Probably approximately correct-Bayesian Criterion (PBC) in Wiener processes selection

In recent decades, various models have been proposed for specific degradation scenarios, using benchmark models like the Wiener process and general path models. However, model evaluation and selection often rely on available degradation data from tests, limiting the assessment of performance on unseen data. This scenario could be encountered when we have a limited sample size in the degradation test and are concerned about the model's performance on unseen data. It could also arise when we only have degradation data from a similar product but need to assess the performance of the model on a new product lacking degradation data. To this end, we propose a probably approximately correct-Bayesian criterion (PBC) to select the model with the best generalization performance. The proposed PBC can set a theoretical bound for the generalization error of a model on unseen data and offer a closed-form upper bound when the degradation model is a Wiener process. The proposed criterion shows potential for extending to other degradation models, such as the general path model. Comprehensive experiments and case studies further illustrate the effectiveness of the PBC model selection criterion over the existing Akaike information criterion (AIC) and Bayesian information criterion (BIC).