Everything You Need to Know About PERT Chart

Do you need help mapping tasks in project management? A PERT chart is a perfect solution for professionals struggling to track dependencies. This article will cover the five steps, show you an example, and explain how to use a PERT chart effectively.

What is a PERT Chart? 

PERT, or the Program Evaluation and Review Technique, is a method that analyzes the time required to complete each task and its associated dependencies and determines the minimum amount of time necessary to complete a specific project. The process takes into consideration three different time estimates:

• Optimistic Time (To): The minimum time required to complete the project, assuming everything goes better than expected.
• Pessimistic Time (Tp): The maximum time required to complete the task, assuming things go wrong.
• Most Likely Time (Tm): The most likely time required to complete the tasks, assuming everything goes alright. 

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How Do You Make a PERT Chart?

• Define the project scope: Determine the project's objectives and goals and list all the tasks required to achieve those objectives.
• Establish task dependencies: Identify the dependencies between tasks and determine the order in which tasks must be completed.
• Determine task duration: Estimate the time each task will take to complete.
• Create a network diagram: Use arrows to connect the tasks and show their dependencies on each other. Number the tasks and events and list their estimated duration.
• Add critical path information: Determine the critical path and the sequence of tasks that determines the minimum overall project duration.
• Update the chart regularly: Revisit the PERT chart regularly to reflect changes in the project, such as changes in task dependencies, duration, or priority.
• Present the chart: The final PERT chart should clearly show the relationships between tasks, the critical path, and the estimated duration of each task.

PERT Chart Terms and Concepts

Before we get into the PERT Analysis process, we must discuss some important concepts: Events and Activities. Let’s understand these terms with the help of a network diagram (the method's final output).

Event

A circle represents events that occur at the start and end of an activity. Event 1 is the tail event, and Event 2 is the head event. In our example, node 1 will be referred to as the tail event, and 2 will be referred to as the head event.

Activity

Activities represent actions and the consumption of resources like time, money, and energy required to complete the project. In our example, A, B, C, D, and E represent the activities taking place between their respective events.

Dummy Activity

A dummy activity represents a relationship between two events. In the example below, the dotted line represents a relationship between nodes 3 and 2. The activity between these nodes will not have any value.

Other rules that need to be considered are: 

• The network should have a unique starting and ending node.
• No activity can be represented by more than a single arc (the line with an arrow connecting the events) in the network.
• No two activities can have the same starting and ending node.

Also Read: Important Rules of Project Management

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The PERT Analysis Method

In the question here, we have three objectives: 

1. Draw the network diagram. 

2. Find the mean and variance.

3. Find the critical path and estimated time of completion.

Now, let’s draw the network diagram.

First, let’s look at the activities and their immediate predecessors.

We can see that activities A, B, and C don’t have any immediate predecessors. This means that we can draw individual arcs to each of them. Let’s draw the nodes for the first activity, activity A. We can see that activity A acts as the immediate predecessor for the activity D.

Similarly, activities B and C don’t have any immediate predecessors and hence, can be directly connected to node 1. Node B acts as an immediate predecessor for E, while node C acts as the immediate predecessor for activities F and G. Let’s go ahead, and draw that.

Let’s have a look at activity D. This activity is the immediate predecessor for activity A. This means that we can directly draw an arc from node 2.

Now, we’ve drawn activities A, B, C, and D as part of the PERT analysis. Now, looking at activity E, it acts as the immediate predecessor to activity H along with activity F. Since it’s preceded only by activity B, we can directly connect it to node 3.

Now, for activity F. If we have a look at the table, we can see that a combination of the activities E and F act as immediate predecessors for activity H. This means that activities E and F need to come together at node 6. 

Next up, let’s have a look at activity G. It is immediately preceded by activity C, and acts as an immediate predecessor for activity J, along with activity H. Since it’s an independent activity, we can draw it like so:

For activity H, we can see that it and G act as immediate predecessors for activity J. This means that nodes 6 and 7 need to be connected.  

And finally, we activities I and J. These activities don’t act as immediate predecessors for any other activity. This means that they’ll connect directly to the final node.

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Now that we’ve created the network diagram let’s proceed. Next, as part of the PERT analysis, let’s examine how to determine the mean and variance.

The mean, which is also the estimated time can be determined using the formula:

We can calculate the variance using this formula: 

Let’s apply the formula to each activity.

