Beyond the Yield Barrier: Variational Importance Sampling Yield Analysis

TL;DR

This paper introduces VIS, a variational framework that systematically refines importance sampling methods for yield analysis, significantly improving accuracy and efficiency over traditional approaches.

Contribution

The paper presents VIS, the first variational analysis framework for yield problems, revealing the suboptimality of classic OMSV and providing systematic improvements.

Findings

Achieves up to 29.03x speedup over state-of-the-art methods.

Provides a systematic refinement of OMSV including covariance and failure region modeling.

Enhances yield optimization methods like ASAIS with performance and efficiency gains.

Abstract

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.