I have discussed many activity on node diagram (AON) methods; e.g. critical path method and critical chain method. Now is the time to discuss PERT . PERT stands for Program Evaluation and Review Technique (also known as Project Evaluation and Review Technique), is used to analyze the activity when there is no exact duration of activity is known. This technique was developed by the US Navy in 1957.

PERT is a statistical tool, and these days is widely used in project management for developing the project schedule for very large, complex, and one time projects where usually no historical records are available to be reviewed.

At first glimpse, you may think that PERT Diagram Method is similar to the critical path method; however, there are many differences between these two techniques, such as:

- Critical Path Method (CPM) is activity oriented, while PERT is event oriented
- Critical Path Method is used when you have definitive time estimate, while in PERT there is no certainty in time estimate
- In CPM diagram, activity is shown on the node, while in PERT Diagram, activity is shown on the arrow, and nodes represent the milestones. (
*Therefore, PERT diagrams are also known as Activity on Arrow (AOA) diagram*) - PERT Diagram can only have a “Finish to Start” type of relationship, while the CPM method can have any type of dependency; e.g. Start to Finish, Finish to Start, etc.
- In CPM diagram, rectangles represent the nodes. In PERT diagram, circles represent nodes

PERT methodology is used mainly on very large and complex project where time is a more important factor than the cost. PERT is mainly used in research type projects where you cannot predict the time duration of any activity accurately; therefore, you have to plan your work based on the milestones.

The critical path method is a deterministic model where you use a fixed time estimate for activities. CPM helps you run the project efficiently if the time estimates are definitive; however, if there is a variation in time estimate, it may affect your project badly. The solution to this drawback of CPM method is built into the PERT methodology, which helps you complete project successfully with less cost and time.

Since there is an uncertainty in the duration of an activity, you will use three estimates to determine the PERT estimate for an activity so that the uncertainty in the activity completion time can be reduced. These three estimates are as follows:

- Most Likely Estimate
- Optimistic Estimate
- Pessimistic Estimate

#### Most Likely Estimate (T_{m})

This is the time duration where there is a high probability of completing the task within the given time duration.

#### Optimistic Estimate (T_{o})

In this scenario, the estimate is determined considering all favorable conditions; i.e. it is a best case scenario. In other words, you can say that this is the shortest time in which you may complete the task.

#### Pessimistic Estimate (T_{p})

Here, estimate is determined considering all un-favorable conditions; i.e. worst case scenario. In other words, this is the longest time the activity might require to complete itself.

The formula to calculate the PERT is as follows:

PERT Estimate = (T_{o} + 4T_{m} + T_{p})/6

And,

Standard Deviation = (T_{p} – T_{o})/6

The two formulas above are very important from a PMP Exam point of view, as you may see few questions based on these formulas.

#### Benefits of PERT

Following are the few benefits of PERT:

- This technique is very useful where there is very little or no historical schedule data are available
- It makes planning easier
- It shows the critical path
- It reduces the uncertainty from the project; i.e. reduces the risk
- It gives a more accurate project completion date
- It helps management to optimize the resources

#### Limitations of PERT

Following are the few limitations of PERT:

- PERT requires subjective time analysis of activities, and accuracy of PERT estimate depends on these estimates. If people finding these estimates are either less experienced or biased, it might affect the schedule
- There is also difficulty in managing the critical path in the PERT network because it is not always guaranteed that the critical path will remain the critical path throughout the project completion
- Like Critical Path Method, this technique also assumes that all resources will be available to the project
- Updating, amending, and maintaining the PERT diagram can be time and cost consuming

This was all about the PERT methodology, and now let us see one example on PERT and Standard Deviation.

#### Question

For an activity, your team members told you that this activity is most likely to be completed in 20 days. However, in the worst case it might take 30 days, and if all conditions are favorable, it might be completed in 15 days.

Determine the PERT Time estimate, and the Standard Deviation for this activity.

#### Solution

To determine the PERT estimate, we need Optimistic Time, Pessimistic Time and Most Likely Time for the activity.

Question says that, it is most likely that the task can be completed in 20 days, hence:

Most Likely Time = 20 days

It further says that in the worst case it may take 30 days, hence:

Pessimistic Time = 30 days

It also says that if all conditions are favorable, it will take 15 days to complete the task. Hence:

Optimistic Time = 15 days

Now,

PERT Estimate = [Optimistic Time + 4X(Most Likely Time) + Pessimistic Time]/6

= [15 + 4X20 + 30]/6

= [15 + 80 + 30]/6

= 125/6

= 20.83 days

Hence, PERT estimate for this activity is 20.83 days.

Standard Deviation = (Pessimistic Time – Optimistic Optimistic)/6

= (30 – 15)/6

= 15/6

= 2.5

Hence, the Standard Deviation is 2.5 days.

