Performing an uncertainty analysis with the collocation method is an iterative process, because we need to approximate the uncertain output variables in terms of the uncertain input variables. Due to the complexity of the model, we normally do not have enough insight to set up an accurate approximation in the beginning. Therefore we recommend that you always begin with the simplest approximation and add complexity as you gain more insight into the model along the way. The simplest approximation means that you will set the highest order of the polynomials to 2 on the Setup Uncertainty Analysis panel. If you think there is strong inter-dependency between some uncertain input variables, you can add polynomial cross terms involving these variables. Keep in mind that the combined order of all variables in a cross term cannot exceed the highest order of the approximation.

After clicking the Do Analysis button on the Running Uncertainty Analysis panel, you will see the results of both error analysis and variance analysis. The error analysis provides two measures of accuracy for the approximation: relative sum-square-root error and index of agreement. A very small relative sum-square-root error (that is, << 1.0) and a high index of agreement (that is, very close to 1.0) indicate good accuracy. If either of these requirements is not satisfied, the accuracy is considered low. To improve the accuracy, you can revise the uncertainty analysis setup in two ways:

You should always consider adding polynomial cross terms before increasing the highest order of polynomial approximation to be greater than 3. An order greater than 5 is not recommended unless it has shown clear improvement in the accuracy.

The variance analysis will indicate which uncertain input variables have the least impact on the variation of the uncertain output variables. However, the results of the variance analysis are valid only if the approximation has enough accuracy, as indicated by the results of the error analysis. With reasonable accuracy, you can remove uncertain input variables from the analysis if they have shown little impact on the variations of all uncertain output variables. This will reduce the dimensionality of the approximation and reduce the number of model runs needed for each iteration.