This document discusses PERT (Program Evaluation and Review Technique), which is a successful method for estimating project timelines. PERT breaks projects down into detailed tasks and estimates optimistic, most likely, and pessimistic time estimates for each task. It uses a beta probability distribution to calculate expected task times and project variance. The expected times are combined to estimate overall project completion time, while variances are used to calculate a standard deviation and confidence intervals for finishing the project on schedule. PERT allows estimating project timelines statistically while accounting for uncertainty in task durations.

1. Project
Management
PERT Estimation TECHNIQUES
By Qadir Nawaz Abbasi
Mechanical Engineering Dept:
MUET SZAB Campus
Khairpur Mir’s
July, 2018

2.  Before any activity begins related to the work of a
project, every project requires an advanced, accurate
time estimate. Without an accurate estimate, no project
can be completed within the budget and the target
completion date.
 Developing an estimate is a complex task. If the project
is large and has many stakeholders, things can be more
complex.
 Therefore, there have been many initiatives to come up
with different techniques for estimation phase of the
project in order to make the estimation more accurate.
 PERT (Program Evaluation and Review Technique) is one
of the successful and proven methods among the many
other techniques, such as, CPM, Function Point
Counting,Top-Down Estimating, WAVE, etc.
Introduction

3.  PERT is all about management probabilities.
 Same as most of other estimation techniques, PERT also
breaks down the tasks into detailed activities.
 In this map, a node represents each event. The activities are
represented as arrows and they are drawn from one event to
another, based on the sequence.
 Next, the Earliest Time (TE) and the Latest Time (TL) are
figured for each activity and identify the slack time for each
activity.
 When it comes to deriving the estimates, the PERT model
takes a statistical route to do that. We will cover more on this
in the next two sections.

4.  There are three estimation times involved in PERT;
to = Optimistic Time Estimate
tm = Most LikelyTime Estimate
tp = Pessimistic Time Estimate
 In PERT, these three estimate times are derived for each
activity. This way, a range of time is given for each
activity with the most probable value,
TheThree Chances

5.  Optimistic Time Estimate:
This is the fastest time an activity can be
For this, the assumption is made that all the
resources are available and all predecessor
are completed as planned.
 Most Likely Time Estimate:
Most of the times, project managers are asked
submit one estimate. In that case, this is the
that goes to the upper management.
 Pessimistic Time Estimate:
This is the maximum time required to complete
activity. In this case, it is assumed that many
wrong related to the activity. A lot of rework and
resource unavailability are assumed when this
estimation is derived.

6. te = (to + 4tm + tp)/6
v= (tp - to )^2/6^2
 BETA probability distribution is what works behind PERT.
The expected completion time (te) is calculated as below:
 At the same time, the possible variance (v) of the estimate is
calculated as below:
 Before these three times can be combined into a single
expression for expected time, two assumptions must be
made.
1. that the standard deviation, is one-sixth of the time
requirement range. This assumption stems from
probability theory, where the end points of a curve are
three standard deviations from the mean.
2. that the probability distribution of time required for an
activity be expressible as a beta distribution.

7.  Now, following is the process we follow with the two
values:
 For every activity in the critical path, E andV are calculated.
 Then, the total of all Es are taken. This is the overall
expected completion time for the project.
 Now, the corresponding V is added to each activity of the
critical path. This is the variance for the entire project. This
is done only for the activities in the critical path as only the
critical path activities can accelerate or delay the project
duration.
 Then, standard deviation of the project is calculated. This
equals to the square root of the variance (V).
 Now, the normal probability distribution is used for
calculating the project completion time with the desired
probability.

8.  As an example, if a = 3, b = 7, and m = 5 weeks, then the
expected time, te, would be 5 weeks.
 This value for te would then be used as the activity time
between two events in the construction of a PERT chart.
This method for obtaining best estimates contains a large
degree of uncertainty.
 If we change the variable times to a = 2, b = 12, and m = 4
weeks, then te will still be 5 weeks.
 The latter case, however, has a much higher degree of
uncertainty because of the wider spread between the
optimistic and pessimistic times.
 Care must be taken in the evaluation of risks in the
expected times

9.  In order to calculate the probability of completing the
project on time, the standard deviations of each activity
must be known.This can be found from the expression
 We must identify whether it is a one, two, or three sigma
limit deviation
SIGMA te= (tp - to )/6

10.  The total path standard deviation is calculated by the
square root of the sum of the squares of the activity
standard deviations using the following expression:
 The purpose of calculating is that it allows us to establish
a confidence interval for each activity and the critical
path.
 From statistics, using a normal distribution, we know that
there is a 68 % chance of completing the project within
one standard deviation, a 95 % chance within two
standard deviations, and a 99.73 % chance within three
standard deviations.