Reliability modeling and statistical analysis of accelerated degradation process with memory effects and unit-to-unit variability

2023-10-28

Applied Mathematical Modelling

AI Summary

To address the modeling challenge of degradation processes in high-reliability systems—characterized by both non-Markovian memory effects and unit-to-unit heterogeneity—this paper proposes an accelerated degradation statistical model integrating fractional stochastic processes with random effects. Departing from the conventional independent-increment assumption, the model employs fractional Brownian motion to capture temporal dependence in degradation paths and incorporates a mixed-effects structure to account for individual variability. Parameter estimation is performed via a hybrid approach combining the EM algorithm and Bayesian inference. Experimental validation on turbine blade and electrolytic capacitor datasets demonstrates a 32% reduction in remaining useful life prediction error and an average R² of 0.91 for individual degradation trajectory fitting, significantly improving early fault detection accuracy. This work establishes the first unified framework jointly incorporating fractional-order processes and random effects, offering a novel paradigm for reliability assessment of non-Markovian degradation systems.

Problem

• Model non-Markovian degradation with memory effects
• Address unit-to-unit variability in degradation paths
• Improve reliability estimation accuracy in accelerated testing

Innovation

• Uses fractional Brownian motion for memory effects
• Incorporates unit-to-unit variability in model
• Applies expectation maximization algorithm for estimation