Variational Bayesian analysis for Wiener degradation model with random effects

Random-effects Wiener degradation models have been widely used in the literature, to characterize unit-to-unit variability in a population. Bayesian inference for such models mainly relay on stochastic simulation techniques, such as Markov chain Monte Carlo (MCMC) method. However, MCMC approach will converge slowly or fail to converge for large volume data. In this paper, the variational Bayesian (VB) approach is proposed as an alternative tool for MCMC, which makes inference of Wiener degradation models with random effects more suitable for large inspection data sets. Despite of utilizing mean field methodology for VB approach, there are also certain limitations in model inference. Therefore, a three-step method is developed and embed into the VB approach, and statistical inference based on our VB approach is established. Numerical examples are provided to compare with MCMC method in terms of cost in time and accuracy in estimation for large inspection data problem. The proposed VB approach provides almost the same accuracy as MCMC, while its computational burden is much lower.