PERT and the Beta Distribution

Conceptual Overview: Explore the beta distribution corresponding to PERT parameters.

Specifying optimistic, pessimistic, and most likely or mode times are sufficient to generate the beta distribution describing completion times. The applet opens with values Optimistic $=2$ weeks, Pessimistic $=11$ weeks, and Mode $=4$ weeks. Drag the mode line inside the distribution to see how the shape changes as expectations about the most likely outcome change. Drag between $0$ and the current Optimistic value to change the Optimistic value. Drag, in either direction, beyond the upper end to change the pessimistic value.

NOTE: To prevent extreme beta distributions that are difficult to graph, there are limits on how much the parameters can be changed. In general, dragging is limited so that the boundaries are least $10\%$ of the range between the pessimistic and optimistic values. The maximum pessimistic value is also limited to approximately three times the initial pessimistic value. If the graph becomes poorly displayed, reload the item.

$0$

$2$

$4$

$6$

$8$

$10$

Time $($weeks$)$

Relative Likelihood

Mode $=4\mathrm{.}61$

Mean $=5\mathrm{.}41$

Created by Gary H$.$ McClelland, Professor Emeritus $|$ University of Colorado Boulder