  Variability in multiple independent input parameters makes it difficult to
estimate the resultant variability in the system's overall response. The
Propagation of Errors and Monte-Carlo techniques are two major methods to
predict the variability of a system. However, in the former method, the
formalism can lead to an inaccurate estimate for systems that have parameters
varying over a wide range. For the latter, the results give a direct estimate
of the variance of the response, but for complex systems with many parameters,
the number of trials necessary to yield an accurate estimate can be very large
to the point the technique becomes impractical. In this study, the
effectiveness of the Tolerance Design method to estimate variability in complex
systems is studied. We use a linear elastic 3 point bending beam model and a
nonlinear extended finite elements crack growth model to test and compare the
PE and MC methods with the TD method. Results from an MC estimate, using 10,000
trials, serve as a reference to validate the result in both cases. We find that
the PE method works suboptimal for a coefficient of variance above 5% in the
input variables. In addition, we find that the TD method works very well with
moderately sized trials of designed experiment for both models. Our results
demonstrate how the variability estimation methods perform in the deterministic
domain of numerical simulations and can assist in designing physical tests by
providing a guideline performance measure.
