Beyond the yield barrier: Variational importance sampling yield analysis

Optimal mean shift vector (OMSV)-based importance sampling methods have long been prevalent in yield estimation and optimization as an industry standard. However, most OMSV-based methods are designed heuristically without a rigorous understanding of their limitations. To this end, we propose VIS, the first variational analysis framework for yield problems, enabling a systematic refinement for OMSV. For instance, VIS reveals that the classic OMSV is suboptimal, and the optimal/true OMSV should always stay beyond the failure boundary, which enables a free improvement for all OMSV-based methods immediately. Using VIS, we show a progressive refinement for the classic OMSV including incorporation of full covariance in closed form, adjusting for asymmetric failure distributions, and capturing multiple failure regions, each of which contributes to a progressive improvement of more than 2×. Inheriting the simplicity of OMSV, the proposed method retains simplicity and robustness yet achieves up to 29.03× speedup over the state-of-the-art (SOTA) methods. We also demonstrate how the SOTA yield optimization, ASAIS, can immediately benefit from our True OMSV, delivering a 1.20× and 1.27× improvement in performance and efficiency, respectively, without additional computational overhead.