On degradation-based imperfect repair and induced generalized renewal processes

Maxim Finkelstein, Ji Hwan Cha

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)1026-1045
Number of pages20
Issue number4
StatePublished - Dec 2021


  • Gamma process
  • Imperfect repair
  • Remaining lifetime
  • Renewal processes
  • Stochastic comparisons
  • Virtual age


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