Reliability modelling and requirement derivation for automated railway inspection systems under operational fallback

• Proposes a framework linking reliability modelling and operational fallback. • Derives admissible reliability requirements from operational consequences. • Introduces requirement back-propagation for inspection support systems. • Demonstrates the approach with an automated railway inspection case study. • Supports procurement and verification of reliability requirements. Automated inspection systems are increasingly deployed in railway maintenance to reduce workshop-based inspection workload and to support availability-driven planning. Yet, there is limited guidance on how to derive verifiable reliability requirements that are explicitly conditioned by the operational and economic consequences of workshop fallback when automation is unavailable. This paper proposes a consequence-conditioned requirement-derivation framework that (i) models inspection-system availability bottom-up from a modular decomposition, (ii) quantifies fallback-induced functional loss through additional workshop workload, and (iii) formulates an economic admissibility constraint that yields a maximum admissible failure-rate threshold (equivalently, a minimum mean time between failures ( MTBF )) consistent with predefined operational-economic targets. The structural properties of this admissibility constraint (feasibility and monotonicity) are analytically characterised to support transparent robustness assessment. The admissible threshold is then operationalised via back-propagation, cast as constrained lifetime-tuning to produce auditable element-level procurement targets under alternative allocation policies. The framework is demonstrated through an industrial automated underframe inspection system, showing how an MTBF requirement for a selected inspection subsystem can be derived from a break-even condition between annual benefit and expected fallback cost, and how required lifetime improvements depend on the allocation policy. The approach positions reliability modelling as a decision-support mechanism for validating the operational and economic viability of automated maintenance-inspection architectures.