Critical Path, Criticality Analysis, and Criticality Index

Imagine the following scenario. You are in charge of managing a big match in a stadium. The venue can hold over 100,000 people. The audience is as passionate about watching, as their favorite players are about playing. Any untoward incident can create problems. You want to have the security, monitoring, and all other aspects of management under control. You want to have a quick response time for any incident, and you want to quickly spot and manage any disruption right away. But, your resources and budget are limited!

Will you go for multiple exit routes in the stadium or just a few?

Of course, you will likely prefer few exit routes. With fewer exits, you can have better management, as well as control, over the event.

Project management, encompassing schedule and associated risks, is quite similar. Just as the event manager would like to have minimal exit routes, a project manager wants to minimize ways the project’s end date could be impacted. If there are tasks (or activities) within the project that could be problematic, the PM would like to have them spotted quickly, analyzed for risks, and monitored.

This leads us to the topic of Critical Path and Critical Path Method (CPM).

Critical Path and Critical Path Method

As documented by Project Management Institute (PMI), the critical path is defined as “the sequence of activities that represents the longest path through a project, which determines the shortest possible duration.”

We can breakdown the above statement into two shorter ones:

• A critical path is the longest path through a project.
• A critical path is the shortest possible duration within which a project will be completed.

Although the two short statements sound contradictory, they are actually informing complementary concepts. Let’s take a look at an example to better understand. Below, we have a schedule network diagram, shown with activities (or tasks) and their durations in days and milestones, as well as dependencies among the activities and milestones. Going forward, in this article, the words “tasks” and “activities” are interchangeably used.

Note the paths in the above network diagram.

• Path 1: Start – A – B – Finish = 14 days
• Path 2: Start – C – B – Finish = 10 days
• Path 3: Start – C – D – Finish = 8 days
• Path 4: Start – E – D – Finish = 10 days
• Path 5: Start – E – F – Finish = 8 days

Obviously, the longest path is “Start – A – B – Finish.” Hence, it is the critical path, as shown in below figure. This satisfies our first statement in the definition for critical path (the longest path in a project’s network diagram).

But, what about the second statement in our definition (the shortest possible duration within which the project can be completed)? Let’s see.

Path 3, “Start – C -D – Finish,” has a length of 8 days. It is definitely shorter than Path 1, our critical path, but it is not the critical path because the milestone “Finish” is dependent on Task-D, as well as Task-B. The project can only be finished when both Task-B and Task-D are completed. So, Path 3 can’t be the critical path because it is not the shortest possible duration within which the project can be completed.

Consider that Task-B is on two paths—both Path 1 and Path 2. That said, Path 2, with a length of ten days, cannot be the critical path either, because the start of Task-B is dependent on both Task-C, as well as Task-A.

The shortest possible duration within which our small project can be completed is again “Start – A – B – Finish.” Notice that the second part in the definition of critical path complements the first.

In this case, we have only one critical path, “Start – A – B – Finish.” The activities A and B are called critical path activities, because they are on the critical path. The rest of the activities (C, D, E and F) are non-critical path activities.

What we just walked through, is known as critical path analysis (CPA), and we employed critical path method (CPM) to look at the data. CPM is a scheduling method defined by PMI as “a method used to estimate the minimum project duration and determine the amount of schedule flexibility on the logical network paths within the schedule model.”

So, critical path not only estimates the minimum project duration, but also the schedule flexibility of the network paths within the schedule model. The schedule flexibility part is determined by available floats, which we will see shortly.

At this stage, you might be wondering if there can be multiple critical paths? The answer is yes. There can be many paths which are longest in the network diagram and are also of same length. That said, let’s analyze the implications of having multiple critical paths.

Critical Paths and Risks

As critical path is the longest path, if you delay any task on the critical path, it will push the end date of the project out.

Remember the illustration at the beginning of this article?  The more exit routes in the stadium, the harder management, monitoring, and control becomes.

Similarly, if there are many critical paths for a project, there will be many ways the project schedule can be delayed. In such a case, you have more risks from a schedule perspective. Additionally, with many critical paths, it becomes harder to monitor the resulting large number of tasks.

It is fair to conclude that the more critical paths, the more risk the project will have.

But, there is also another way to look at the critical path. A number of project-portfolio management software users refer to this definition, which says, “Critical path is that network path in which the total float of activities can be less than or equal to zero.”

To understand this definition, we need to understand a concept called “total float” or “total slack.”

Total Float (Total Slack)

The definition of total float (TF), as documented by PMI is, “The amount of time that a schedule activity can be delayed without delaying the project finish date or violating a schedule constraint.”

