eldo_user

Monte Carlo Analysis
Primary Statistics of Uncertainty Analysis
The third line contains another confidence interval, known as the Wilson score interval
(WCI). This interval has better properties, even for a small number of runs. The formula
is:
• The results of the phase noise extract indicate that no fail simulation was found, because
the reported failure probability is zero. Only the value of q σ (which represents a
normalized distance of the user specification) and the extract confidence interval (ECI)
are reported for this case. The ECI gives an upper bound on the “true” failure
probability. Refer to “Zero Failure Probability and True Failure Probability” on
page 482 for more information.
Zero Failure Probability and True Failure Probability
If a certain event related to a user specification does not occur in a sample of size n, the reported
failure probability is zero. The standard Monte Carlo method provides a conservative estimator
of the true failure probability, which might actually be non-zero. However, use of this estimator
will result in “overdesign” of the circuit characteristics by taking large margins.
Given a random variable Y and a threshold y, the probability π y = Pr{Y ≤ y} has estimator:
where:
The expectation and the variance of this empirical estimator are:
Since S n follows a binomial law with parameters n and π y , an exact confidence upper bound
b n, α on π y is available such that Pr(π y ≤ b n, α ) ≥ 1 - α. When S n = 0, which happens with
probability (1 - π y ) n , the (1 - α)-confidence interval is [0, 1 - α 1/n ]. For a 95% confidence level (α
= 0.05), the upper bound is approximately given by:
482
Eldo® User's Manual, 15.3