Today, we will discuss the **PERT (Program Evaluation and Review Technique), PERT Formula, PERT Chart, Technique, and its example**.

Schedule baseline and cost baseline are the two important performance measurements for a project. The latter helps you assess the project’s cost performance, while the former involves the duration.

Clients are concerned about the schedule because it can delay the project and affect their business. Project managers can develop schedules using PERT Chart, CPM diagram, or Gantt chart.

Developing a schedule is a complex task requiring a thorough knowledge of schedule network diagramming techniques and experience.

Diagramming techniques include:

- Critical Path Method
- Critical Chain Method
- Program Evaluation and Review Technique

I have discussed the critical path and chain methods in other blog posts. We will discuss the Program Evaluation and Review Technique (PERT) here.

## PERT: Definition, Meaning & Example

Definition: PERT stands for Program (or Project) Evaluation and Review Technique is a diagramming technique to develop a project network diagram. You can use this technique when you cannot estimate the activity duration with certainty.

The U.S. Navy developed this technique in 1957 to successfully plan the schedule for the Polaris Project.

The PERT helps you find a duration estimate of activities when there are uncertainties, which is why it is called a probabilistic technique.

It is a statistical tool mainly used in research projects where you cannot predict the activity duration and must plan your work based on milestones. This term means a significant point or event in a project, like a Kick-off meeting.

Let’s consider the network diagram (PERT Chart) below to distinguish milestones and activities quickly. Activities are indicated by the arrows, while the milestones are nodal points in the circles.

The PERT helps you develop the schedule for large, complex, and one-time projects when no records are available. You can do it using software like Scitor Project Scheduler PS8 and SPERT.

The PERT is a three-point estimation technique. Other project estimation techniques are called analogous, parametric, and bottom-up.

Estimating helps to make important project decisions, such as whether to proceed with the project. Afterward, it helps you develop project baselines.

Once you develop the project estimation, you can refine it as you progress and gain more information.

That said, the project team must be professional, as there are instances where the final costs or schedules far exceed the original estimate. Two such examples of incorrect estimation are as follows:

- In 1995, the Denver International Airport opened 16 months late, an estimated USD 2.7 billion over budget!
- In 1973, the Sydney Opera House, estimated initially at AU$ 7 million, was completed ten years later, and the final cost was AU$ 102 million.

So, when you hear a project is late, ask how the team came up with the estimate in the first place.

### Three-Point Estimate Technique (Using PERT Formula)

This uses three different estimates to arrive at a final estimate. A weighted average reduces bias and uncertainty from the estimation and improves accuracy.

These three estimates are:

- Most Likely Estimate
- Optimistic Estimate
- Pessimistic Estimate

The PERT technique is based on beta distribution, a probability distribution suitable for factoring uncertainties in estimating.

A brief look at the beta probability distribution shows how the probabilities for most likely, optimistic, and pessimistic estimates are assigned.

The most likely estimate takes the highest probability (about 0.5 or 50%), while the pessimistic and optimistic take about 0.1 or 10%. Since we are dealing with time, the shorter duration represents optimism while the longer represents pessimism.

Another insight from the beta distribution is a skew (flattening to the right), which tells us how (in most cases) our estimate is tilted towards optimism rather than the pessimistic end.

This distribution captures the reality of estimation.

#### The PERT Formula

The PERT formula to calculate the PERT estimate is as follows:

PERT Estimate = (Tp + 4Tm + To) / 6

and

Standard Deviation SD = (Tp – To) / 6 while

Variance is the square of the SD.

Where:

**Most Likely Estimate (Tm):** The chance of completing an activity is highest within this duration.

**Optimistic Estimate (To):** Here is a best-case scenario, considering all favorable conditions. This is the shortest duration to complete the task.

**Pessimistic Estimate (Tp):** This is a worst-case scenario. Here, you determine the estimate by considering all unfavorable conditions and the longest time the activity may take to complete.

The PERT estimate removes uncertainties around the duration estimate by providing three task duration possibilities.

PERT is a reasonable estimation technique, applicable when meeting a scheduled date is important.

It provides a better estimate by considering all possible scenarios.

Imagine a project manager asked you to estimate for the pipe-laying project. If he says it will take two days without looking at pessimistic scenarios, what happens when there is a heavy downpour? As a result, the team was hindered for a day, delaying delivery.

Giving possible ranges of the scenario does not change the project duration but provides an opportunity to make intelligent decisions, such as:

- What may cause pessimism?
- What can enhance the optimistic scenarios?
- How do we reduce the chances of pessimistic duration?

