A Formal Framework for Robustness Preservation Claims in Systems Engineering

Robustness requirements in systems engineering are frequently mis‐specified because informal notions conflate three distinct preservation concerns: preservation of required input‐output transformations, preservation of performance bounds, and preservation of mission‐level outcomes. This conflation leads to ineffective redesign when component‐level improvements fail to address coordination breakdowns, and to late discovery of failures when outcome guarantees are incorrectly inferred from verification evidence. This paper develops a formally typed framework for robustness grounded in systems theory and set‐theoretic semantics. We define functional robustness, capability robustness, and outcome robustness as distinct preservation properties, each evaluated over explicitly declared variation sets induced by system boundary and interaction structure. Robustness claims are shown to be well‐formed only when they specify what is preserved, over which operational variation, and through which boundary‐crossing interactions variation enters the system. Six theorems establish that the three robustness types are logically independent and expose common but unsound assumptions used in requirements refinement, robustness allocation, and verification reuse. A sufficiency theorem provides constructive guidance by identifying conditions under which outcome robustness can be guaranteed through jointly satisfied capability predicates, while clarifying why outcome robustness itself cannot be allocated to subsystems. The framework supports robustness‐aware requirements specification, architecture trade studies, verification planning, and failure diagnosis by making explicit whether failures arise from transformation loss, performance bound violations, or cross‐boundary coordination breakdowns, rather than treating robustness as a single undifferentiated property.