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 2x. Inheriting the simplicity of OMSV, the proposed method retains simplicity and robustness yet achieves up to 29.03x 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 1.20x and 1.27x improvement in performance and efficiency, respectively, without additional computational overhead.

翻译：基于最优均值偏移向量（OMSV）的重要性采样方法长期以来作为行业标准在良率估计与优化中占据主导地位。然而，大多数基于OMSV的方法都是启发式设计的，缺乏对其局限性的严格理解。为此，我们提出了VIS，这是首个针对良率问题的变分分析框架，能够对OMSV进行系统性改进。例如，VIS揭示了经典的OMSV是次优的，而最优/真实的OMSV应始终位于失效边界之外，这为所有基于OMSV的方法提供了无需成本的即时改进。利用VIS，我们展示了对经典OMSV的渐进式改进，包括以闭合形式纳入全协方差、针对非对称失效分布进行调整，以及捕获多个失效区域，其中每一项改进都贡献了超过2倍的渐进式性能提升。所提方法继承了OMSV的简洁性，保持了简单性和鲁棒性，同时相比最先进（SOTA）方法实现了高达29.03倍的加速。我们还展示了最先进的良率优化方法ASAIS如何能立即从我们的真实OMSV中获益，在不增加额外计算开销的情况下，分别实现了1.20倍和1.27倍的性能和效率提升。