Academia.eduAcademia.edu

Figure from:A Study of Variance Reduction Techniques for Estimating Circuit Yields

See full PDFdownloadDownload figure
Tektronix, and Intel for computer-aided design of integrated circuits. His research interests include all aspects of the computer-aided design of integrated circuits with emphasis on simulation, automated layout techniques, and design methods for VLSI integrated circuits. Dr. Newton is a member of Sigma Xi.

Figure 1 Tektronix, and Intel for computer-aided design of integrated circuits. His research interests include all aspects of the computer-aided design of integrated circuits with emphasis on simulation, automated layout techniques, and design methods for VLSI integrated circuits. Dr. Newton is a member of Sigma Xi.

Related Figures (9)

nominal point inside the acceptable region (i.e., 0 in [aa, ba] ), then it might be logical to distort the distribution such that more failures are generated for the failure estimator. (Note: This problem could be translated to a nonzero nominal point without altering the results.) One logical way to do this is to sample from the uniform distribution (see Fig. 1). The stan- dard estimator for (15) and its variance have been discussed previously. The importance sampling estimator is
nominal point inside the acceptable region (i.e., 0 in [aa, ba] ), then it might be logical to distort the distribution such that more failures are generated for the failure estimator. (Note: This problem could be translated to a nonzero nominal point without altering the results.) One logical way to do this is to sample from the uniform distribution (see Fig. 1). The stan- dard estimator for (15) and its variance have been discussed previously. The importance sampling estimator is
YIELD AND EFFICIENCIES FOR A DIMENSIONALITY OF FIVE YIELD AND EFFICIENCIES FOR A DIMENSIONALITY OF ONE TABLE I
YIELD AND EFFICIENCIES FOR A DIMENSIONALITY OF FIVE YIELD AND EFFICIENCIES FOR A DIMENSIONALITY OF ONE TABLE I
YIELD AND EFFICIENCIES FOR A DIMENSIONALITY OF TEN of one, five, and ten, respectively. For each entry, the top number is the yield and the lower number is the efficiency factor referenced to the standard estimation technique and assuming equal work factors. For the multidimensional cases all the a;’s were set equal to each other, likewise for the b,’s; hence, R, is parameterized by simply a and b. TABLE ITI
YIELD AND EFFICIENCIES FOR A DIMENSIONALITY OF TEN of one, five, and ten, respectively. For each entry, the top number is the yield and the lower number is the efficiency factor referenced to the standard estimation technique and assuming equal work factors. For the multidimensional cases all the a;’s were set equal to each other, likewise for the b,’s; hence, R, is parameterized by simply a and b. TABLE ITI
VARIANCE RATIOS FOR VARIOUS WEIGHTS AND APPROXIMATIONS Table IV shows the values of n(b) for various weights and for various ratios H,,/H,,. The results in this table are not too encouraging, as the best variance ratio achieved was 1.92. This corresponds to about a 50-percent reduction in the sample size necessary for a certain accuracy, but overall this could easily be overshadowed by the overhead associated with generating the approximation M and setting up the method. Fig. 2. Sallen and Key lowpass filter.
VARIANCE RATIOS FOR VARIOUS WEIGHTS AND APPROXIMATIONS Table IV shows the values of n(b) for various weights and for various ratios H,,/H,,. The results in this table are not too encouraging, as the best variance ratio achieved was 1.92. This corresponds to about a 50-percent reduction in the sample size necessary for a certain accuracy, but overall this could easily be overshadowed by the overhead associated with generating the approximation M and setting up the method. Fig. 2. Sallen and Key lowpass filter.
Fig. 4. Variance ratios for yield and failure estimators. and its ratio with the variance of the standard Monte Carlo estimator is
Fig. 4. Variance ratios for yield and failure estimators. and its ratio with the variance of the standard Monte Carlo estimator is
Fig. 5. Strata and region of acceptability for post-stratification example.
Fig. 5. Strata and region of acceptability for post-stratification example.
Fig. 6. Optimal efficiency versus D for various yields, Useful approximations for the above formulas are
Fig. 6. Optimal efficiency versus D for various yields, Useful approximations for the above formulas are
Fig. 7. Efficiency versus D for various work ratios and 50-percent yield.
Fig. 7. Efficiency versus D for various work ratios and 50-percent yield.