Configuring the Random Variables

You can use the Random Variables tab to select the parameters that you want to use as random variables for your design problem.

  1. Double-click the SDI component icon .

    The SDI Component Editor appears.

  2. From the SDI Component Editor, click the Random Variables tab.

  3. Right-click in the table to access various options for working with random variables.

    For more information, see Setting Table Options.

  4. Determine which parameters you want to use as random variables by selecting the corresponding check boxes in the first column.

    Alternatively, you can click the button at the bottom of the tab to add all the parameters. To clear all the parameters, click the button.

    If no parameters are selected, you are prompted to add all parameters as random variables.

    Once you select a random variable, its name is displayed in the Distribution Information area, and the rest of the tab is activated.

  5. Click Correlation Matrix if you want to use random variable correlation to sample the random variable distributions.

    This option induces the required correlations on the given sample of random variables while preserving the individual distributions.

    1. Type the values (–1.0 to 1.0) in the white text boxes in the dialog box.
    2. Click OK to accept your changes and to return to the component editor.

  6. Set any of the following options, some of which vary based on your Distribution selection:

    Option Description
    Distribution Sets the probability distribution option for the random variable. Similar to sampling techniques, random variable distributions are implemented as plug-ins used by the SDI component. They are extendable by creating new plug-ins for new distributions.

    Isight provides the following distribution plug-ins:

    • Discrete – Uniform
    • Exponential
    • Gumbel – largest
    • Gumbel – smallest
    • Lognormal
    • Normal
    • Skewed Normal
    • Triangular
    • Uniform
    • Weibull

    Note: For more information about these distribution options, see Available Distribution Types.
    Mean This distribution parameter represents the measure of central tendency of a random variable. Its default setting is the current value of the parameter.
    Standard Deviation This distribution parameter represents the measure of dispersion of a random variable. Its default setting is 10% of the mean value.

    (optional) Click Fix to fix the standard deviation and vary the coefficient of variation depending upon the mean value during run time. Changing the standard deviation value in the editor updates the coefficient of variation irrespective of the option that is fixed. This option is applied at run time if you have selected the Update random variable mean values to current parameter values before execution option.
    Coefficient of Variation This distribution parameter is the value of the standard deviation divided by the mean for the random variable. The default value is 0.1.

    (optional) Click Fix to fix the coefficient of variation and vary the standard deviation depending upon the mean value during run time. Changing the coefficient of variation in the editor updates the standard deviation irrespective of the option that is fixed. This option is applied at run time if you have selected the Update random variable mean values to current parameter values before execution option.
    Allowed Values (Discrete-Uniform distribution only) This distribution parameter is the discrete set of values that the random variable may take. Each value has an equal probability (equal to 1/(number of values))
    Lambda (Exponential distribution only) This distribution parameter is the scale parameter for the exponential distribution and is equal to one over the mean value and/or one over the standard deviation (mean and standard deviation are equal for the exponential distribution).
    Alpha (Gumbel, Lognormal, Weibull, and Skewed Normal distributions) This distribution parameter is the location parameter for the Gumbel and Lognormal distributions, the scale parameter for the Weibull distribution, and the skewness parameter for the Skewed Normal distribution. Skewness is a measure of the asymmetry of the probability distribution function. When alpha is zero, the probability distribution function is symmetric resulting in the standard normal distribution in the case of skewed normal distribution.
    Beta (Gumbel, Lognormal, and Weibull distributions) This distribution parameter is the scale parameter for the Gumbel distributions and is the shape parameter for the Lognormal and Weibull distributions.
    Omega (Skewed Normal distribution only) This distribution parameter is the scale parameter and determines the statistical dispersion of the probability distribution.
    Xi Location (Skewed Normal distribution only) This distribution parameter is the location parameter and determines the “shift” or “origin” for a distribution.
    Low (Triangular and Uniform distributions) This distribution parameter is the lower limit for the triangular and uniform distributions.
    Mode (Triangular distribution only) This distribution parameter is the shape parameter of the triangular distribution, representing the peak of the triangle.
    High (Triangular and Uniform distributions) This distribution parameter is the upper limit for the triangular and uniform distributions.
    Truncate Distribution Tail(s) Select this option if you want to truncate a distribution tail or both the lower and upper tail. Upon selection, entries appear for lower and upper, referring to the lower tail and the upper tail. Distribution values below the lower truncation value and above the upper truncation value are not sampled. The distribution preview graphs are updated to display the effects of truncation.

  7. Click the button at the bottom of the editor to set variable options.

    For more information, see Editing Attributes for Multiple Parameters.

  8. Review the preview graphs on the right side of the tab.

    These graphs are updated automatically based on changes made to the selected random variables distribution properties. A legend below the graph explains the color coding. The graphs display the following information:

    Option Description
    Probability Density This graph shows the actual shape of the selected distribution with regard to the probability density function.
    Cumulative Distribution This graph shows the actual shape of the selected distribution with regard to the cumulative distribution function.

  9. If desired, you can map any of the above settings to a parameter.

    For more information, see Mapping Options and Attributes to Parameters.

  10. If desired, click Update random variable mean values to current parameter values before execution if you want to automatically change the settings to the current point when the SDI component executes.

    Selecting this option automatically updates the mean values of all random variables to the current parameter values in this component, prior to executing the SDI component. This option is useful if the SDI component is executed after another component and parameter values are taken from the previous component.

  11. Click OK to save your changes and to close the SDI Component Editor.