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Monte Carlo Analysis
Primary Statistics of Uncertainty Analysis
where α = 0.05 = 5%. The relative half-range of this interval is therefore given by:
The approximation comes from the fact that we have
. The last term is two times
the coefficient of variation of the mean estimator. The RSEM value gives a relative estimate of
the committed error in the empirical estimator of .
We also give standard deviation based on nominal run StdNom.
Confidence Intervals
Confidence limits for the mean are an interval estimate for the mean. Interval estimates are
often desirable because the estimate of the mean varies from sample to sample. Instead of a
single estimate for the mean, a confidence interval generates a lower and upper limit for the
mean. The interval estimate gives an indication of how much uncertainty there is in our estimate
of the true mean. The narrower the interval, the more precise is our estimate.
Confidence limits are expressed in terms of a confidence coefficient. Although the choice of
confidence coefficient is somewhat arbitrary, in practice 90%, 95%, and 99% intervals are often
used, with 95% being the most commonly used.
Confidence limits are defined as:
where is the sample mean, s is the sample standard deviation, n is the sample size, α is the
desired significance level, and t (α/2, ν−1) is the upper critical value of the t distribution with n -1
degrees of freedom. Note that the confidence coefficient is 1 −α.
From the formula, it is clear that the width of the interval is controlled by two factors:
• As n increases, the interval gets narrower from the term. That is, one way to obtain
more precise estimates for the mean is to increase the sample size.
Eldo® User's Manual, 15.3 479