Statistical inference for Wiener degradation models under imperfect maintenance and general observation schemes

Degradation modelling is essential in reliability engineering and predictive maintenance. In real-world industrial applications, systems frequently undergo imperfect maintenance that only partially restore their health, and degradation measurements are often irregular or incomplete.

This work introduces a framework to overcome these practical limitations. We model the underlying continuous degradation using a Wiener process and represent the effect of imperfect maintenance through the Arithmetic Reduction of Degradation (ARD) model. We develop a Maximum Likelihood Estimation (MLE) methodology capable of handling a general observation scheme, including missing data and varying inspection schedules (before, after, or between maintenance actions). This model is extended to bivariate degradation processes, using a shared-noise approach to capture environmental dependencies between multiple components.

To support practical decision-making, we derive provide prediction intervals that capture the uncertainty of both the model and the parameter estimation. The practical applicability of this methodology is demonstrated through a real-world case study on critical components from the energy sector, showing how this framework can effectively forecast future degradation and optimize maintenance scheduling.