The analysis of remaining useful life (RUL) of systems and 'equipment enables the prevention of failures, so that effective maintenance can be performed in time to correct failures that are close to happening. The degradation signal of a variable can be used as a basis for estimating the RUL of a given system since this signal is modeled mathematically correctly. In this paper, the RUL of cyclic processes is analyzed with the determination of the number of remaining cycles (NRC) in order to maximize production, guaranteeing operational safety. Two approaches will be considered: Bayesian methodology and time series. The Bayesian methodology is based on Bayesian inference to update the stochastic parameter, providing better representativeness in the estimation of the NRC. The deterministic parameters and the hyperparameters in the prior distribution of the stochastic parameter are estimated through the maximum likelihood estimation method, while the stochastic parameter in the degradation model of a system can be updated every time a new degradation data is obtained. On the other hand, the time series is based on training sets to be able to fit a model that is similar to the set used for validation. In the estimation of NRC, a stationary model (simple exponential smoothing), a nonstationary model (double exponential smoothing), and a model that considers the component of seasonality (triple exponential smoothing) are considered. A case study of a temperature swing adsorption unit for natural gas dehydration will be used to evaluate these two approaches in predicting NRC in cyclic processes. In this case study, we propose a novel cycle-packaging methodology that creates a new dimension, allowing the application of NRC forecasting methodologies, which is the main contribution of this article. The results suggest that the Bayesian methodology is the most indicated in the NRC estimation, while the time series are adequate to identify the cyclic pattern of the process.