Condition-based maintenance for a deteriorating system subject to random shocks and environmental changes

International audienceMany models are developed for systems with increasing degradation evolving in a stationary environment. However in most industrial applications, the system is influenced by different risk factors, which are called explanatory variables (covariates). These variables describe the dynamical environment in the experiments of life science and engineering. This paper deals with a deteriorating system whose deterioration constitutes of wear damages and random accumulative shock damages both affected by environmental conditions. The wear damage is modeled by a non-stationary Gamma process and the random shock damage is modeled by a generalized Pareto distribution satisfying Poisson arrival. The effect of the environment on the mean deterioration rate is modeled by covariates via the Cox proportional hazards model. It is supposed that the system can only be observed by inspections. In this framework, the system is correctively replaced if the deterioration level exceeds a fixed level called failure threshold. To avoid the failure, the system is preventively replaced if the deterioration level is higher than the preventive threshold but still lower than the corrective threshold. Replacements takes place only in inspection times and a non-periodic inspection scheme based on the deterioration level of the system is proposed. The performances of the proposed condition-based replacement policy with non-periodic inspections are studied through numerical implementations. The optimal maintenance policy leading to the minimal cost criterion is obtained