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On degradation-based imperfect repair and induced generalized renewal processes

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  • Maxim Finkelstein

    (University of the Free State
    University of Strathclyde)

  • Ji Hwan Cha

    (Ewha Womans University)

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.

Suggested Citation

  • Maxim Finkelstein & Ji Hwan Cha, 2021. "On degradation-based imperfect repair and induced generalized renewal processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 1026-1045, December.
    • Handle: RePEc:spr:testjl:v:30:y:2021:i:4:d:10.1007_s11749-021-00765-z
    DOI: 10.1007/s11749-021-00765-z
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    References listed on IDEAS

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    10. Maxim Finkelstein & Ji Hwan Cha, 2013. "Burn-in for Heterogeneous Populations," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 261-312, Springer.
    11. Ji Hwan Cha & Maxim Finkelstein, 2018. "Point Processes for Reliability Analysis," Springer Series in Reliability Engineering, Springer, number 978-3-319-73540-5, September.
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    13. Nil Kamal Hazra & Maxim Finkelstein & Ji Hwan Cha, 2018. "Stochastic ordering for populations of manufactured items," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 173-196, March.
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    16. Maxim Finkelstein & Ji Hwan Cha, 2013. "Shocks as Burn-in," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 313-361, Springer.
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