Abstract
The yield of an Integrated Circuit (IC) is commonly expressed as the fraction (in %) of working chips overall manufactured chips and often interpreted as the failure probability of its analog blocks. We consider the Importance Sampling Monte Carlo (ISMC) as a reference method for estimating failure probabilities. For situations where only a limited number of simulations is allowed, ISMC remains unattractive. In such cases, we propose an unbiased hybrid Monte Carlo approach that provides a fast estimation of the probability. Hereby we use a combination of a surrogate model, ISMC technique and the stratified sampling.
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Notes
- 1.
The approach can be extended for other distributions assuming that the original input distributions can be transformed into a standard Gaussian distribution.
- 2.
Surrogate models mimic the complex behaviour of (circuit) simulation model. The study of surrogate models is out of scope of this paper. A review on surrogate models is given in [3].
- 3.
An allocation means the partition of N.
- 4.
We keep sampling from g(x) until we have N i accepted samples.
- 5.
- 6.
In theory, the reference probability is the true failure probability to which the simulated results to be compared. However, in practice, we do not know the true probability. Thus, an approximation (with a high accuracy) of the true probability is used.
References
Bucklew, J.A.: Introduction to Rare Event Simulation. Springer Series in Statistics. Springer, New York (2004)
Cannamela, C., Garnier, J., Iooss, B.: Controlled stratification for quantile estimation. Ann. Appl. Stat. 2(4), 1554–1580 (2008)
Chen, V.C.P., Tsui, K.-L., Barton, R.R., Meckesheimer, M.: A review on design modeling and applications of computer experiments. IIE Trans. 38(4), 273–291 (2006)
Ciampolini, L., Lafont, J.-C., Drissi, F. T., Morin, J.-P., Turgis, D., Jonsson, X., Descléves, C., Nguyen, J.: Efficient yield estimation through generalized importance sampling with application to NBL-assisted SRAM bitcells. In: Proceedings of the 35th International Conference on Computer-Aided Design (2016). Article No. 89
Homem-de-Mello, T., Rubinstein, R.Y.: Estimation of rare event probabilities using cross-entropy. In: Yücesan, E., Chen, C.-H., Snowdon, J.L., Charnes, J.M. (eds.) Proceedings of the 2002 Winter Simulation Conference (2002)
Jourdain, B., Lelong, J.: Robust adaptive importance sampling for normal random vectors. Ann. Appl. Probab. 19(5), 1687–1718 (2009)
Tyagi, A.K.: Speeding up rare-event simulations in electronic circuit design by using surrogate models. PhD thesis, Department of Mathematics and Computer Science, 10 (2018). Proefschrift
Tyagi, A.K., Jonsson, X., Beelen, T.G.J., Schilders, W.H.A.: Speeding up rare event simulations using Kriging models. In: Proceedings of IEEE 21st Workshop on Signal and Power Integrity (SPI). IEEE, New York (2017).
Tyagi, A. K., Jonsson, X., Beelen, T.G.J., Schilders, W.H.A.: Hybrid importance sampling monte carlo approach for yield estimation in circuit design. J. Math. Ind. 8(1), 11 (2018)
Acknowledgement
The first author is grateful to the financial support from the Marie Curie Action.
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Tyagi, A.K., Jonsson, X., Beelen, T., Schilders, W.H.A. (2020). An Unbiased Hybrid Importance Sampling Monte Carlo Approach for Yield Estimation in Electronic Circuit Design. In: Nicosia, G., Romano, V. (eds) Scientific Computing in Electrical Engineering. SCEE 2018. Mathematics in Industry(), vol 32. Springer, Cham. https://doi.org/10.1007/978-3-030-44101-2_22
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