A stage-dependent Markov-switching fractional Brownian motion model for reliability analysis considering random effects and long-term memory

Reliability management is crucial for ensuring stable operation of mechatronics components, as well as reducing the downtime and the operating costs. However, the existing degradation models based on Markov properties are not applicable because of the long-term memory of the components. In addition, the degradation of many components in their life cycle exhibits multi-stages, and dependencies exist between different degradation stages. Therefore, this paper proposes a stage-dependent Markov-switching fractional Brownian motion (FBM) model allowing to better capture the characteristics of nonlinearity, randomness, unit-to-unit variability, long-term memory, and dependency of multi-stage degradation. More precisely, the long-term memory of degradation is represented by the FBM process, and random effects are used to describe the unit-to-unit variability. Moreover, a stage-dependent Markov-switching process is proposed for describing the state transitions of multi-stage degradation processes. The working conditions of the different degradation stages are then used to describe the stage impact levels. Furthermore, the unknown parameters of the Markov-switching process and the nonlinear degradation model with FBM are determined based on the two-stage parameter estimation method. Finally, a simulation study and a real case on hydraulic pumps are conducted to demonstrate the high performance of the proposed model.