pert program evaluation and review technique

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.

pert three points estimate

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


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

Variance is the square of the SD.


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.


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.


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.

statistical pert spert

It involves following steps:

  1. 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.
  2. Indicate how likely your most likely estimate is or its confidence level. SPERT, a statistical PERT tool, provides six levels, as shown below:
statistical pert spert table

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


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


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

pert table 2

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. 


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.

Fahad Usmani, PMP

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.