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

Kai Song; Xun Xiao; Zhisheng Ye

doi:10.1109/TR.2026.3660907

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

Kai Song, Xun Xiao Zhisheng Ye

IEEE transactions on reliability, Vol.75, pp.876-887

03/02/2026

: https://doi.org/10.1109/TR.2026.3660907

https://hdl.handle.net/10523/49913

Bayes methods

Bayesian inference

bivariate degradation

Degradation

Mathematical models

Maximum likelihood estimation

Modeling

Monitoring

Numerical models

Numerical simulation

Reliability

sampling

Stochastic processes

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.

: 9926847273901891
: Bayesian Analysis of Bivariate Degradation Data Using Hybrid Wiener-Inverse Gaussian Marginal Processes and a Shared Frailty
: Kai Song
Xun Xiao
Zhisheng Ye
: IEEE transactions on reliability, Vol.75, pp.876-887
: Mathematics and Statistics; Statistics
: IEEE
: From data to decisions: Statistical methods for uncertainty mitigation in complex networks of infrastructure assets, 24-UOO-071, Royal Society Te Apārangi (New Zealand, Wellington)
: 12301375 / National Natural Science Foundation of China
: 03/02/2026
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: English
: Journal article