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Journal Articles European Journal of Operational Research Year : 2020

Steady-state imperfect repair models

Abstract

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.
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Dates and versions

hal-02547433 , version 1 (22-08-2022)

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Attribution - NonCommercial - CC BY 4.0

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Xingheng Liu, Maxim Finkelstein, Jørn Vatn, Yann Dijoux. Steady-state imperfect repair models. European Journal of Operational Research, 2020, ⟨10.1016/j.ejor.2020.03.057⟩. ⟨hal-02547433⟩
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