Bivariate degradation modeling and reliability analysis based on generalized nonlinear Wiener processes and a shared frailty factor

Abstract The complexity of product functionality and composition often involves at least two or more interrelated performance characteristics jointly reflecting the degradation. At the same time, the intricacy of the underlying failure mechanisms often results in degradation processes exhibiting intricate nonlinear patterns, where the mean and variance can display different nonlinear behaviors. Additionally, the random effect of the degradation process should not be overlooked. Therefore, an accurate depiction of degradation regulation is a crucial prerequisite for reasonable model construction and effective reliability analysis. To settle the challenges posed by complex nonlinear scenarios, this paper proposes a bivariate degradation model based on generalized nonlinear Wiener processes, incorporating a shared frailty factor to characterize the correlation between performance features. An approximate analytical expression for the cumulative distribution function of the first hitting time is derived for reliability analysis. Furthermore, unknown parameter estimation is carried out through a combination of the expectation–maximization algorithm and the genetic algorithm. Finally, the effectiveness of the proposed model and reliability analysis method is validated through a comprehensive simulation investigation and a practical case study involving fatigue crack propagation.