Skip to main content
Log in

Modified Latin Hypercube Sampling Monte Carlo (MLHSMC) Estimation for Average Quality Index

  • Published:
Analog Integrated Circuits and Signal Processing Aims and scope Submit manuscript

Abstract

The Monte Carlo (MC) method exhibits generality and insensitivity to the number of stochastic variables, but it is expensive for accurate Average Quality Index (AQI) or Parametric Yield estimation of MOS VLSI circuits or discrete component circuits. In this paper a variant of the Latin Hypercube Sampling MC method is presented which is an efficient variance reduction technique in MC estimation. Theoretical and practical aspects of its statistical properties are also given. Finally, a numerical and a CMOS clock driver circuit examples are given. Encouraging results and good agreement between theory and simulation results have thus far been obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. C. Zhang and M. A. Styblinski, Yield and Variability Optimization of Integrated Circuits. Kluwer Academic Publisher, 1995.

  2. R. Y. Rubinstein, Simulation and the Monte Carlo Method. John Wiley & Sons, Inc., 1981.

  3. D. E. Hocevar, M. R. Lightner, and T. N. Trick, “A study of variance reduction techniques for estimating circuit yields.” IEEE Trans. Computer-Aided Design CAD-2(3), pp. 180-192, 1983.

    Google Scholar 

  4. M. D. McKay, R. J. Beckman, and W. J. Conover, “A comparison of three methods for selecting values of input variables in analysis of output from a computer code.” Technometrics 21(2), pp. 239-245, 1979.

    Google Scholar 

  5. M. Keramat and R. Kielbasa, “Latin hypercube sampling Monte Carlo estimation of average quality index for integrated circuits.” Analog Integrated Circuits and Signal Processing 14(1/2), pp. 131-142, 1997.

    Google Scholar 

  6. M. Keramat and R. Kielbasa, “Worst case efficiency of Latin hypercube sampling Monte Carlo (LHSMC) yield estimator of electrical circuits.” in Proc. IEEE Int. Symp. Circuits Syst. Hong Kong, pp. 1660-1663, 1997.

  7. A. Torralba, J. Chavez, and L. G. Franquelo, “Circuit performance modeling by means of fuzzy logic.” IEEE Trans. Computer-Aided Design of Integrated Circuits Syst. 15(11), pp. 1391-1398, 1996.

    Google Scholar 

  8. Cox, P. Yang, S. S. Mahant-Shetti, and P. Chatterjee, “Statistical modeling for efficient parametric yield estimation of MOS VLSI circuits.” IEEE Trans. Electron Devices ED-32(2), pp. 471-478, 1985.

    Google Scholar 

  9. M. A. Styblinski and A. Ruszczynski, “Stochastic approximation approach to statistical circuit design.” Electronics Letters 19(8), pp. 300-302, 1983.

    Google Scholar 

  10. M. Keramat and R. Kielbasa, “A study of stratified sampling in variance reduction techniques for parametric yield estimation.” IEEE Trans. Circuits and Syst.-II: Analog and Digital Signal Processing, vol. 45,no. 5, pp. 575-583, May 1998.

    Google Scholar 

  11. A. Papoulis, Probability, Random Variables, and Stochastic Process, 3rd edition. McGraw-Hill, Inc., 1991.

  12. M. Keramat, “Properties of average quality index in statistical circuit design.” Ecole Superieure d'Electricite (SUPELEC) Paris, France, Tech. Rep. No. SUP-0496-12, 1996.

  13. R. L. Iman and W. J. Conover, “Small sample sensitivity analysis technique for computer models, with an application to risk assessment.” Communications in Statistics A9-(17), pp. 1749-1874, 1980.

    Google Scholar 

  14. A. M. Mood, F. A. Graybill, and D. C. Boes, Introduction to Theory of Statistics 3rd ed. McGraw-Hill, New York, 1974.

    Google Scholar 

  15. P. Aldebert and R. Klielbasa, “OMEGA: system of electric simulator, user's manual.” Version 6.0, Ecole Superieure d'Electricite (SUPELEC) Paris, France, Tech. Rep., 1993.

  16. The Mathworks, Inc., MATLAB: External Interface Guide 1993.

  17. M. Keramat, “Using Matlab in interprocess communications.” Ecole Superieure d'Electricite (SUPELEC) Paris, France, Tech. Rep. No. SUP-0496-7, 1996.

  18. R. S. Soin and R. Spence, “Statistical exploration approach to design centring.” IEE Proc. 127G(6), pp. 260-269, 1980.

    Google Scholar 

  19. H. A. Steinberg, “Generalized quota sampling.” Nuc. Sci and Eng. 15, pp. 142-145, 1963.

    Google Scholar 

  20. Raj and Des, Sampling Theory. McGraw-Hill, New York, 1968

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Keramat, M., Kielbasa, R. Modified Latin Hypercube Sampling Monte Carlo (MLHSMC) Estimation for Average Quality Index. Analog Integrated Circuits and Signal Processing 19, 87–98 (1999). https://doi.org/10.1023/A:1008386501079

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008386501079

Navigation