Cumulative Plot
A Cumulative Distribution is, mathematically speaking, the integral of the normalized probability density function. Practically speaking, a point on the cumulative distribution gives us the probability that a random variable will be LESS THAN OR EQUAL TO a specified value.
That is, if (X,Y) is a point on the cumulative distribution S-curve, then Y = the probability that the random variable will be <= X.
To plot a Cumulative Distribution after a Probabilistic Analysis:
- Select Cumulative Plot
from the toolbar or the Statistics menu.
- In the Cumulative Plot dialog, select the data you would like to plot. The following data can be plotted:
- Any Random Variable that you have defined for the Probabilistic Analysis (these will appear first in the drop-down list of Data to Plot).
- The Factor of Safety for any analysis method which was used (these will be listed after the input data Random Variables).
- The Number of Bins used to create the plot can be customized if desired.
- Select the Plot button to generate the Cumulative plot. Note:
- Once a plot is generated, there are many different options available, if you right-click the mouse on the plot. See below for details.
The mean, standard deviation, minimum and maximum values for the data plotted, will be listed at the bottom of the plot. If you have plotted Factor of Safety, then the Probability of Failure (PF = ##) and Reliability Index (RI = ##) will also be listed.
Sampling a Cumulative Plot
A useful feature of Cumulative Plots in Slide2 is the ability to easily sample the values at any point on the curve. This can be done graphically, as follows:
An alternative to the graphical procedure described above is as follows:
TIP: if you are viewing a Cumulative Plot of Safety Factor, the Cumulative Probability at Factor of Safety = 1, is equal to the Probability of Failure.
Right-Click Options
Other options are available if you right-click on a Cumulative Plot. For example:
- Select the Change Plot Data option to change the data viewed on the plot.
- Select the Chart Properties option to customize the appearance of the plot.
Experiment with the different options available in the right-click menu.