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On degradation-based imperfect repair and induced generalized renewal processes

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Abstract

In this paper, we suggest and justify a new, basic approach to modelling the imperfect repair and the corresponding imperfect repair processes for items with observable degradation. We consider monotone processes of degradation with independent increments. Imperfect repair reduces degradation of an item on failure to some intermediate level. To define the state of an item after this imperfect repair, the random virtual age is introduced. Some stochastic properties describing the corresponding remaining lifetime are considered. The generalized renewal process based on the suggested notion of imperfect repair is described, and some of its properties are studied. An alternative approach that considers the imperfect repair process defined in the degradation scale is outlined.

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Acknowledgements

The authors greatly appreciate the Associate Editor’s and reviewers’ helpful comments and advices. The work of the second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2019R1A2B5B02069500). The work of the second author was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2019R1A6A1A11051177).

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Authors and Affiliations

  1. Department of Mathematical Statistics, University of the Free State, Bloemfontein, South Africa

    Maxim Finkelstein

  2. University of Strathclyde, Glasgow, UK

    Maxim Finkelstein

  3. Department of Statistics, Ewha Womans University, Seoul, 120-750, Republic of Korea

    Ji Hwan Cha

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  1. Maxim Finkelstein
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  2. Ji Hwan Cha
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Correspondence to Ji Hwan Cha.

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Finkelstein, M., Cha, J.H. On degradation-based imperfect repair and induced generalized renewal processes. TEST 30, 1026–1045 (2021). https://doi.org/10.1007/s11749-021-00765-z

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