The Risk Breakdown Structure (RBS) is mostly used in Risk Management, whereas the Work Breakdown Structure (WBS) is in Scope Management. But then they can be combined to provide you better value from both the breakdown structures.
"RBS can be used in combination with WBS to identify potential sources of risk. For example, the XYZ work package of WBS can be technical, environmental and political risk categories."
In my interactions with management practitioners, when I inform them, surprised looks come-up with certain questions:
How can RBS be used with a WBS?
What are the advantages in having a combined structure and analysis?
In this article, we will explore just that!
Let’s start with a sample WBS.
A Sample Work Breakdown Structure (WBS)
I’ll reuse another WBS from one of my previous articles. This is depicted below. I’ve modified the WBS from the linked article a bit.
As shown above, it’s only up-to Level 2 (L2). The reason is that I’m not going to identify the risks at the lowest level, but at a higher level. This way, I can refine more as I build the final-cut of RBS. This will be based on the areas identified in the WBS.
Also, you’d have noticed that I’ve added another level (L0), which is the overall “Book Project”. Interpreting the above figure, you can say:
At Level – 0, we have the Book Project. I’ve added L0 so that the WBS is synchronized in its structure with the RBS.
At Level – 1, we have, Book – Risk Management.
At Level – 2, we have Manuscript, Write Book, Edit Book, Publish Book.
Next, let’s take a look at the sample RBS.
A Sample Risk Breakdown Structure (RBS)
For the sample RBS, I’ll use it from my previous article (with modifications for the book) as well and I’ll keep the structure at a higher-level (L2).
As shown above:
The Book Project is at the highest level, which is Level - 0 of the RBS.
Under it, at Level – 1 of the RBS, there is Book – Risk Management.
Next, at Level – 2 of the RBS, we have multiple risks such as Writer’s Risk (e.g., writer’s block), Hosting Risk (e.g., online hosting problems), Editing Risk (e.g., wrong interpretation of meaning), Publishing Risk (e.g., publisher being unavailable).
Finally, we are going to combine the RBS with the WBS, which will help us in identification of risks.
Combined RBS and WBS
While combining, I’ll keep the WBS in the X-axis (horizontal) and the RBS in the Y-axis (vertical).
Let’s understand and interpret the above figure:
The risks are identified by considering the L2 of RBS and L2 of WBS.
In the lowest row of the table shown with tick marks, the “Writer’s Risk” category of the RBS is associated with “Write Book” and “Edit Book” of the WBS.It means one can have a cluster of writer’s risks while going for the deliverables of Write Book and Edit Book.
Taking another example, in the topmost row of the table with tick marks, the “Publishing Risk” category is associated with “Manuscript” and “Publish Book” deliverables.
Hence, considering the second bullet point above, one can say that a number of writer's risks (from the RBS) can be found while writing the book and editing the book (from the WBS). Similarly, one can say a number of publishing risks can be found during the development of manuscript and of course, while publishing the book.
Conclusion
When you combine the RBS and analyze the risk categories with the WBS, you can find the areas when the project is most likely to exhibit the most risk.
As demonstrated in the final figure, one can quickly find the areas of the project, where you can find various categories of risk. In turn, it helps to build a more refined Risk Register.
A breakdown structure is what the name tells. It's basically a hierarchical decomposition and each lower level gives more details or information. One of the best-known breakdown structures is the Work Breakdown Structure (WBS). In this article, however, we will know more on the Risk Breakdown Structure (RBS). The Standard for Risk Management and the PMBOK 6th edition use RBS as a tool, whereas in the PMBOK 7th edition, it's an artifact and kept under Model-Methods-Artifacts (MMAs).
RBS is not a much-understood concept, but very useful in real-world risk management. But before you proceed further, I'll suggest that you read this article on WBS, to understand breakdown structure more.
Other Breakdown Structures in Management
Other than Risk Breakdown Structure, here are some of the breakdown structures that you need to know in Project Management, Program Management and Agile management. This will be useful and helpful in your professional work.
Product Breakdown Structure (RBS): A hierarchical chart showing a product's components and deliverables. It's mainly used in Scope Management.
Organizational Breakdown Structure (OBS): A hierarchical chart showing the project organization. It’s mainly used in Resource Management.
Resource Breakdown Structure (ReBS): A hierarchical chart showing the resources by category and type. Examples of categories can be personnel, material, equipment etc. Examples of type can be role 1 (engineer), role 2 (plumber), which can be further broken down into levels (Level 1 engineer). It’s also mainly used in Resource Management.
Story Breakdown Structure (SBS): A hierarchical chart showing the breaking down of epics into stories and finally into tasks. This is my term and I use it in an Agile context. You can learn more about it in this article on stories.