For activity A,

The mean will be: (To + 4*Tm + Tp) /6 =  (6 + 4*7 + 8) /6 = 7

For activity B,

The mean will be: : (To + 4*Tm + Tp) /6 = (3 + 4*5 + 7) /6 = 5

For activity C,

The mean will be: : (To + 4*Tm + Tp) /6 = (4 +4*7 +10) /6 = 7

For activity D,

The mean will be: : (To + 4*Tm + Tp) /6 = (2 + 4*3 +4) /6 = 3

For activity E,

The mean will be: : (To + 4*Tm + Tp) /6 = (3 + 4*4 + 11) /6 = 5

For activity F,

The mean will be: : (To + 4*Tm + Tp) /6 = (4 + 4*8 + 12) /6 = 8

For activity G,

The mean will be: : (To + 4*Tm + Tp) /6 = (3 + 4*3 + 9) /6 = 4

For activity H,

The mean will be: : (To + 4*Tm + Tp) /6 = (6 + 4*6 + 12) /6 = 7

For activity I,

The mean will be: : (To + 4*Tm + Tp) /6 = (5 + 4*8 + 11) /6 = 7

For activity J,

The mean will be: : (To + 4*Tm + Tp) /6 = (3 + 4*3 + 9) /6 = 4

This mean can be applied to the network, to each of the activities.

Now, let’s find the variance for each of these activities.

2 = [(Tp - To) /6]2

For activity A:

2 = [(Tp - To) /6]2= 2 = [(8 - 6) /6]2= 0.11

For activity B:

2 = [(Tp - To) /6]2= 2 = [(7 - 3) /6]2= 0.44

For activity C:

2 = [(Tp - To) /6]2= 2 = [(10- 4) /6]2= 1

For activity D:

2 = [(Tp - To) /6]2= 2 = [(4 - 2) /6]2= 0.11

For activity E:

2 = [(Tp - To) /6]2= 2 = [(11 - 3) /6]2= 1.77

For activity F:

2 = [(Tp - To) /6]2= 2 = [(12 - 4) /6]2= 1.77

For activity G:

2 = [(Tp - To) /6]2= 2 = [(9 - 3) /6]2= 1

For activity H:

2 = [(Tp - To) /6]2= 2 = [(12 - 6) /6]2= 1

For activity I:

2 = [(Tp - To) /6]2= 2 = [(11 - 5) /6]2= 1

For activity J:

2 = [(Tp - To) /6]2= 2 = [(9 - 3) /6]2= 1

Now, for the third part of the PERT analysis. We need to find the critical path and the estimated time.

For this, we’ll need to find two values, Earliest Start Time (Es) and Latest Completion Time (Lc).

The process of determining the Es for all events is called a forward pass.

The process of determining the Lc for all events is called a backward pass.

Let’s get into the forward pass. For this first, we must create boxes at all nodes. We then divide these into two. The lower half of the box represents the earliest start time of the node, while the lower half represents the latest completion time.

Your network diagram should look something like this. 

For this, we’ll be using the formula, Esj = max (Esi + Dij)

Which when simplified, the earliest start time for the second node (head node), is the maximum of the combination of the earliest start time of the tail node and the duration between the two nodes.

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So, for node 1, the earliest start time is always zero.

For node 2,

Es2 = 0 (Es1) + 7(D1-2) = 7

Next node 3.

Es3 = 0(Es1) + 5(D1-3) = 5

Now, for node 4.

Es4 = 0(Es1) + 7(D1-4) = 7

Next, we have node 5.

Es5 = 7(Es2) + 3(D2-5) =10

Now for node 6.

Since there are two arcs connecting to the node, we need to choose the maximum of the two options available.

Es6 = 5(Es3) + 5(D3-6) = 10 or

Es6 = 7(Es4) + 8(D4-6) = 15

We must choose the maximum of the two, so we’ll select 15.

Next, we have node 7. Since there are two nodes connecting to it; we need to choose the maximum among the two options.

Es7 = 15(Es6) + 7((D6-7) = 22 or

Es7 = 7(Es4) + 4(D4-7) = 11

We’ll need to choose the maximum, and we’ll choose 22.

And finally, we’ll need to find the earliest start time for node 8.

Es8 = 10(Es5) + 7(D5-8) = 17 or

Es8 = 22(Es7) + 4(D7-8) = 26

Since we need to choose the maximum value, we’ll choose 26.

And like that, the forward pass is complete. Now, for the second part of the PERT Analysis.  Let’s take up the backward pass. For that, we will be using the following formula.

Lci = min(Lcj - Dij)

This, when put simply, means the latest completion time of the tail node is equal to the latest completion time of the head node minus the distance between the two.