Going back to our network diagram above, can you tell what the TF values will be for our critical path activities?

They will have a TF of zero because if you delay a critical task by one day, it will push the end date of the project or delay the project. Note that total float can also be negative, if it violates a schedule constraint.

What about the non-critical tasks? Let’s take a look at Task-C and calculate total float. This task is on Path 2, “Start – C – B – Finish,” which has a length of ten days. It is also on Path 3, “Start – C – D – Finish,” which has a length of eight days. If you consider Path 2, you delay Task-C by four days, whereas, if you consider Path 3, you delay by six days. Which is the best option? Of course, four days delay is better than six. We conclude that total float for Task-C is four days. Note that you can calculate TF values for non-critical tasks, too.

Using Microsoft Project 2016, you can calculate the critical path, critical tasks, and total float (slack) in a matter of minutes. This is shown in the below figure.

The start and finish milestones are represented with filled black diamonds. Each task is represented with a horizontal bar. Critical and non-critical tasks are highlighted in red and blue colors, respectively. The duration of a task is inside the bar and the total float value is noted next to the bar.

Criticality Analysis

Earlier, I pointed out that the more critical paths, the more risk (schedule-wise) for the project, but what about the individual schedule activities, including near-critical and non-critical activities? Do they pose risks to the project?

Duration estimates for activities (or work packages) are uncertain in nature. When you give an estimate, of course, you can’t say it is 100% accurate. These uncertainties can lead to individual project schedule risks, and individual tasks can also pose schedule risks to a project.

During quantitative risk analysis, we use a simulation such as the Monte Carlo simulation, and with the help of software tools, check for the combined effect of individual project risks on the overall project objectives. The overall objectives can be looked at from schedule perspective, cost perspective, and/or any other point of view. As we are talking of critical and non-critical activities, let’s focus on schedule risks due to estimation uncertainties or variations in duration estimates. For schedule risks, we take the below inputs for a simulation.

• Schedule network diagram
• Activity (or work package) duration estimates
• Probability distribution of duration estimates (i.e. triangular, beta, uniform, etc.)

The output of the Monte Carlo simulation is a (quantitative) risk model. On this risk model, we can perform “Criticality Analysis.” Criticality analysis determines which elements of the risk model, i.e., critical or non-critical activities, have the greatest impact on a project’s critical path(s).

The criticality analysis is represented many times with a “Criticality Path Report.” In this report, you have the criticality index values for the activities.

Criticality Index

The criticality index is calculated after criticality analysis is performed. The criticality index informs how often a particular task or activity was on the critical path during criticality analysis.

This index is expressed as a percentage number. The higher the percentage value, the higher chance for the task to be on the critical path, and therefore a higher chance of delaying the project. That said, the reverse is also true. Tasks with zero percent or low critical index values, are less likely to delay the project.

We already know that critical tasks have zero or negative total float. While calculating the criticality index for a task, the total float of the task is taken into consideration. Tasks with high criticality index values are more likely to be on the critical path. The critical path tasks will usually have criticality index values as 99% or 100%.

When you monitor tasks with high criticality index values, your project is more likely meet the schedule objective and finish on time. With criticality analysis, you can focus on tasks with high criticality index values during risk response planning (done as part of a “Plan Risk Response” process). This often follows quantitative risk analysis (done as part of a “Perform Quantitative Risk Analysis” process).

A sample criticality analysis report with criticality index value is shown in the below figure. This diagrammatic representation is known as “Tornado Diagram,” as the shape is that of a tornado. This is drawn with Primavera Risk Analysis by taking the Microsoft Project Plan (.mpp) file created with the tasks from our schedule network diagram example.

As shown above, the tasks on the critical path have criticality index values of 99%. In other words, Task-A and Task-B have a high chance to impact the project’s finish date. For a complex project with many network paths and activities, you will have many such activities, which will need to be monitored carefully.

As an aspiring Project Management Professional (PMP) or Risk Management Professional (RMP), these are important concepts to know. You can expect situational and scenario questions, as well as questions with graphs for analysis, in your exams.

References:

[1] I Want To Be A RMP: The Plain and Simple Way To Be A RMP, by Satya Narayan Dash
[2] Project Management Body of Knowledge (PMBOK) Guide, 6th Edition, by Project Management Institute (PMI)
[3] Practice Standard for Project Risk Management, by Project Management Institute (PMI)
[4] I Want To Be A PMP: The Plain and Simple Way To Be A PMP, by Satya Narayan Dash

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