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Monte Carlo Analysis
Introduction to Uncertainty Analysis
If the mean is zero, the relative standard deviation scaled by
is used instead:
The coefficient of variation is defined as a multiple of the RSEM. Refer to “Mean and
Standard Deviation” on page 478 for more information.
Uncertainty as an Interval
Under the assumptions that the probability distribution of the output measure can be assumed to
be normal (Gaussian). The uncertainty is often defined as an interval about the measurement
result that may be expected to cover a given fraction of the distribution of values. This interval
can be associated to a number u(H) obtained by multiplying the standard deviation by a
coverage factor κ p :
The number p is the coverage probability or level of confidence of the interval. A measurement
is then conveniently expressed as:
Then for example, one may take κ p = 2 for having an interval with confidence interval of
approximately 95 percent. By taking κ p = 3, a confidence level of approximately 99 percent
would be obtained.
It is important to understand that the assumption of normality cannot be used in any cases, and
this motivates the introduction of Monte Carlo simulation methods as general and flexible tools
for addressing difficult estimation problems. The Monte Carlo method provides a numerical
approximation of the output distribution, which may be non-Gaussian. This distribution is in
general not symmetric, and a coverage interval is not necessarily centered on the average value.
Yield and Failure Probability Estimation
You may want to compute the probability values associated with lower and upper bounds
(y L , y U ) for a circuit performance Y. Conversely, you may want to compute the bound or
threshold that corresponds to a target probability value π L, U .
Eldo® User's Manual, 15.3 413