Non-constant imperfect maintenance effects in Inverse Gaussian degradation models for multiple repairable systems

Abstract

This paper proposes a degradation model tailored for multiple repairable systems subject to imperfect maintenance actions, incorporating three key assumptions: (i) the underlying degradation process follows an Inverse Gaussian distribution; (ii) the non-constant effects of imperfect maintenance are modeled using the Arithmetic Reduction of Degradation with memory one $\left({\text{ARD}}_1\right)$ framework; and (iii) systems undergo regular inspections, with degradation levels measured immediately before, after, and between inspections. This approach provides a flexible representation of degradation dynamics while accounting for the imperfect nature of maintenance interventions and their evolving impact over time. To evaluate the proposed model, we conduct a simulation study to assess the asymptotic properties of the parameter estimators obtained via the maximum likelihood method. The study demonstrates the robustness and reliability of the estimation process, highlighting the model’s ability to capture the degradation behavior accurately. Additionally, a practical application is presented using real-world data from LASER device degradation under various maintenance scenarios. The ability to account for the effects of imperfect maintenance is especially important as, in practice, repairs rarely return systems to a like-new condition, nor do they leave them as degraded as they were before. The proposed framework contributes to the advancement of degradation modeling, offering a robust tool for reliability engineers and practitioners dealing with repairable systems and imperfect maintenance conditions.