Formal Foundations for Known Good Reliable Die Screening in Chiplet-Based AI Systems-on-Chip

Prashanthi Metku, Chandra Gandu

The rapid growth of chiplet-based artificial intelligence systems-on-chip (SoCs) has exposed a fundamental gap in semiconductor test methodology. Existing Known Good Die (KGD) screening guarantees pre-assembly functional correctness, yet it offers no probabilistic assurance of post-assembly reliability lifetime. To address this limitation, the present work formalizes the transition from KGD to Known Good Reliable Die (KGRD) screening as a constrained inference problem over incomplete pre-assembly observability. Building upon this formulation, four interlocking contributions are presented: (i) a Bayesian probabilistic risk model that maps pre-assembly telemetry to post-assembly failure likelihood with a quantified observability bias bound; (ii) a safety-gated decision architecture that provides a provable post-assembly failure probability guarantee; (iii) uncertainty-aware disposition boundaries derived from Bayes-optimal decision theory; and (iv) a constrained closed-loop feedback mechanism that delivers consistent model improvement without violating reliability constraints. A Monte Carlo simulation study on N = 4,000 synthetic dies verifies all four theoretical properties and confirms that the safety guarantee holds uniformly across the full range of tested gate threshold.