Solid rocket motors (SRMs) are prone to bore cracking due to material degradation mechanisms and temperature changes that occur during storage and service life, and therefore early damage detection is of crucial importance. Structural health monitoring (SHM) strategies aim at measuring the load redistribution caused by a crack through embedded strain sensors. By acknowledging the existence of uncertainties, both in the material and measurement systems, this work employs a Neyman–Pearson detector that treats the crack identification problem as a binary statistical pattern recognition one. A typical SRM geometry, at its healthy state and with a bore crack of variable size, is considered in a probabilistic computational setting. A surrogate model is trained with synthetic data generated from a physics-based finite element model and then used for uncertainty propagation. Detection is first treated as a deterministic signal within noise, and next as an uncertain signal described by a probabilistic distribution. The system’s architecture is assessed through a procedure for arriving at the optimal number and location for sensor placement in conjunction with the SHM’s detection performance. The latter is described by receiver operating characteristic curves.