Discussing some approaches to delta-shock modeling

Finkelstein, Maxim and Cha, Ji Hwan (2024) Discussing some approaches to delta-shock modeling. TOP: Transactions in Operations Research. ISSN 1863-8279 (https://doi.org/10.1007/s11750-024-00665-z)

[thumbnail of Finkelstein-Cha-TOP-2024-Discussing-some-approaches-to-delta-­shock-modeling] Text. Filename: Finkelstein-Cha-TOP-2024-Discussing-some-approaches-to-delta-_shock-modeling.pdf
Accepted Author Manuscript
Restricted to Repository staff only until 14 February 2025.
License: Strathprints license 1.0
Download (787kB) | Request a copy

Abstract

We revisit the ‘classical’ delta-shock model and generalize it to the case of renewal processes of external shocks with arbitrary inter-arrival times and arbitrary distribution of the ‘recovery’ parameter delta. Our innovative approach is based on defining the renewal points for the model and deriving the corresponding integral equations for the survival probabilities of interest that describe the setting probabilistically. As examples, the cases of exponentially distributed and constant delta are analyzed. Furthermore, delta shock modeling for systems with protection and two shock processes is considered. The first process targets the defense system and can partially destroy it. In this case, the second process that targets the main, protected system can result in its failure. The damages of the defense system are recovered during the recovery time delta. As exact solutions of the discussed problems are rather cumbersome, we provide simple and easy approximate solutions that can be implemented in practice. These results are justified under the assumption of ‘fast repair’ when the recovery time delta is stochastically much smaller than the inter-arrival times of the shock processes. The corresponding numerical examples (with discussion) illustrate our findings.

  • Item type:Article
    ID code:88608
    Dates:
    Date
    Event
    14 February 2024
    Published
    14 February 2024
    Published Online
    18 January 2024
    Accepted
    10 July 2023
    Submitted
    Notes:Copyright © 2024 Springer-Verlag. This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s11750-024-00665-z
    Subjects:Science > Mathematics > Probabilities. Mathematical statistics
    Department:Strathclyde Business School > Management Science
    Depositing user: Pure Administrator
    Date deposited:03 Apr 2024 15:05
    Last modified:30 Apr 2024 07:07
    URI:https://strathprints.strath.ac.uk/id/eprint/88608
CORE (COnnecting REpositories)