This chapter presents conceptual and computational comparisons between EOLE (Expansion Optimal Linear Estimation) and AR (Auto-Regressive) models to represent stochastic processes in the context of time-dependent reliability analysis. Even though expansion techniques, such as EOLE, are appropriate for problems where the properties of the stochastic process are explicitly known, such information is rarely available in practical situations. On the other hand, time series models, such as AR, are widely employed to represent stochastic processes from real time monitoring or available historical data. For this reason, here we compare EOLE and AR in the context of time-dependent reliability analysis. We first demonstrate how AR models can be calibrated to represent a given stochastic process with known properties. It is then demonstrated that similar results for time-dependent reliability can be obtained using the two approaches. This is an important contribution from both conceptual and practical reasons, since it demonstrates that existing AR models (and likely other types of time series models) can be directly employed for time-dependent reliability analysis, without the need to first obtain an equivalent EOLE model.