Parametric Analysis

Once equation coefficients are generated in IC-CAP Statistics, you can build a variety of statistical models or load the equation data directly into IC-CAP and perform a simulation. You can test your model, based on a reduced set of parameters, against the raw data to see how well it performs.

There are three choices for parametric analysis:

Monte Carlo Analysis

Monte Carlo analysis provides an efficient solution to problems involving elements of uncertainty that are too complex to be solved by strict analytic methods. Instead of calculating all possible combinations, this method uses a small set of randomly generated values to approximate a solution.

Corner Modeling

Corner modeling is used to select worst-case models from a given data set. This method is computes the dependent parameters of a data set to arrive at a set of correlated parameters. Traditional worst-case modeling uses corner models. Corner modeling chooses a set of extreme values at the outside of the real multi-dimensional probability density function (PDF) and requires 2 ⁿ simulations for an n-dimensional problem.

Parametric Boundary Modeling

Parametric boundary modeling chooses a set of extreme values at the boundary of the real multi-dimensional PDF, and only needs 2n simulations for an n-dimensional problem.

For example, if you chose 10 factors, the number of simulations with parametric boundary models would be 20 compared to 1024 using corner models.

Parametric boundary modeling is used to extract a nominal model from a given data set. Although most effective with a large number of data points, boundary modeling can be used for data sets as small as 20 points.

Boundary modeling is used to generate an estimate for the density of data about every point in a data set. These density estimates are then sorted to determine the nominal points and the boundary points for the data set.

Boundary modeling circumvents the typically large simulation times required for a Monte Carlo analysis. However, its results are qualitative in comparison to a full Monte Carlo analysis, and it does not provide a yield estimate.

Boundary modeling provides a superior alternative to traditional worst-case modeling. It does this by using a statistically robust method to isolate existing deviant models that stress the design rather than constructing models that may not occur in practice.