In this chapter, a new approach is proposed for fault detection and spatial localization in parabolic distributed parameter systems with limited sensors. The baseline behavior of the distributed parameter systems is first characterized under restricted sensor availability. Subsequently, the spatio-temporal dynamics are decoupled through time–space separation. The temporal coefficients are then further processed using independent component analysis, from which the dominant temporal modes are extracted. Based on these, spatial residuals are constructed to derive two monitoring statistics. By employing kernel density estimation, the confidence intervals of these statistics in the fault-free case are obtained as reference thresholds. Distinct from traditional model-based techniques that rely on explicit mathematical formulations, the proposed strategy is data-driven and exploits only the separable property of parabolic distributed parameter systems. Its effectiveness is validated through studies on a representative parabolic process and a snap-curing oven.