Phased array radar (PAR) systems are critical for modern defense and surveillance applications, but their reliability and availability are affected by various factors, including physical and performance degradation. Furthermore, implementing prognostics and health management (PHM) framework for the whole radar system is challenging. To address these issues, this paper proposes an efficient solution by hierarchically implementing PHM frameworks in an active PAR (APAR) system. The proposed framework subsumes device-level, subsystem-level, and system-level health prediction models to enable comprehensive health monitoring and maintenance decision-making. This approach addresses the unique challenges involved in implementing PHM for the APAR system and facilitates the transition from traditional reactive maintenance practices to a predictive maintenance approach, thereby improving the overall system. Mathematical models that relate the radar's physical degradation to its performance deterioration are formulated, analyzed and presented. Subsequently, a Bayesian long short-term memory (BayesLSTM) architecture is developed and integrated into the proposed framework for estimating the remaining useful life (RUL) of critical devices/subsystems. The effectiveness of the proposed deep learning-based prognostic framework is evaluated through simulations and experimental studies. The proposed hierarchical framework has the potential to be applied to other radar systems that require effective health monitoring strategy.