Computationally-efficient surrogate models based on a Polynomial Chaos Expansion (PCE) are developed to quantify the uncertainties in the fracture behavior and lifetime of a self-healing thermal barrier coating system (SH-TBC) and a benchmark conventional TBC system. The surrogate models are built using deterministic information from micromechanical finite element simulations of thermal cycling of the systems, which are conducted until failure by spallation. Fracture and healing events are simulated using a cohesive-zone based crack healing model. The thermally-grown oxide layer (TGO) interface amplitude and its growth rate, the diameter and volume fraction of healing particles, and the mean distance of particles from the interface are used as training variables. Statistical characteristics and sensitivity indices are obtained from the trained models. It is found that the interface amplitude is the most significant contributor to the variance in the TBC lifetime, with other parameters displaying a relatively minor influence. Healing particles extend the expected value of TBC lifetime, however they also increase the uncertainty of thermal fatigue life. The analysis of self-healing TBCs exemplifies how PCE-based surrogate models can serve as a powerful tool for deriving design insights in complex material systems.