PERT is a planning tool for estimating project completion time.

It is also useful in risk analysis, where it uses three estimates. In addition, it helps the Monte Carlo simulation to generate a statistical analysis of the probability of completing the project under budget or within schedule.

The PERT provides a quantitative method of considering uncertainty or risk.

### PERT Vs CPM

The following are a few differences between PERT and the critical path method:

- CPM is activity-oriented, while PERT is event-oriented.
- Duration estimates are definitive in CPM but not in PERT. In other words, CPM uses deterministic values, and PERT uses probabilistic values.
- The CPM diagram shows the activity on the node while this is shown on the arrow in the PERT chart, and nodes represent the milestones. Therefore, many experts call the PERT result an Activity on Arrow (AOA) diagram.
- The PERT chart has a “Finish to Start” relationship, while the CPM diagram can have any dependency: Start to Finish, Finish to Start, etc.
- On a CPM diagram, rectangles represent the nodes, while circles represent nodes on the PERT chart.

The critical path method is a deterministic model because the activities have fixed estimates. Therefore, any delay in an activity’s duration estimate will affect your schedule. The PERT counteracts this drawback to help you build a schedule when a definitive time estimate is unavailable.

### Benefits of the PERT

- Help in planning.
- Schedule uncertainty reduced.
- Useful when few or no records are available.
- The completion date is more accurate.
- Helps optimize resources.

### Limitations of the PERT

- The PERT requires a subjective analysis of activities, and the accuracy depends on these estimates. In addition, team members doing the estimation can affect the schedule if they are inexperienced or biased.
- Managing the critical path is difficult with the PERT because it might change before the project ends.
- This is an optimistic model that assumes resources will be available.
- Updating, amending, and maintaining the PERT diagram can be time- and cost-consuming.

Now, let us look at a PERT example and Standard Deviation.

### PERT Example

Your team members tell you that an activity you are working on is most likely to be completed in 20 days. However, it takes 30 days in the worst case, and if all conditions are favorable, you can complete it in 15.

Determine the PERT time estimate for this activity.

Solution:

We need the activity’s Optimistic Time, Pessimistic Time, and Most Likely Time to determine the PERT estimate.

The question says it is likely that you can complete the task in 20 days; hence the Most Likely Time = 20 days.

It also says that in the worst case, it may take 30 days; hence the Pessimistic Time = 30 days.

Finally, it says that if all conditions are favorable, it will take 15 days to complete the task; hence the Optimistic Time = 15 days.

Now, we can use the PERT formula.

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

= [15 + 4*20 + 30] / 6 = [15 + 80 + 30] / 6 = 125 / 6 = 20.83 days

Hence, the PERT estimate for this activity is 20.83 days.

Let’s look at the confidence of these estimates. If it is high, the spread between the min and max will be less, and S.D. will be less.

SD = (Tp – To) / 6

= (30-15)/6

= 2.5

Imagine that the pessimistic estimate is 60 days. This implies a low level of confidence, a higher spread, and that the deviation from the mean (PERT estimate) will be more.

SD = (Tp – To) / 6

= (60-15)/6

= 7.5

### Statistical PERT (SPERT)

The statistical approach shows stakeholders the risk associated with the estimate.

It involves following steps:

- Enter a three-point estimate of optimistic, most likely, and pessimistic to generate a probability distribution. The optimistic and pessimistic are the two extremes of the distribution. They are possible but improbable as their chances of occurrence are very slim. The most likely outcome is the mode. You remember the mode of distribution being the largest frequency outcome.
- Indicate how likely your most likely estimate is or its confidence level. SPERT, a statistical PERT tool, provides six levels, as shown below:

You can use Microsoft Excel to evaluate the probability of your estimate.

NORM.DIST (x, Mean, SD, TRUE)

The mean is from our PERT formula.

SD for SPERT is simply = (Tp – To)*p

Where p is the assigned probability from your confidence level.

Since we are dealing with the PERT estimates, mostly with high uncertainties and limited historical data, the assigned probability (from the above table) could be 42%.

SPERT SD= (30-15)* 42/100

= 6.3 days

Having these three variables (x, mean, and SD), we open MS Excel and run the simulation.

Recall the mean is the PERT formula estimate = 20.83 days

On an Excel cell type:

= NORM.DIST (x, mean, SD, TRUE) and press enter

You will get the risk-adjusted probability, which reflects our confidence level.

