Steady-state imperfect repair models

Xingheng Liu (1, 2) , Maxim Finkelstein (3) , Jørn Vatn (2) , Yann Dijoux (1)

1 LM2S - Laboratoire Modélisation et Sûreté des Systèmes
2 NTNU - Norwegian University of Science and Technology [Trondheim]
3 UFS - University of the Free State [South Africa]

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.

Domaines: Recherche opérationnelle [math.OC]

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⟩