Physics-Informed Diagnostics for Education Technology Benchmarking Assessment Assets in Kenya: Out-of-Distribution Fault Detection and Lifecycle Cost Trade-offs

The central problem is that conventional data-driven fault detectors trained on laboratory or urban school data degrade silently when confronted with out-of-distribution operating regimes, while maintenance decisions based on fixed thresholds ignore lifecycle cost trade-offs between premature replacement, run-to-failure risk and assessment disruption. The analysis formalises asset dynamics as differential-algebraic constraints and derives residual-based health indicators that remain interpretable under domain shift, then characterises out-of-distribution detection as a hypothesis test on joint data-physics scores with explicit control of false-alarm rates. A sequential decision model links detection performance to discounted lifecycle cost, yielding conditions under which physics-informed regularisation reduces expected cost despite higher modelling effort. The contribution is a set of verifiable design criteria for deploying robust diagnostics in resource-constrained, geographically dispersed assessment networks.