For 15 days estimate, the certainty is:

=NORM.DIST(15,20.83,6.3, TRUE) and press Enter

= 18%

For 20 days estimate, the certainty is:

= NORM.DIST (20,20.83,6.3, TRUE) and press Enter

=44.76%

Do this for 30 days and others, as shown in the table below:

So, if you want to increase your chance of completing the task to a 96% confidence level, the duration will be 32 days.

But if the sponsor says the PERT estimate is high and insists on 18 days, the SPERT tool helps you calculate the probability of meeting it (32.66%). Without the above computations, if you agree on 18 days as the duration for the above exercise, a sponsor may be impressed, but the probability of success reduces to 32.66%.

So, the Statistical PERT (SPERT) does two things; it helps align stakeholder expectations and helps make informed estimate decisions.

To remove bias from the three-point estimates, you may use the Delphi Technique.

### Summary

The PERT (Program Evaluation and Review Technique) is a network diagraming technique for projects with high uncertainties. This tool helps project managers develop a sound schedule when precise activity duration is not available. In the PERT chart, nodes are milestones, and activities are on arrows.

The success of the PERT depends on the experience of the professionals. The project manager’s job is to remove the biases from the estimation, as they can affect PERT estimation and schedule.

This topic is important from a PMP exam point of view; therefore, understand it well.

I am Mohammad Fahad Usmani, B.E. PMP, PMI-RMP. I have been blogging on project management topics since 2011. To date, thousands of professionals have passed the PMP exam using my resources.

hi i have a question

Sure Joe.

I got answer for te as integer type.I convert into non integer .for example 4.5=5 .whether it is correct or not?

If you must change to non decimal, as per my understanding you should go for 5. If an activity is completing in 4.5 days, you can not say it as 4.0 because you may be in trouble while competing the activity.

However, 5 is safe.

Very Helpful.. Thanks !

You are welcome…

Bro

I want to know about this PERT Estimate = (To + 4Tm + Tp) / 6 formula

Why we take “4tm” in the formula.

Can you evaluate bro

Please

This is weighted average, that is why we have given more weightage to optimistic time. Derivation of this formula is out of scope of the PMP exam.

Yes, you can but it depends on the project and deliverable. Many times milestones cannot be a deliverable but a point, specially in a research project.

Hi Fahad,

Milestone vs Deliverable:

A Milestone includes 1 or more Deliverable, a Milestone cannot be delivered in itself to the Client, as it is only a point in time on the schedule with zero duration, while the Deliverable is a product that will require delivery to the Client.

Therefore, I would suggest using Deliverable rather than Milestone on the Node for PERT.

Example: prelim design completion is a Milestone while prelim design report, plan etc are deliverables.

Your Thoughts

Can you show me the calculation?

Hi Fahad,

We have a question where we need to calculate the most optimistic time. The most likely time is given as 20, most pessimistic is 60, and expected is 10. This yields a negative answer for the most optimistic duration (-80). Is that possible and what does that mean?

Hello Fahad,

Just wanted to thank you for your clear and easy to understand comments helping all the interested parties, through your blogs.

Keep on the good job, its much appreciated!

AA

Thank you AA for your visit and leaving comment.

How do we calculate variance and probability?

These are mathematical concepts and cannot be explained here.

Hi sir,

What does Primavera and MS Project uses? PERT or CPM?

I dont have experience in either of two software.

Hi

I am giving exam this month end

what different types of question will come on PERT ,CCM, and CPM or infact on Time management chapter .

Hello Savita, I have written detailed blog posts on CCM and CPM. Please visit the following page to find such blog posts and study them.

https://pmstudycircle.com/study-notes/

I head Activity on Node method is not allowed in PERT, Only activity on arrow works

IS it true, if yes why and if no then also y?

PERT diagram are based on milestones that is why they are called activity on arrow diagram.

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

Thanks

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

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?

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.

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

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 ?

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

Bro

I want to know about this PERT Estimate = (To + 4Tm + Tp) / 6 formula

Why we take “4tm” in the formula.

Can you evaluate bro

Please.

Hi Fahad,

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

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

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

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

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

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.

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

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.

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.

Triangular Distribution is simpler form of beta distribution.

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?

Hello Gokhan,

~~Early start and late finish dates are determined the same way as you do in Critical Path Method.~~Please explain how ES and EF dates can be find out in PERT, need example to calculate.

Thank you very much

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

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

Hello Sunshine,

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

please share eBook name

Here is the link for eBook:

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

Okay, keep up the great work!

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

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

Bro,

thanks for your explanation.

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

Many Thanks.

Corrected.

Corrected.