Pert Chart

PERT Weighted Average (expected time) (mean)=(O+4M+P)/6
Sandard Deviation (SIGMA)=(P-O)/6
Variance =(Standard Deviation)2
Lowest= mean-(Sigma*6)
1 Sigma 68.3%   2 sigma  95.5%  3 sigma  99.7 %  6 sigma 99.99%


CPM is a method that uses a fixed time estimate for each activity based on historical , expert references. CPM does not consider the time variations that may have a great impact on the completion time of a complex project.

The Program Evaluation and Review Technique (PERT) .emphasizes future probabilities in time estimates (optimistic, pessimistic, and expected time)

The Network Diagram

PERT originally was an activity on arc network, in which the activities are represented on the lines and milestones on the nodes. Over time, people began to use PERT as an activity on node network.

YearsLater CPM and PERT were developed, the two terms are used interchangeably as each technique has borrowed from one other. Currently, two network techniques are used extensively in project management scheduling networks: Activity-on-Arc (AOA) (is also known as Activity-on-Arrow (because an arc is sometimes called an arrow). When you use AOA, you use arcs or arrows, called activities, to connect events. Consequently, AOA is event-oriented uses DUMMY Activity)  and Activity-on-Node (AON) Instead of circles and labels on arcs, AON uses a user-friendly flowcharting approach.) It is the most popular project management network scheduling technique for complex, large projects. The name  (Activity-on-Node, AON) is not widely used. Most calls it a PERT chart.

Key Network Scheduling Principles

Regardless what network scheduling technique you use, understand and follow these key principles:

Earliest start: The earliest an activity can begin based on its relationship to its predecessor's duration.
Latest start: The latest an activity can begin and still satisfy requirements set forth by successor activities.
Earliest finish: Based on the relationship with a predecessor, the earliest an activity can be completed.
Latest finish: Based on the relationship with a successor, the latest an activity can be completed.
Float time: The amount of free time (slack time) an activity has without impacting due date of the project.
Forward pass: A technique that works forwards, starting with the first node in the network, 
to determine earliest start and finish times.
Backward pass: A technique that works backwards, starting with the last node in the network, 
to determine latest start and finish times.
Steps in the PERT Planning Process
  • Identify the specific activities and milestones.

  • Determine the proper sequence of the activities.

  • Construct a network diagram.

  • Estimate the time required for each activity.

  • Determine the critical path.

  • Update the PERT chart as the project progresses.

    1.  Identify Activities and Milestones

    The activities are the tasks required to complete the project.
     The milestones are the events marking the beginning and end of one or more activities.

    2.  Determine Activity Sequence

    3.  Construct the Network Diagram

    4.  Estimate Activity Times

    • Optimistic time – generally the shortest time in which the activity can be completed.

    • Most likely time – the completion time having the highest probability.

    • Pessimistic time – the longest time that an activity might require.

    5.  Determine the Critical Path

    • ES – Earliest Start time

    • EF – Earliest Finish time

    • LS – Latest Start time

    • LF – Latest Finish time

    Since the critical path determines the completion date of the project, the project can be accelerated by adding the resources required to decrease the time for the activities in the critical path. Such a shortening of the project sometimes is referred to as project crashing.

    6.  Update as Project Progresses

    Benefits of PERT

    • Expected project completion time.

    • Probability of completion before a specified date.

    • The critical path activities that directly impact the completion time.

    • The activities that have slack time and that can lend resources to critical path activities.

    • Activity start and end dates.


    The following are some of PERT’s weaknesses:

    • The activity time estimates are somewhat subjective and depend on judgement. In cases where there is little experience in performing an activity, the numbers may be only a guess. In other cases, if the person or group performing the activity estimates the time there may be bias in the estimate.

    • the actual distribution may be different.

    • other paths can become the critical path if their associated activities are delayed, PERT consistently underestimates the expected project completion time.

    To overcome , Monte Carlo simulations can be performed  to eliminate this optimistic bias in the expected project completion time.

      The second advantage of PERT is that one can determine the probability of meeting specific deadlines by development of alternative plans. If the decision maker is statistically sophisticated, he can examine the standard deviation and the probability of accomplished data.
    So, standard deviation gives an idea of the probability of whether a task will happen. .

  • Scroll to Top