Let’s start from the final node, number 8.

The Lc for this node will always be equal to its Es.
So, Lc8 = 26

Now let’s go to node 7. Since it’s an independent node, we’ll directly apply the formula. 

Lc7 = 26(Lc8) - 4(D7-8) = 22

Next up, let’s take a look at the latest completion time for node 6. Again, since it’s an independent node, we can directly apply the formula.

Lc6 = 22(Lc7) - 7(D6-7) = 15

Now, for node 5. 

Node 5 is an independent node. We’ll directly apply the formula here.

Lc5 = 26(Lc8) - 7(D5-8) = 19

The network diagram as part of the PERT Analysis will look like so. 

Now that we’re done with node 5, let’s go to node 4. 

Here, we can see that two arcs connect it to nodes 6 and 7. We need to choose the minimum latest completion time from these two nodes. 

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Applying the formula, 

Lc4 = 22(Lc7) - 4(D4-7) = 18 or

Lc4 = 15(Lc6) - 8(D4-6) = 7 

Since we have to choose the minimum, we’ll choose 7. 

Next, we have node 3. Since it’s an independent node with a single connection, we can directly apply the formula to it.

Lc3 = 15(Lc6) - 5(D3-6) = 10

Now for node 2. 

We can directly apply the formula to node 2. 

Lc2 = 19 (Lc5) - 3(D2-5) = 16

And finally, we have node 1. Since there are multiple nodes connected to node1, we’ll have to choose the minimum latest completion time.

Lc1 = 16(Lc2) - 7(D1-2) = 9 or

Lc1 = 10(Lc3) - 5(D1-3) = 5 or

Lc1 = 7(Lc4) - 7(D1-4) = 0

Since we need to choose the minimum, we’ll choose 0.

And that’s the backward pass, complete in the PERT Analysis. 

Now, for the ultimate step of the critical path method. To determine the critical path, there are three major criteria that need to be satisfied. 

Esi = Lci

Esj = Lcj

Esj - Esi = Lcj - Lci = Dij

From the diagram, we can see that nodes that satisfy the requirements are: 

1 - 4 - 6 - 7 - 8 or C - F - H - J

The estimated time is: 7 + 8 + 7 + 4 = 26 days. 

Advantages of Using a PERT Chart

1. Visualization: PERT charts provide a visual representation of project tasks, allowing for a clear understanding of project timelines, dependencies and critical paths.
2. Planning and scheduling: PERT charts help project managers to create a detailed project plan, including defining tasks, estimating task durations, and setting deadlines.
3. Risk Management: PERT charts allow project managers to identify and analyze potential risks, enabling them to develop mitigation strategies.
4. Resource Allocation: PERT charts help project managers to identify resource requirements and allocate resources effectively, reducing the risk of delays or overloading.
5. Improved communication: PERT charts can be shared with all stakeholders, helping to ensure clear communication of project plans and progress.
6. Adaptability: PERT charts can be easily updated to reflect changes in the project, ensuring that project plans remain relevant and accurate.

Disadvantages of Using PERT Chart

1. Complexity: PERT charts can be challenging for those needing project management experience.
2. Time-consuming: Creating a PERT chart can be time-consuming and requires significant effort.
3. Dependent on accurate information: PERT charts rely on precise information about task durations and dependencies, and errors in this information can significantly impact the chart's effectiveness.
4. Limited scope: PERT charts are limited in their scope and may not be suitable for larger, more complex projects.
5. Over-reliance: Over-reliance on PERT charts can lead to a lack of flexibility and an inability to respond to changes in the project.
6. Inflexibility: Once a PERT chart has been created, it can be difficult to make changes to the project plan, limiting the ability to respond to changes in project requirements.

PERT Chart vs Gantt Chart

PERT (Program Evaluation and Review Technique) and Gantt charts are both tools used in project management, but they serve different purposes:

PERT Charts

• Visualize task dependencies and their interrelatedness in a project
• Emphasize the sequence and timing of tasks
• Are helpful in planning and scheduling projects with multiple tasks and dependencies

Gantt Charts

• Visualize task progress over time
• Emphasize the duration of tasks and their start/end dates
• They are useful for monitoring progress and ensuring tasks are completed on time.

In summary, PERT charts focus on the relationships between tasks, while Gantt charts focus on the progress of jobs over time.

