Journal
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
Volume 286, Issue 2, Pages 538-546Publisher
ELSEVIER
DOI: 10.1016/j.ejor.2020.03.057
Keywords
Maintenance; Imperfect repair; Virtual age process; Renewal theory; Limiting distribution
Funding
- Ministere de L'enseignement Superieur et de la Recherche (French Minister of Education and Research)
- European Regional Development Fund
- Universitede Technologie de Troyes
- Government of the Russian Federation [08-08]
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Imperfect maintenance models are widely used in reliability engineering. This paper discusses relevant asymptotic properties for the steady-state virtual age processes. It is shown that the limiting distributions of age, the residual lifetime and the spread that describe an ordinary renewal process can be generalized to the stable virtual age process, although the cycles of the latter are not independent. Asymptotic distributions of the virtual age at time t, as well as of the virtual ages at the start and the end of a cycle containing t (as t tends to infinity) are explicitly derived for two popular in practice imperfect maintenance models, namely, the Arithmetic Reduction of Age (ARA) and the Brown-Proschan (BP) models. Some applications of the obtained results to maintenance optimization are discussed. (C) 2020 Elsevier B.V. All rights reserved.
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