Abstract
Membrane filtration, including reverse osmosis filtration, is widely applied in water treatment worldwide, offering solutions to a broad range of separation challenges. However, due to the porous structure of membranes, they are prone to fouling, which reduces their efficiency and can eventually render the membranes incapable of functioning. In such cases, a systemic intervention becomes necessary, highlighting the importance of accurately predicting the expected fouling time. Various approaches for estimating fouling processes and times are well documented in the literature. However, a common limitation of these methods is that they typically assume constant and well-defined operating parameters over time. Under such stable conditions, the process can be described deterministically, and the fouling time can be predicted using straightforward extrapolation techniques. However, in industrial practice, process conditions often fluctuate due to multiple influencing factors, making fouling time a variable quantity. Therefore, it can be more appropriately treated as a random variable characterized by a mean value and standard deviation. Rather than predicting a precise fouling time, it is more relevant to define a probabilistic interval within which the fouling is expected to occur with a specified confidence level (e.g., 95%). The associated maintenance scheduling can then be optimized based on economic criteria. The probability-based model presented herein defines this interval based on operational measurements, thereby providing users with a time window during which maintenance should be planned. From this point forward, the exact timing of interventions becomes a matter of technical feasibility and economic optimization.