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Monte Carlo Analysis
Importance Sampling Monte Carlo
Figure 11-10 illustrates the general principle underlying the ISMC method. The top plot
represents the probability distribution function of the output measure Y = H(X). The vertical
lines at y t are associated with the failure boundary curves C t = {x | H(x) = y t } shown in the
bottom plot. The difficult problem of estimating the very small probabilities is broken down
into a sequence of simpler intermediate problems of the form:
where the levels y t are a chosen monotone sequence that tend to the goal value y.
At each iteration t, an intermediate sample X t is generated in order to estimate the intermediate
probability π t . This intermediate sample is a standard Monte Carlo random sample of size at
least NRUN_PILOT. The number of steps needed to compute a single tail probability is
approximately NRUN_PILOT × IS_MAXITER. When both bounds are specified, the number
of steps needed is approximately double this value. Refer to “Probability and Quantile
Estimators” on page 480 and “Importance Sampling Monte Carlo Examples” on page 528 for
more information.
Yield and Failure Probability Computation using MCPROB
The yield value and probability of failure are complementary quantities used to measure how
well a given circuit conforms to a set of user-defined specifications. For practical reasons, the
ISMC method only considers failure probabilities.
The MCPROB function computes the probability π y that a given response is greater than or less
than a bound y:
• To calculate a left-tail probability:
use the following command:
.EXTRACT MC LABEL=LABEL MCPROB(OUTPUT, LE, BOUND)
where OUTPUT is the name of the output response H(X), and where BOUND is y.
• To calculate a right-tail probability:
use the following command:
.EXTRACT MC LABEL=LABEL MCPROB(OUTPUT, GE, BOUND)
where OUTPUT is the name of the output response H(X), and where BOUND is y.
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Eldo® User's Manual, 15.3