Initial Top Points
I've used ReBS to distinguish between the Risk Breakdown Structure (RiBS). In this article, I'll use RBS acronym for risk breakdown structure.
The Project Management Institute (PMI) gives a simple definition for the Risk Breakdown Structure (RBS):
"A hierarchical representation of potential sources of risk."
As it’s a representation of potential sources of risk, it’s widely used in risk identification, or specifically in the Identify Risks process.
Following are the top points about RBS at this stage:
Can be generic or specific. Generic ones are used across projects, whereas specific ones are developed for a specific project.
Can be tailored, which is an extension of the previous point.
Can be broken down to any level, from Level 0 to Level N.
When broken down, each low level will give more information.
Levels in an RBS
As noted earlier, you breakdown into any levels while building an RBS. But you have to be careful. Don’t make it too fine-grained and hence, difficult to manage.
Following are the levels in an RBS:
Level – 0 (L0): This is the project level, just like the WBS. After all, the project itself will have all potential sources of risk. But do note, not all project management literature considers L1 to be the project level.
Level – 1 (L1): Here we breakdown into the higher-level categorization of risks such as Technical, Political, Environmental, External, among others.
Level – 2 (L2): The one level below L1 and it has more information with respect to one of the previous categories. For example, considering Technical, it can be broken down into Scope, Requirements, Technology.
Level – 3 (L3): This is further refinement of the previous level. For example, consider Scope, it be “Scope definition”, “Scope change” etc.
While breaking down, I’d generally suggest that you don’t go beyond L3, unless really needed.
Progressive Elaboration and Breaking of RBS
As is the used norm, a hierarchical chart is generally progressively elaborated. I hope you have read the previous linked article on WBS. I'll slightly change the definition of progressive elaboration in the context of RBS.
"Progressive elaboration is the iterative process of increasing the level of detail in an RBS as more information is known about the project."
The definition is important, because building an RBS is not a one-time activity, but it’s developed and iterated over the project’s life cycle. If one finds more information and/or more categories of risks, then it should be added to the RBS.
In other words, during risk management strategy and planning, the first-cut of the RBS is available. However, if it's a multi-phase project or as you progress with respect to the project, the RBS will be updated.
An Example
To understand more clearly, let’s take an example. A sample RBS (reference taken from PMI) is shown below.
Interpreting the above figure, one can say the followings:
Level – 0: The highest level and it’s the level of the project.
Level – 1: You have categories such as Technical, Management, Commercial etc.
Level – 2: A further breakdown of each at Level – 1. For example, technical has been broken down into 'Scope', 'Requirement'.
Level – 3: L2 is further broken down with more information. For example, scope has been broken down to ‘Scope definition’, ‘Scope change’.
Another important point to note in RBS is that every element in the RBS is associated with the RBS Identifier (RBS ID), which uniquely identifies the elements. For example:
1. Technical Risk
1.1 Scope
1.1.1 Scope definition
1.1.2 Scope change
1.2 Requirements
1.2.1 Requirement definition
1.2.2 Requirement change
2. Envionmental Risk
2.1 Market
2.2 Industry changes
This is very much like the WBS IDs, where each element in the WBS is uniquely identified with the IDs such as 1.1, 1.2.2.
By this time, you would have realized that an RBS can not only be represented in a chart, but it can also be tree structure, tabular structure. The one shown above with RBS IDs is a tree structure, whereas the table shown before, depicts the RBS in a tabular structure.
Final Words – Usage of RBS
Finally, as we reach this basic article, some more final key points with respect to the Risk Breakdown Structure. These are important to know!
The lowest level of RBS (available risk categories) can be used as a prompt-list to identify individual project risks.
Along with this prompt-list, you can apply the brainstorming to get more information with respect to risks.
RBS can be used in combination with WBS to identify potential sources of risk. For example, the XYZ work package of WBS can be technical, environmental and political risk categories.
One can combine the results of qualitative risk analysis (specifically the Perform QLRA process) with the project’s RBS to show clusters of risks, which are coming from specific sources.
This is in continuation of the earlier series of questions for the mutlti-response or multi-answer questions for the PMI-RMP® examination. I call them multi-response, multi-choice quesitons.
I'd strongly suggest that you take both the parts together when you try to attempt the questions. That way you will get a feel of questions and how to answer them. Do note that these are not verbatim questions from PMI-RMP exam, however, these questions covers the areas needed for the exam. These questions are taken from the following courses and book:
Again do note that the PMBOK 7th edition is a reference for the new RMP exam. It's explicitly listed in the exam content outline (RMP-ECO).
The RMP Live Lessons course also comes with a dedicated full-length question for this purpose (PMBOK7 and ECO).
