Configuring the Random Variables

You can configure the parameters that you want to use as random variables for your design problem.

See Also
Probability Distributions
  1. From the Flow section of the action bar, click Monte Carlo and drop it on the process diagram.
  2. Double-click Monte Carlo.
  3. From the Monte Carlo Editor that appears, select the Random Variables tab.
  4. Select the input (or input/output) parameters to use as random variables.
  5. Specify the Random Variables options. The available options depend on the type of probability distribution you selected:
    OptionDescription
    Distribution The probability distribution option for the random variable.
    Mean The measure of central tendency of a random variable. The default value is 0.0.
    Standard Deviation The measure of dispersion of a random variable. The default value is 1.0.

    During execution Optimization Process Composer fixes the standard deviation and varies the coefficient of variation depending on the value of the mean. Optimization Process Composer applies this option during execution if you have selected After execution, reset to mean value point and run from the General tab.

    Coefficient of Variation The value of the standard deviation divided by the mean for the random variable. The default value is 1.0.
    Alpha (Gumbel, Lognormal, Weibull, and Skewed Normal distributions) 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) The scale parameter for the Gumbel distributions and the shape parameter for the Lognormal and Weibull distributions.
    Allowed Values (Discrete – Uniform distribution) 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) The scale parameter for the exponential distribution. Equal to one over the mean value and/or one over the standard deviation (mean and standard deviation are equal for the exponential distribution).
    Omega (Skewed Normal distribution) The statistical dispersion of the probability distribution.
    Xi Location (Skewed Normal distribution) The “shift” or “origin” for a distribution.
    Low (Triangular and Uniform distributions) The lower limit for the triangular and uniform distributions.
    Mode (Triangular distribution) The shape parameter of the triangular distribution, representing the peak of the triangle.
    High (Triangular and Uniform distributions) The upper limit for the triangular and uniform distributions.
    Lower Truncation The lower limit of the probability distribution. The Monte Carlo adapter will not sample values of the distribution below this limit.
    Upper Truncation The upper limit of the probability distribution. The Monte Carlo adapter will not sample values of the distribution above this limit.
  6. Optional: Click Correlation Matrix to use correlations to sample the random variable distributions. Optimization Process Composer applies the correlation matrix to the sample of random variables while preserving the individual distributions.
    1. Enter the correlation coefficients (-1.0 ≤ value ≤ 1.0) above the diagonal of the matrix. Optimization Process Composer applies the same correlation coefficients below the diagonal of the matrix.
    2. Click OK.
  7. Optional: Select Update random variable mean values to current parameter values before execution to update the value of all the random variables means to the current parameter values before running the Monte Carlo adapter.

    Select this option when the Monte Carlo adapter will run after another adapter and you want the parameter values in the Monte Carlo adapter to be taken from the previous adapter.

  8. Click Ok to save your changes and to close the Monte Carlo Editor.