A Bayesian multivariate Student-t degradation model for dependent log-increments

This work proposes the use of the multivariate Student-t distribution to describe log-increments of degradation measurements within an experimental unit. This approach captures both the dependence between log-increments and the heavy-tailed behavior which can be observed in some real-world data. Within the Bayesian analysis framework, a Markov chain Monte Carlo algorithm with the use of a Gibbs sampler is developed to estimate the model parameters. The Monte Carlo method is used to conduct lifetime predictions due to the lack of the additive property of the corresponding log-Student-t distribution. Critical aspects such as the sensitivity of results to prior specifications and the challenges of achieving adequate chain mixing are also addressed. To demonstrate the practical application of the model, two real examples are analyzed. Finally, a simulation study is conducted to assess that the proposed model is robustness to assumption variations.