Statistical rare event analysis using smart sampling and parameter guidance

Abstract

In this paper, we propose a new efficient statistical method for failure probability estimation of analog circuits with rate failure events, which is a time-consuming process using the existing Monte Carlo method. On top of this, the new method can also provide the estimation of parameter regions to achieve targeted performance to facilitate the design process, which is missing in the traditional fast statistical methods such as the statistical blockage based method. The new method employs two new techniques to speed up the analysis. First, to reduce the large number of samples for rare event analysis, the new approach employs a smart sample selection scheme, which can consider the effectiveness of samples and well-coverage for the parameter space. As a result, it can reduce an additional simulation costs by pruning less effective samples while keeping the accuracy of failure estimation. Second, the new approach identifies the failure regions in terms of parameters to provide a good design guideline for designers and optimization tools. This is enabled by applying the variance based feature selection to find the dominant parameters. A quasi-random sampling with dominant parameters is then applied to determine in-spec boundaries of those parameters. In addition, we also provide the complete formula for the probability determinations of failure regions in the iterative failure region searching framework. We demonstrate the advantage of our proposed method using two test benches: 6T-SRAM reading failure diagnosis with 27 process parameters, charge pump operation failure diagnosis in a PLL circuit with 81 process parameters. Experimental results show that the new method can be 4X more accurate than the recently proposed REscope method. Furthermore, the new method reduces the simulation cost by 2X than the recursive statistical blockage (RSB) method with same accuracy level. Our approach also provides the precise guidance of diverse parameters with 1.21% estimation error.