# Probabilistic Analysis Overview

**RocSupport** can perform statistical analysis on input data when in probabilistic mode. The results of the analysis can be presented as a histogram plot, cumulative plot or scatter plot.

## Distributions

To perform statistical analysis, at least one of the input variables must have a statistical distribution. Otherwise the program performs the same calculation as in deterministic mode. Most of the tunnel and rock parameters can be given distributions, but support parameters are fixed. Seven statistical distributions are available in **RocSupport**: Normal, Uniform, Triangular, Beta, Exponential, Lognormal and Gamma.

## Simulation

**RocSupport** performs the statistical simulation each time the user makes changes to input data, or selects the Compute option. First, it generates samples (the number of samples is specified in Project Settings) for all distributions of input variables, then it generates distributions of output variables by calculating results for each sample.

The simulation process can be quite lengthy, depending on the number of samples and number of input variables that have distributions. The progress is indicated on the status bar at the bottom of the main window.

## Probability of Failure

In probabilistic mode, **RocSupport** determines a mean Factor of Safety and a Probability of Failure. The Probability of Failure is defined as the percentage of samples from the factor of safety distribution that are less than 1. For example, if a total of 1000 samples are generated, and 250 samples have a factor of safety less than 1, then the probability of failure is 25%.