Focusing on nonmonotonic degradation processes, we have cooperated artificial neural network (ANN) with Wiener process to utilize its powerful ability on curve fitting. While, the degradation processes of some actual products are determined as monotonic. Furthermore, the process uncertainty issue is also neglected, which is inevitable in engineering practice. Hence, focusing on monotonic degradation dataset, this research introduces ANN-based stochastic process for reliability analysis under multiple uncertainties, including random effects, process uncertainty and mean function uncertainty. The ANN-supported inverse Gaussian and Gamma process models subject to random effects are built. The related parameter estimation and updating methods are also constructed by utilizing moment estimation (ME), Akaike information criterion (AIC) and fully Bayesian inference methods. According to the simulation experiment and actual case study, the proposed method provides higher accuracies on population degradation modeling and monitoring individual degradation prediction.