A Hierarchical Bayesian Multivariate Wiener Process Model With Dependent Degradation Rates and Volatilities

Multidimensional degradation processes commonly arise in complex engineering systems such as aerospace equipment, military devices, and new-energy vehicles. These systems exhibit degradation behaviors characterized by multidimensionality, dependence, and heterogeneity. To effectively capture these features, this paper proposes a parameter-dependent multivariate Wiener process degradation model that simultaneously accounts for correlations among multiple degradation characteristics, dependencies between degradation rate and volatility, and individual heterogeneity within subsystems. A hierarchical Bayesian inference framework based on Gibbs sampling is developed for joint parameter estimation and uncertainty quantification. To address estimation bias issues in high-dimensional covariance structures, a hierarchical inverse Wishart prior is introduced, improving the accuracy of covariance estimation, particularly under small-variance conditions. Furthermore, a Monte Carlo–based reliability estimation scheme is proposed to approximate the first-passage time distribution of multidimensional systems. Extensive simulation studies demonstrate the superior estimation accuracy and credible interval coverage of the proposed method compared to traditional priors. Finally, applications to real-world engineering degradation data validate the model's practical effectiveness, showing that neglecting the dependence between degradation rate and volatility can lead to substantial bias in reliability assessments and maintenance decisions.