Here this blog post about the PERT is completed; I hope you would have enjoyed reading it.

If you have any thoughts, you are welcome to add them in comments section.

Faiaslg says

Bro,

thanks for your explanation.

I just would to correct that 4×20=80, Not 60

Many Thanks.

Fahad Usmani says

Corrected.

Fahad Usmani says

Corrected.

Hotaki says

SA Fahad,

I took my exam yesterday, and did really well. I prepared for the exam well by not only reading Kim Fieldman’s and other book, but also reading and clarify many topics from Pmstudycircle.com. Your journals were brief, clear, and with good examples. In my opinion, you should write a book …

Thank you,

Hotaki

Fahad Usmani says

WAS Hotaki,

Thanks for your comments and I am happy that my blog helped you pass the exam.

I have already written an ebook on pmp practice questions, and second ebook is on its way…

Fahad

Hotaki says

Okay, keep up the great work!

Shalini G says

please share eBook name

Fahad Usmani says

Here is the link for eBook:

http://pmstudycircle.com/pmp-question-bank/

sunshine says

thank you so much you explain everything so well. Could you do a simple calculation on decision trees as they pertain to the EMV

Fahad Usmani says

Hello Sunshine,

soon you will see a post on Earn Value Management and Decision Tree.

Gokhan says

Hi

I am currently tyring to get ready for the PMP exam and following you regularly. You are helping out us a lot throughout this journey just I would like to ask you that how standart variation can be used in a project? Does it mean that in your example, this job can be finished between 18.33 days and 23.33 days? And can I use this numbers as early start and Late finish in AON?

Fahad Usmani says

Hello Gokhan,

~~Early start and late finish dates are determined the same way as you do in Critical Path Method.~~Tauseef Qureshey says

Please explain how ES and EF dates can be find out in PERT, need example to calculate.

Thank you very much

Fahad Usmani says

In PERT you have most likely, optimistic and pessimistic estimate. Early start, early finish, etc are used in critical path.

Tauseef Qureshey says

When I can use Triangular distribution formula and when I can use Beta distribution?

Fahad Usmani says

In triangular distribution you use three parameters: minimum, mode (most likely), and maximum. PERT is based on the triangular distribution.

In beta distribution you get a curved shape. You can say that the triangular distribution is a simpler form of beta distribution.

Som says

Traditional PERT is based on Beta Distribution. However, triangular distribution are also used. If not informed specifically in the question, I’ll say use beta distribution formula, not triangular distribution.

Fahad Usmani says

Triangular Distribution is simpler form of beta distribution.

Tauseef Qureshey says

I did appeared in the PMP exam in July 2013 but unfortunately could not passed, can I take a date for my exam in 2015 year, am I still eligible to write an exam. I am already been doing preparation for PMP exam with the help of your exam preparing material.

Waiting for reply

Thank you very much

Tauseef Qureshey

Fahad Usmani says

Since you attempted the exam on July 2013, it is now more than one year; therefore, you eligibility is expired.

So, if you want to sit for the exam now, you have to re-apply for it.

swapna says

Hi Fahad,

In PERT or AOA,which relationship is used.. Is it FInish to start or Start to finish.and please explain why..

Fahad Usmani says

It is Finish to Start because PERT is an event oriented network diagram.

Tauseef Qureshey says

As per your notes “PERT Diagram can only have a “Start to Finish” type of relationship, while the CPM method can have any type of dependency; e.g. Start to Finish, Finish to Start, etc.

You replied to SWAPNA ” It is Finish to Start because PERT is an event oriented network diagram

Which one is correct your notes or your reply to SWAPNA, please explain. Thanks

Fahad Usmani says

This was an error, and I have corrected it. In PERT you will only have finish to start type of relationship.

Tauseef Qureshey says

1. Can I use Bottom-up Estimate for calculating duration of an activity?

2. In your above notes standard deviation that is 2.5 where we use it, if iam not wrong in finding Early start that could be 18.33 and late finish could be 23.33 is that ok, or it has some other means, please let me know.

Fahad Usmani says

For the project duration, you can go for the bottom up estimation, not for an activity.

It should be activity start date between 18.33 to 23.33

Sameh says

Fahed

As per PMP book , we can use bottom up estimation in the calculation of activity resources or activity cost , how we can use it for the project duration ?

Fahad Usmani says

You will add all activities duration to get the total project duration.

Kate says

Hi there, so I have a project about PERT. The question is whats the most likely activity time for x activity (nearest day) be adjusted to if the probability of any path through the network being completed in 69 days must not be less than 0.94?

Tauseef Qureshey says

Can we find out Variance in Beta distribution or triangular distribution just by taking Square of St deviation?

Thanks

Fahad Usmani says

Variance is the spread between many data sets, not application for a single activity.