IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v147y2022icp423-455.html
   My bibliography  Save this article

Change-level detection for Lévy subordinators

Author

Listed:
  • Al Masry, Zeina
  • Rabehasaina, Landy
  • Verdier, Ghislain

Abstract

Let X=(Xt)t≥0 be a process behaving as a general increasing Lévy process (subordinator) prior to hitting a given unknown level m0, then behaving as another different subordinator once this threshold is crossed. This paper addresses the detection of this unknown threshold m0∈[0,+∞] from an observed trajectory of the process. These kind of model and issue are encountered in many areas such as reliability and quality control in degradation problems. More precisely, we construct, from a sample path and for each ε>0, a so-called detection level Lε by considering a CUSUM inspired procedure. Under mild assumptions, this level is such that, while m0 is infinite (i.e. when no changes occur), its expectation E∞(Lε) tends to +∞ as ε tends to 0, and the expected overshoot Em0([Lε−m0]+), while the threshold m0 is finite, is negligible compared to E∞(Lε) as ε tends to 0. Numerical illustrations are provided when the Lévy processes are gamma processes with different shape parameters.

Suggested Citation

  • Al Masry, Zeina & Rabehasaina, Landy & Verdier, Ghislain, 2022. "Change-level detection for Lévy subordinators," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 423-455.
    • Handle: RePEc:eee:spapps:v:147:y:2022:i:c:p:423-455
    DOI: 10.1016/j.spa.2022.01.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922000369
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.01.022?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. Fouladirad, Mitra & Grall, Antoine & Dieulle, Laurence, 2008. "On the use of on-line detection for maintenance of gradually deteriorating systems," Reliability Engineering and System Safety, Elsevier, vol. 93(12), pages 1814-1820.
    2. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.
    3. Krawiec, Michał & Palmowski, Zbigniew & Płociniczak, Łukasz, 2018. "Quickest drift change detection in Lévy-type force of mortality model," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 432-450.
    4. Zeina Al Masry & Sophie Mercier & Ghislain Verdier, 2017. "Approximate Simulation Techniques and Distribution of an Extended Gamma Process," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 213-235, March.
    5. Fouladirad, Mitra & Grall, Antoine, 2011. "Condition-based maintenance for a system subject to a non-homogeneous wear process with a wear rate transition," Reliability Engineering and System Safety, Elsevier, vol. 96(6), pages 611-618.
    Full references (including those not matched with items on IDEAS)

    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. Zhang, Aibo & Zhang, Tieling & Barros, Anne & Liu, Yiliu, 2020. "Optimization of maintenances following proof tests for the final element of a safety-instrumented system," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    2. Alaswad, Suzan & Xiang, Yisha, 2017. "A review on condition-based maintenance optimization models for stochastically deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 54-63.
    3. Fouladirad, Mitra & Grall, Antoine, 2011. "Condition-based maintenance for a system subject to a non-homogeneous wear process with a wear rate transition," Reliability Engineering and System Safety, Elsevier, vol. 96(6), pages 611-618.
    4. Esposito, Nicola & Mele, Agostino & Castanier, Bruno & GIORGIO, Massimiliano, 2023. "A hybrid maintenance policy for a deteriorating unit in the presence of three forms of variability," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    5. Tiedo Tinga & Rene Janssen, 2013. "The interplay between deployment and optimal maintenance intervals for complex multi-component systems," Journal of Risk and Reliability, , vol. 227(3), pages 227-240, June.
    6. Ponchet, Amélie & Fouladirad, Mitra & Grall, Antoine, 2010. "Assessment of a maintenance model for a multi-deteriorating mode system," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1244-1254.
    7. N. C. Caballé & I. T. Castro, 2019. "Assessment of the maintenance cost and analysis of availability measures in a finite life cycle for a system subject to competing failures," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 255-290, March.
    8. Giorgio, Massimiliano & Pulcini, Gianpaolo, 2024. "The effect of model misspecification of the bounded transformed gamma process on maintenance optimization," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    9. de Jonge, Bram, 2019. "Discretizing continuous-time continuous-state deterioration processes, with an application to condition-based maintenance optimization," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 1-5.
    10. Zhang, Nan & Fouladirad, Mitra & Barros, Anne, 2018. "Optimal imperfect maintenance cost analysis of a two-component system with failure interactions," Reliability Engineering and System Safety, Elsevier, vol. 177(C), pages 24-34.
    11. Caballé, N.C. & Castro, I.T. & Pérez, C.J. & Lanza-Gutiérrez, J.M., 2015. "A condition-based maintenance of a dependent degradation-threshold-shock model in a system with multiple degradation processes," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 98-109.
    12. Tinga, Tiedo, 2010. "Application of physical failure models to enable usage and load based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 95(10), pages 1061-1075.
    13. Pedersen, Tom Ivar & Liu, Xingheng & Vatn, Jørn, 2023. "Maintenance optimization of a system subject to two-stage degradation, hard failure, and imperfect repair," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    14. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    15. Cai, Yue & Teunter, Ruud H. & de Jonge, Bram, 2023. "A data-driven approach for condition-based maintenance optimization," European Journal of Operational Research, Elsevier, vol. 311(2), pages 730-738.
    16. Medina-Oliva, G. & Weber, P. & Iung, B., 2013. "PRM-based patterns for knowledge formalisation of industrial systems to support maintenance strategies assessment," Reliability Engineering and System Safety, Elsevier, vol. 116(C), pages 38-56.
    17. Song, Kai & Shi, Jian & Yi, Xiaojian, 2020. "A time-discrete and zero-adjusted gamma process model with application to degradation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    18. Thomas Michael Welte & Iver Bakken Sperstad & Espen Høegh Sørum & Magne Lorentzen Kolstad, 2017. "Integration of Degradation Processes in a Strategic Offshore Wind Farm O&M Simulation Model," Energies, MDPI, vol. 10(7), pages 1-18, July.
    19. Finkelstein, Maxim & Cha, Ji Hwan & Langston, Amy, 2023. "Improving classical optimal age-replacement policies for degrading items," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    20. Phuc Do & Christophe Bérenguer, 2022. "Residual life-based importance measures for predictive maintenance decision-making," Journal of Risk and Reliability, , vol. 236(1), pages 98-113, February.

    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:spapps:v:147:y:2022:i:c:p:423-455. 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: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/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.