The expanding implementation of hot deep drawing manufacturing equipment in mission-critical sectors such as aerospace and rail transportation has significantly heightened research focus on operational reliability within advanced manufacturing studies. To address persistent reliability design challenges originating from the inherently multilevel and highly coupled nature of these systems, this paper proposes a hierarchical Bayesian network (BN) model to conduct comprehensive design reliability analysis. The methodology employs a three-tiered equipment-subsystem-component topological framework to develop an integrated network model comprising seven major subsystems—specifically the frame, blank holder, heating system, hydraulic station, water-cooling system, control system, and feeding mechanism. Through systematic synthesis of operational field data from comparable industrial installations with domain expert knowledge, a structured sensitivity analysis was performed to identify critical systemic vulnerabilities. Quantitative results demonstrate that under the stringent reliability requirement (MTBF ≥ 2000 hours), the water-cooling system, heating platform, and hydraulic station collectively exhibit the highest operational failure probabilities. Consequently, targeted design enhancements focused on these critical components constitute a fundamental prerequisite for achieving substantial improvements in overall system reliability and operational robustness.