On degradation-based imperfect repair and induced generalized renewal processes

Maxim Finkelstein () and Ji Hwan Cha ()
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Maxim Finkelstein: University of the Free State
Ji Hwan Cha: Ewha Womans University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2021, vol. 30, issue 4, No 10, 1026-1045

Abstract: 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.

Keywords: Imperfect repair; Virtual age; Renewal processes; Remaining lifetime; Stochastic comparisons; Gamma process; Primary 60K10; Secondary 62P30 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11749-021-00765-z

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