Reducing degradation and age of items in imperfect repair modeling

Finkelstein, Maxim and Cha, Ji Hwan (2022) Reducing degradation and age of items in imperfect repair modeling. TEST, 31 (4). pp. 1058-1081. ISSN 1863-8260 (https://doi.org/10.1007/s11749-022-00813-2)

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Abstract

We develop new models for imperfect repair and the corresponding generalized renewal processes for stochastic description of repairable items that fail when their degradation reaches the specified deterministic or random threshold. The discussion is based on the recently suggested notion of a random virtual age and is applied to monotone processes of degradation with independent increments. Imperfect repair reduces degradation of an item on failure to some intermediate level. However, for the nonhomogeneous processes, the corresponding age reduction, which sets back the 'clock' of the process, is also performed. Some relevant stochastic comparisons are obtained. It is shown that the cycles of the corresponding generalized imperfect renewal process are stochastically decreasing/increasing depending on the monotonicity properties of the failure rate that describes the random failure threshold of an item.

  • Item type:Article
    ID code:80637
    Dates:
    Date
    Event
    31 December 2022
    Published
    5 May 2022
    Published Online
    29 March 2022
    Accepted
    Notes:This version of the article has been accepted for publication, after peer review, 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/s11749-022-00813-2
    Keywords:imperfect repair, virtual age, renewal process, remaining lifetime, stochastic comparisons, gamma process, Probabilities. Mathematical statistics, Statistics and Probability
    Subjects:Science > Mathematics > Probabilities. Mathematical statistics
    Department:Strathclyde Business School > Business Faculty Services
    Depositing user: Pure Administrator
    Date deposited:10 May 2022 13:38
    Last modified:23 Mar 2023 02:23
    URI:https://strathprints.strath.ac.uk/id/eprint/80637
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