In this part, we will have final 10 multi-answer/response questions. I hope you are able to do most of the questions on your own! If not, do send a mail as noted below.
Subscribe to the site (top-right corner) for fresh updates.
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Question – 11: For a project, the risk manager has all the planning related work, implementing the risk responses and currently monitoring the risks. For certain risks, while monitoring, the plan is to trigger a response based on analysis. Which of the following can be used (choose two)?
A. Affinity diagrams.
B. Contingency planning.
C. Variance analysis.
D. Residual impact analysis.
E. Trend analysis.
Question – 12: Which of the following are not correct about reserve analysis (choose two)?
A. Informs the amount of reserves remaining to the amount of risk remaining at any time in the project.
B. Use in both Perform Quantitative Risk Analysis and Monitor Risks process.
C. Can be plotted with a cause-and-effect diagram.
D. Burndown charts can be used to represent the reserve remaining.
E. Tells if the remaining reserve is adequate.
Question – 13: For a project, a number of risk related activities, but conditions ones, are added with changes to the project schedule. These have been approved and integrated, which in result in updates to (choose two):
A. Project schedule.
B. Project schedule management plan.
C. Project management plan.
D. Project schedule baseline.
E. Project resource management.
Question – 14: A planning session is ongoing in order to build a common understanding of the risk approach between stakeholders and to gain agreement for managing risks in a project, which will be part of the portfolio. The output of this meeting can have which of the following (choose two):
A. Introduction, Portfolio description, Stakeholder risk appetites.
B. Identified risks, Risk owners, Risk Response Owners.
C. Project description, Criteria for success, Thresholds and corresponding definitions.
D. Communications management plan, Risk breakdown structure, Contingency plans.
E. Risk management organization, Roles, responsibilities, and authority, Risk management techniques and guidelines for use.
Question – 15: Risk identification is about all of the following, except (choose two):
A. Develop a comprehensive list of all known uncertainties that could project objectives.
B. Use various tools and techniques such as variance analysis and trend analysis to identify new risks.
C. Write the risk statements in a three-part statement for clarity.
D. Use matrix method-based techniques such as analytical hierarchical process (AHP) to identify risks.
E. Remove biases and an array of human behavior patterns stand in the way of identifying unknown risks.
Question – 16: An example of unknown-known can be all of the followings, but (choose two):
A. A known fact.
B. A hidden assumption.
C. A hidden fact.
D. An unknowable.
E. An ignored assumption.
Question – 17: Delphi technique is one of the core techniques used to identify various uncertainties in a project and hence, associated risks. However, one of the key stakeholders opposes and outlines a number of reasons about its drawbacks. Why can this stakeholder be right (choose two)?
A. Limited to technical risks.
B. Iterative and hence gets unnecessarily refined.
C. Removes sources of bias.
D. Dependent on actual expertise of experts.
E. Can't be used for reserve estimation.
Question – 18: A project is getting closed. The risk manager and team members have tried to manage the risks to a large extent possible, but still some of the risks remained. As the project draws to a closure, what should be done with these risks, except (choose two)?
A. Include a summary of any risks or issues encountered on the project and how they were addressed.
B. Check the risk register and close all the risk before closing the phase.
C. Move the content of the risk register into the lessons learned register.
D. Hand-over the remaining risks into the next phase of the project.
E. Check the risk report in order to see the status of high-priority risks.
Question – 19: For a multi-geographical project under a satellite program, a project manager is currently collecting the performance information. In addition to it, which of the following can be done, except (choose two)?
A. Checking the status of the risks that have already been identified.
B. Evaluating whether or not the impact can be contained within the limits of the project budget.
C. Verifying whether any known risk has not occurred or is not about to occur.
D. Monitoring the status of all actions implemented to respond to the detection or occurrence of a risk.
E. Adding additional activities or work packages to update the project’s baselines or product backlog.
Question – 20: For a project, the risk owner has been monitoring the actions to determine the effectiveness and to identify if any secondary risks have arisen. The risk action owners while informing the status of response actions say that the undertaken actions are closed. What should the risk owner do next (choose two)?
A. Check if the risk has been effectively dealt with.
B. Inform the project manager about it and close the risk.
C. Determine if any additional actions need to be planned and implemented.
D. Keep the risk in the register and manage the risk through subsequent risk management processes.
E. Immediately perform an audit of this risk to determine the effectiveness of response.
The Risk Management Professional (RMP®) exam from PMI® has various types of questions, including the multi-response questions. Indeed, if you are appearing for the latest RMP exam in 2024 and beyond, then you will face both multi-choice and multi-response questions. There is a subtle difference between the two.
Multi-choice questions: There will be four radio-button choices. ONLY one of the choices will be correct. I call it single-response, multi-choice question. These questions are relatively not that difficult. But considering PMI, the standard will be high.
