The PERT acronym stands for *Program Evaluation and Review Technique*.
PERT was developed jointly by representatives of the U.S. Navy, Lockheed,
and the consulting firm of Booz, Allen and Hamilton working on the Polaris
missile system. Since many of the tasks required in the development of
the Polaris had never been done before, the time required to complete the
tasks was uncertain. Thus, PERT was designed for projects where the time
required to perform each activity is essentially a random variable. PERT
focuses on estimating the *probability distribution* for total project
time based on the uncertainties in the durations of individual activities.

The PERT modeling technique involves probability distributions for each
activity duration in the project, and hence is an example of a stochastic
model. Instead of a single representative time, one takes three different
times for each activity, namely

In order to simulate the project duration statistic for a project, one must "fill in" a probability distribution between a

__BETA DISTRIBUTIONS__

To get an idea of the variety of shapes available within the family
of beta distributions, we have plotted three examples below of which the
first is skewed right, the second is symmetric, and the third is skewed
left. By variation of the mean and variance statistics with repect to the
minimum and maximum parameters, one gets a wide variety of shapes which
can be expected to fit most practical situations pretty well. In these
examples the range has been normalized from zero to one, the mean for the
symmetric case is at the midpoint 0.5, whereas for the skewed cases the
mean has been placed at 0.33 and 0.67 respectively. The variance is the
same in all cases, being determined by the PERT approximation formula as
(1/6)2 or 1/36.

We will consider the beta distribution formulas in more detail below,
but first we need to look at the PERT approximation formulas for mean and
variance which will be used as a basis for selecting the appropriate beta
distribution parameters.