Bayesian Analysis of Bivariate Degradation Data Using Hybrid Wiener-Inverse Gaussian Marginal Processes and a Shared Frailty

In engineering practice, it is common to observe simultaneous degradation of multiple performance characteristics in a system, in which these characteristics are correlated and exhibit differing degradation behaviors. This poses significant challenges to reliability modeling and analysis of multivariate degradation data. In this study, we propose a novel bivariate degradation model to meet the challenge. We employ the Wiener and inverse Gaussian processes to model the marginal processes, allowing for differing degradation patterns in the two dimensions. A shared frailty is then incorporated into the two marginal processes to capture their dependence structure. We derive the closed form of the reliability function for the proposed bivariate degradation model, and we develop an efficient Bayesian procedure for parameter estimation by combining the Gibbs sampler with the Metropolis-Hastings algorithm for posterior sampling. The performance of the Bayesian estimation method, along with the derived reliability formulas, is validated through comprehensive numerical simulations and a practical example involving a permanent magnet brake.