User-Defined Equations

The Weibull++ Monte Carlo utility includes the option to generate simulated values based on equations you enter. When you select User-Defined in the Distribution area on the Main tab of the Monte Carlo utility, the Parameters area will be replaced with an Equation field. Note that any uniform random variable in the equation must be indicated by the variable R.

For example, consider the following equation:

Substituting the value of b = 0.5 and using the variable R to represent x, you could enter the following in the Equation field:

(1/0.5) * exp(-(R/0.5))

Note: A new uniform random variable is chosen for each time R appears in the user-defined equation. For example, if you enter R^2, the software will compute the square of one uniform random number. But if you entering R*R, the software will compute the product of two different uniform random numbers. Thus, these two equations will generate different data sets.

You can also generate data based on distributions calculated in standard folios ("data sources") from your current project. To do this, click the Insert Data Source button to select a standard folio. The software will enter a variable based on that folio's distribution into the Equation area on the Main tab. (If desired, you can also combine equations based on folios with equations that use the uniform random variable R.)

As an example, if you wanted to generate a data set that contains a range of possible area measurements, where each data point is obtained by multiplying a length value obtained from one Weibull++ standard folio data sheet and a height value obtained from another data sheet, your user-defined equation might look like this after you insert the data sources and edit the equation:

'Folio!Length' * 'Folio!Height'

where:

“Folio” is the name of the standard folio that was used to fit a distribution to the available information for length and height.
“Length” is the name of the data sheet containing the length data set.
“Height” is the name of the data sheet containing the height data set.

You could then send the simulated data set for possible area values to a Weibull++ folio and analyze it as you would any other data set.

This functionality gives you the flexibility to generate data sets for a wide variety of applications. For example, you can perform probabilistic design analysis by analyzing the variability of the parts of a product (e.g., computing the distributions for each part’s size) and then creating a user-defined equation that is defined in terms of the distributions associated with each part. Then data can be generated to, for example, analyze the probability that the product will meet certain size specifications. See User-Defined Equation Example for a more detailed example of probabilistic design analysis.