PERT Chart Example

A PERT (Program Evaluation Review Technique) chart is a project management tool used to schedule, organize, and coordinate tasks within a project. Here’s an example to illustrate how a PERT chart can be constructed and used:

Example: Website Development Project

Step-by-Step Process

1. Define the Tasks and Activities

• Task A: Requirement Gathering
• Task B: Design
• Task C: Development
• Task D: Testing
• Task E: Deployment
• Task F: Review and Feedback

2. Estimate Time for Each Task

• Task A: 1 week
• Task B: 2 weeks
• Task C: 3 weeks
• Task D: 1 week
• Task E: 1 week
• Task F: 0.5 week

3. Determine Task Dependencies

• Task A (Requirement Gathering) must be completed before Task B (Design) can start.
• Task B (Design) must be completed before Task C (Development) can start.
• Task C (Development) must be completed before Task D (Testing) can start.
• Task D (Testing) must be completed before Task E (Deployment) can start.
• Task E (Deployment) must be completed before Task F (Review and Feedback) can start.

4. Construct the PERT Chart

• The chart begins with Task A and proceeds sequentially based on dependencies.

Visual Representation

     A (1 week)

       |

       v

     B (2 weeks)

       |

       v

     C (3 weeks)

       |

       v

     D (1 week)

       |

       v

     E (1 week)

       |

       v

     F (0.5 week)

When to Use a PERT Chart?

1. Complex Projects With Interdependent Tasks

• Example: Software development projects where various phases (like design, coding, testing, and deployment) are interdependent.
• Reason: PERT charts help visualize and manage these dependencies, ensuring that each phase is completed in the correct order.

2. Projects With Uncertain Task Durations

• Example: Research and development projects where task durations are estimates rather than certainties.
• Reason: PERT charts allow for multiple time estimates (optimistic, pessimistic, and most likely), providing a range for project completion and helping manage uncertainty.

3. Large and Complex Projects

• Example: Construction projects involving multiple teams, contractors, and tasks.
• Reason: PERT charts break down the project into manageable tasks, helping to coordinate various elements and ensuring timely completion.

4. Projects Requiring Rigorous Planning and Scheduling

• Example: Event planning for large conferences or public events.
• Reason: PERT charts help map out all necessary activities, dependencies, and timelines, ensuring that nothing is overlooked and deadlines are met.

5. Projects With Critical Deadlines

• Example: Launching a new product to market by a specific date.
• Reason: PERT charts identify the critical path and key milestones, allowing project managers to focus on tasks directly impacting the deadline.

6. Projects Needing Efficient Resource Allocation

• Example: Manufacturing projects where resources (materials, labor, equipment) must be optimally allocated.
• Reason: PERT charts provide a clear view of when and where resources are needed, helping to prevent resource conflicts and bottlenecks.

7. Projects Requiring Ongoing Monitoring and Control

• Example: IT infrastructure upgrades that must be closely monitored to minimize downtime.
• Reason: PERT charts facilitate ongoing progress tracking against the plan, allowing for adjustments as needed to stay on schedule.

8. Projects Involving Multiple Stakeholders

• Example: Government projects involving multiple departments and agencies.
• Reason: PERT charts clearly represent the project timeline and dependencies, improving communication and coordination among stakeholders.

9. Educational and Training Purposes

• Example: Teaching project management concepts to students or new project managers.
• Reason: PERT charts offer a practical visual tool for understanding task dependencies, critical paths, and project scheduling.

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What’s Next?

Now that you know the PERT Analysis Method, you can go into some more complex concepts of project management. We recommend signing up for the PMP® Certification Training, which prepares you for your PMP certification exam. You will gain access to cheat sheets, study plans, and exam application support from experts.

FAQs

1. How is the Critical Path determined in a PERT Chart?

The Critical Path in a PERT chart is determined by identifying the longest sequence of dependent tasks that must be completed for the project to finish. This path has the most extended total duration, and any delay in these tasks will directly delay the project's completion. To find the Critical Path, list all possible paths from start to finish, calculate their durations, and the path with the longest duration is the Critical Path.

2. How is the Expected Time (TE) calculated in PERT?

The Expected Time (TE) in PERT is calculated using the formula:

TE=(O+4M+P)/6, where O is the optimistic time, M is the most likely time, and P is the pessimistic time. This weighted average accounts for variability and uncertainty in task durations, providing a more realistic estimate of the time required to complete a task.

3. Can PERT Charts be used for any type of project?

Yes, PERT charts can be used for any project, especially those with complex, interdependent tasks and uncertain durations. They are particularly beneficial for large-scale projects in fields like construction, software development, research and development, event planning, and any project requiring detailed planning and scheduling to manage dependencies and uncertainties effectively.