Mixture importance sampling and its application to the analysis of SRAM designs in the presence of rare failure events

Kanj, Rouwaida; Joshi, Rajiv V.; Nassif, Sani R.

doi:10.1145/1146909.1146930

Cited by 250 publications

(176 citation statements)

References 9 publications

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“…For statistical analysis of SRAM circuits, various methods have been proposed in the literature [2]- [6]. These methods either rely on transistor-level MC simulation [2]- [4] or MC simulation of response surface models of the building blocks [5]- [6].…”

Section: Related Workmentioning

confidence: 99%

“…These methods either rely on transistor-level MC simulation [2]- [4] or MC simulation of response surface models of the building blocks [5]- [6]. In [4], the authors use data classifiers to filter out insignificant samples which are not likely to result in a failure, and thereby, reduce the required number of simulations in transistor-level MC.…”

Section: Related Workmentioning

confidence: 99%

“…In [4], the authors use data classifiers to filter out insignificant samples which are not likely to result in a failure, and thereby, reduce the required number of simulations in transistor-level MC. In [2], the authors employ mixture importance sampling for the same purpose. They use a mixture of probability distribution functions, also called importance functions, to generate important random samples in the subset of the parameter space in which failures occur.…”

Section: Related Workmentioning

confidence: 99%

“…min Pr 1 (2) where N MUX is the column multiplexer factor. In addition to read timing failure, self-timing path delay is also an important performance metric in SRAM design since it is a part of the total read delay.…”

Section: Sram Architecturementioning

confidence: 99%

See 3 more Smart Citations

Efficient statistical analysis of read timing failures in SRAM circuits

Yaldiz

Arslan

et al. 2009

2009 10th International Symposium on Quality of Electronic Design

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A system-level statistical analysis methodology is described that captures the impact of inter-and intra-die process variations for read timing failures in SRAM circuit blocks. Unlike existing approaches that focus on cell-level performance metrics for isolated sub-components or ignore inter-die variability, the system-level performance is accurately predicted for the entire SRAM circuit that is impractical to analyze statistically via transistor-level Monte Carlo simulations. The accurate bounding of read timing failures using this methodology is validated with silicon measurements from a 64kb SRAM testchip in 90nm CMOS. We demonstrate the efficacy of this methodology for earlystage design exploration to specify redundancy, required sense amp offset, and other circuit choices as a function of memory size.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Sram Architecturementioning

confidence: 99%

See 2 more Smart Citations

Efficient statistical analysis of read timing failures in SRAM circuits

Yaldiz

Arslan

et al. 2009

2009 10th International Symposium on Quality of Electronic Design

View full text Add to dashboard Cite

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“…This paper presents the use of the simplest form of Importance Sampling (IS) to drastically increase the accuracy of Monte-Carlo simulations. This technique was applied before in a complex adaptive fashion, requiring complex sampling algorithms and post-processing [3]. This paper presents a form of IS that requires less implementation effort.…”

Section: Introductionmentioning

confidence: 99%

Importance sampling Monte Carlo simulations for accurate estimation of SRAM yield

Doorn

Maten

Croon

et al. 2008

ESSCIRC 2008 - 34th European Solid-State Circuits Conference

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Abstract-Variability is an important aspect of SRAM cell design. Failure probabilities of P fail ≤10-10 have to be estimated through statistical simulations. Accurate statistical techniques such as Importance Sampling Monte Carlo simulations are essential to accurately and efficiently estimate such low failure probabilities. This paper shows that a simple form of Importance Sampling is sufficient for simulating P fail ≤10 -10 for the SRAM parameters Static Noise Margin, Write Margin and Read Current. For the SNM, a new simple technique is proposed that allows extrapolating the SNM distribution based on a limited number of trials. For SRAM total leakage currents, it suffices to take the averages into account for designing SRAM cells and modules. A guideline is proposed to ensure bitline leakage currents do not compromise SRAM functionality.

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Efficient evaluation of small failure probability in high‐dimensional groundwater contaminant transport modeling via a two‐stage Monte Carlo method

Zhang

Lin

et al. 2017

Water Resources Research

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In decision‐making for groundwater management and contamination remediation, it is important to accurately evaluate the probability of the occurrence of a failure event. For small failure probability analysis, a large number of model evaluations are needed in the Monte Carlo (MC) simulation, which is impractical for CPU‐demanding models. One approach to alleviate the computational cost caused by the model evaluations is to construct a computationally inexpensive surrogate model instead. However, using a surrogate approximation can cause an extra error in the failure probability analysis. Moreover, constructing accurate surrogates is challenging for high‐dimensional models, i.e., models containing many uncertain input parameters. To address these issues, we propose an efficient two‐stage MC approach for small failure probability analysis in high‐dimensional groundwater contaminant transport modeling. In the first stage, a low‐dimensional representation of the original high‐dimensional model is sought with Karhunen‐Loève expansion and sliced inverse regression jointly, which allows for the easy construction of a surrogate with polynomial chaos expansion. Then a surrogate‐based MC simulation is implemented. In the second stage, the small number of samples that are close to the failure boundary are re‐evaluated with the original model, which corrects the bias introduced by the surrogate approximation. The proposed approach is tested with a numerical case study and is shown to be 100 times faster than the traditional MC approach in achieving the same level of estimation accuracy.

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Mixture importance sampling and its application to the analysis of SRAM designs in the presence of rare failure events

Cited by 250 publications

References 9 publications

Efficient statistical analysis of read timing failures in SRAM circuits

Efficient statistical analysis of read timing failures in SRAM circuits

Importance sampling Monte Carlo simulations for accurate estimation of SRAM yield

Efficient evaluation of small failure probability in high‐dimensional groundwater contaminant transport modeling via a two‐stage Monte Carlo method

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