Predictive Maintenance (PrM) exploits the estimation of the equipment Residual Useful Life (RUL) to identify the optimal time for carrying out the next maintenance action. Particle Filtering (PF) is widely used as prognostic tool in support of PrM, by reason of its capability of robustly estimating the equipment RUL without requiring strict modeling hypotheses. However, a precise estimate of the RUL requires tracing a large number of particles, and thus large computational times, often incompatible with the need of rapidly processing information for making decisions in due time. To circumvent this problem, the Risk Sensitive Particle Filtering (RSPF) technique is exemplified in this work by way of a case study concerning a mechanical component affected by fatigue degradation.