Flow-induced vibration is a common phenomenon in shell-and-tube heat exchangers. The resulting vibration can lead to component failure by fretting wear due to tube-to-tube support impact or by fatigue. Due to manufacturing considerations, many parameters such as support clearance, alignment, and friction at the supports are not exactly known and are represented by statistical distributions. This makes the use of deterministic equations inaccurate. This paper presents a methodology that can be used during component operation to monitor known flaws and ensure safe operation. The methodology incorporates Monte Carlo simulations to predict remaining service life of a vibrating heat exchanger tube with a small circumferential through-wall crack next to the tube sheet. Vibration excitation includes turbulence and low-level fluid-elastic forces. Leakage calculations are made on the through-wall crack as it grows to fracture. A Weibull distribution is given for the time-to-fracture and for the time for the leak rate to reach a threshold value. This statistical information can then be used to assess the remaining service life and whether LBB criteria will be met.