HARDWARE DIAGNOSTICS FRAMEWORK Suitable for SIS–10 Safety Intelligence System

The increasing complexity of safety critical embedded systems has exposed fundamental limitations in classical reliability modelling, where diagnostic coverage is typically treated as a static scalar and architectural redundancy as the dominant design variable. Modern industrial safety systems require a unified, lifecycle aware formulation in which diagnostics are treated as dynamic, uncertainty bearing subsystems that directly govern system reliability. This work introduces a mathematicallygrounded hardware diagnostics framework in which diagnostic capability is represented as a time dependent state variable H(t). Diagnostic coverage is defined as a functional C(H(t)), while system architecture is reformulated as a downstream transformation operator acting on diagnostic outputs rather than an independent reliability determinant. This inversion establishes diagnostics as the primary causal driver of safety integrity. The framework integrates deterministic failure evolution, stochastic uncertainty, maintenance effects, and adversarial worst case degradation within a single closed form reliability model. It enables confidence bounded Safety Integrity Level (SIL) verification, lifecycle consistent risk quantification, and provably optimal trade offs between diagnostics investment, redundancy allocation,and proof test scheduling. The resulting formulation is regulator complete, lifecycle consistent, and decision optimizing, providing a rigorous basis for safety assurance under both probabilistic and worst case operational regimes. It establishes a unified SIS reliability kernel suitable for next generation safety systems, where validity is preserved across deterministic, stochastic, and adversarial domains.