Damage detection in active-sensing, guided-waves-based Structural Health Monitoring (SHM) has evolved through multiple eras of development during the past decades. Nevertheless, there still exists a number of challenges facing the current state-of-the-art approaches, including low damage sensitivity, lack of robustness to uncertainties, need for user-defined thresholds, and non-uniform response across a sensor network. In this work, a novel statistical framework is proposed for active-sensing SHM based on the use of ultrasonic guided waves. This framework is based on stochastic non-parametric time series models and their corresponding statistical properties in order to readily provide healthy confidence bounds and enable accurate and robust damage detection via the use of appropriate statistical decision making tests. Three such methods and corresponding statistical quantities along with decision making schemes are formulated and experimentally assessed via the use of three structural coupons: an Al plate with a growing notch, a Carbon fiber-reinforced plastic (CFRP) plate with added weights to simulate local damages, and the CFRP panel used in the Open Guided Waves project, all outfitted with piezoelectric transducers and a pitch-catch configuration. The performance of the proposed methods is compared to that of state-of-the-art time-domain damage indices. The results demonstrate the increased sensitivity and robustness of the proposed methods, with better tracking capability of damage evolution compared to conventional approaches, even for damage-non-intersecting actuator-sensor paths. Overall, the proposed statistics in this study promise greater damage sensitivity across different components, with enhanced robustness to uncertainties, as well as user-friendly application.