Reducing degradation and age of items in imperfect repair modeling

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, 2022, vol. 31, issue 4, No 8, 1058-1081

Abstract: 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.

Keywords: Imperfect repair; Virtual age; Renewal processes; Remaining lifetime; Stochastic comparisons; Gamma process; 90B25; 60K10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11749-022-00813-2

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