Imperfect condition-based maintenance for a gamma degradation process in presence of unknown parameters

Abstract

A system subject to degradation is considered. The degradation is modelled by a gamma process. A condition-based maintenance policy with perfect corrective and an imperfect preventive actions is proposed. The maintenance cost is derived considering a Markov-renewal process. The statistical inference of the degradation and maintenance parameters by the maximum likelihood method is investigated. A sensibility analysis to different parameters is carried out and the perspectives are detailed.

Imperfect and worse than old maintenances for a gamma degradation process

“…In this article, similarly to References 23 and 24, the system deterioration is modeled by a non‐homogeneous gamma process 2,3 . The statistical inference of such a process has been studied from several point of view and for several configurations 2,3,24–28 . Moreover, similarly to Reference 24, both perfect and imperfect maintenance through an $$$ {\mathrm{ARD}}_{\infty } $$$ model are considered which means after maintenance, the system is not necessarily restored to as good as new.…”

“…In this context, the available information is very rich in comparison to the lifetime observations but the parameters estimation is also more challenging due to the complexity of the degradation phenomenon under consideration. Under the assumption of perfect maintenance actions, the maintenance parameter estimations can be derived easier than in the case of imperfect maintenance where usually the imperfect maintenance actions restore the system to an unknown level, refer to References 18, 22–24. Kamranfar et al 23 consider truncated gamma distributed reduction parameter where the parameters are to be estimated.…”

“…Kamranfar et al 23 consider truncated gamma distributed reduction parameter where the parameters are to be estimated. Corset et al 24 consider an unknown reduction parameter in the framework of an $$$ {\mathrm{ARD}}_{\infty } $$$ model and the joint estimation of the maintenance and model parameters is addressed where only the degradation level before maintenance is observed.…”

“…In this article, similarly to References 23 and 24, the system deterioration is modeled by a non‐homogeneous gamma process 2,3 . The statistical inference of such a process has been studied from several point of view and for several configurations 2,3,24–28 .…”

“…The statistical inference of such a process has been studied from several point of view and for several configurations 2,3,24–28 . Moreover, similarly to Reference 24, both perfect and imperfect maintenance through an $$$ {\mathrm{ARD}}_{\infty } $$$ model are considered which means after maintenance, the system is not necessarily restored to as good as new. The model considered here is quite different to the one studied by Salles et al 22 in which the authors rather focus on semi‐parametric estimation for a non‐homogeneous gamma process under an $$$ {\mathrm{ARD}}_1 $$$ model for the maintenance effect.…”