(9), pages 1600-1613, July.
    9. Ramírez-Cobo, Pepa, 2017. "Findings about the two-state BMMPP for modeling point processes in reliability and queueing systems," DES - Working Papers. Statistics and Econometrics. WS 24622, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. Maxim Finkelstein & Gregory Levitin, 2020. "On missions’ quality of performance for systems with partially or completely observable degradation," Journal of Risk and Reliability, , vol. 234(5), pages 676-685, October.
    11. Ji Hwan Cha & Maxim Finkelstein & Gregory Levitin, 2017. "Bivariate preventive maintenance for repairable systems subject to random shocks," Journal of Risk and Reliability, , vol. 231(6), pages 643-653, December.
    12. Byun, Ji-Eun & de Oliveira, Welington & Royset, Johannes O., 2023. "S-BORM: Reliability-based optimization of general systems using buffered optimization and reliability method," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    13. Ji Cha & Maxim Finkelstein & Francois Marais, 2014. "Survival of systems with protection subject to two types of external attacks," Annals of Operations Research, Springer, vol. 212(1), pages 79-91, January.
    14. Maxim Finkelstein & Gregory Levitin, 2018. "Optimal Mission Duration for Partially Repairable Systems Operating in a Random Environment," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 505-516, June.
    15. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2018. "Bivariate preventive maintenance of systems with lifetimes dependent on a random shock process," European Journal of Operational Research, Elsevier, vol. 266(1), pages 122-134.
    16. Liu, Baoliang & Cui, Lirong & Wen, Yanqing & Shen, Jingyuan, 2015. "A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 1-8.
    17. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2017. "On preventive maintenance of systems with lifetimes dependent on a random shock process," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 90-97.
    18. Delia Montoro-Cazorla & Rafael Pérez-Ocón, 2022. "Optimizing Costs in a Reliability System under Markovian Arrival of Failures and Reposition by K -Policy Inspection," Mathematics, MDPI, vol. 10(11), pages 1-21, June.
    19. Ji Hwan Cha & Maxim Finkelstein, 2019. "On some characteristics of quality for systems operating in a random environment," Journal of Risk and Reliability, , vol. 233(2), pages 257-267, April.
    20. Pepa Ramírez-Cobo & Rosa Lillo & Michael Wiper, 2014. "Identifiability of the MAP 2 /G/1 queueing system," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 274-289, April.

    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:134:y:2015:i:c:p:126-133. 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.