eldo_user

Monte Carlo Analysis
Global Sensitivity Analysis
is an indicator of the presence of interactions in the model.
• It is possible for the sum of all S i to be close to 0 (therefore a number of S i indices are
also very small). It indicates that the variability of the output cannot be analyzed without
taking into account the interactions. This output is truly non-additive.
In practice, the sum of all S i can be greater than 1. These are some artifacts due to the
approximation procedure of the conditional expectation. Small variations of the order 1% or
less, when cumulated, may give , and some truly non-important parameters would be
classified as important. This is particularly true when the number of statistical parameters is
large. Eldo uses some statistical tests to overcome this situation, refer to the example “Example
17—Monte Carlo Sensitivity of a Two-Stage Operational Amplifier” on page 1309.
Example
A simple example is analyzed here for the purpose of familiarization with sensitivity indices.
The input distributions are X i ~ N(0, 1). The scatter plots of the output Y = X 1 + X 2 2 + X 1 X 2 are
given in Figure 11-20.
Figure 11-20. Scatter Plots of Output
This function has an immediate representation:
• The mean value: .
• The first-order terms: and .
• The interaction term: .
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Eldo® User's Manual, 15.3