Multi-response questions: There will be usually five choices with check-boxes on the left, where you can select the right answers. In this case, there will be more than one correct answer. I call these multi-response, multi-choice questions. These are also called mutli-answer questions. These questions, compared to multi-choice questions, will be relatively difficult.
These questions are taken from the following courses and book:
Understanding of the Standard for Risk Management in Portfolios, Programs and Project. This is the main reference for the RMP exam.
Understanding on the concepts of uncertainties, complexties, ambiguities and risks from both PMBOK Guide 7th edition and PMBOK 6th edition. Yes, PMBOK 7th edition is an explicit reference for the latest RMP exam!
Ability to apply your understanding in the real-world in a varieties of situations and scenarios.
Good understanding of the PMI-RMP exam content outline (ECO), the latest one released in March/April 2022.
In this part, we will have 10 such multi-answer/response (or multi-response, multi-choice) questions.
You will be seeing such questions for the first time. As noted earlier, RMP exam takers are already facing such questions.
I hope you enjoy doing the questions and it helps in your PMI-RMP exam.
Subscribe to the site (top-right corner) for fresh updates.
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Question – 1: One of the principles of risk management is to foster a culture to embrace risk management. Such a culture: (choose two)
A. Identifies threats rather than ignoring them.
B. Identifies opportunities rather than ignoring them.
C. Identifies opportunities by cultivating a positive mindset within an organization.
D. Identifies both threats and opportunities by allocating the right resources.
E. Focuses on most impactful risks first.
Question – 2: Which of the following are not correct about risk attitude (choose two)?
A. Driven by perception and evidenced by observable behavior.
B. Must range from risk seeking to risk averse.
C. Individuals will have inconsistent attitudes towards risks.
D. Not always stable or homogenous.
E. It's the degree to which an individual accepts risks in anticipation of reward.
Question – 3: A risk manager and team members are identifying various sources of uncertainties at the individual project task level and also overall project level. While doing so, they are currently focusing on the quantitative assessment of various project constraints such as cost, schedule, scope, quality among others. Which of the following cannot be inputs for this purpose (choose two)?
A. Cost estimates.
B. Duration estimates.
C. Requirement estimates.
D. Resource estimates.
E. Resource requirements.
Question – 4: Risk management planning process is not only important from the process perspective, but also strategy perspectives. Which of the following are not the purposes of this process (choose two)?
A. Gain a better understanding of individual risks.
B. Have a numerical estimate of the overall effect of risk on the objectives.
C. Develop the overall risk management strategy.
D. Decide how the risk management processes will be executed.
E. Integrate risk management with all other activities.
Question – 5: Considering team members are new to the project and risk management is quite new, which of the following are the key success factors for risk identification (choose two)?
A. Risks linked to objectives.
B. Agreed upon definition of risk terms.
C. Complete risk statement.
D. Appropriate risk data model.
E. Available resources, budget and schedule for responses.
Question – 6: Considering risk owner and risk action owner, which are not correct? (choose two)
A. Risk owner is responsible for monitoring the risk.
B. Risk owner is responsible for selecting and implementing an appropriate risk response strategy.
C. Risk action owner reports the risk owner about the status of the risk response actions.
D. Risk action owner is responsible for finding out the effectiveness of a response.
E. Risk action owner owns the response actions, whereas risk response owner owns the response.
Question – 7: A project has been following the project management body of knowledge (PMBOK) guide's process group model of initiating to closing to manage a project, of which risk management is an integral part. Considering the planning process group of the five process groups, which of the following are considered?
A. Understanding of high-level risks that might impact project objectives.
B. Selection of overall risk management approach for the project.
C. Risk management integration with quality management and execution of stakeholder engagement strategies.
D. Risk management being part of every process in the planning process group.
E. Handing over the remaining known risks prior to closure of the project.
Question – 8: A risk manager is evaluating the effectiveness of risk management processes as documented in the risk management plan. The purposes of the audit can be (choose two):
A. Risk management rules are being carried out as specified.
B. Residual risks response planning is properly taken.
C. Risk management strategy is iterative and integrative.
D. Risk management related lessons are documented properly.
E. Risk management rules are adequate for monitoring and controlling the work.
Question – 9: The risk breakdown structure (RBS) is a hierarchical framework of potential sources of risk and used in risk identification. RBS can be used for all of the following situations, except (choose two):
A. Can be used in association with brainstorming.
B. Ensures coverage of all types of risk.
C. Lowest level of RBS is known as the risk package.
D. Tests for blind spots or emissions.
E. Used for evaluating current risks as well as identifying new risks.
Question – 10: In a meeting for risk identification, the risk manager wants to allow all participants to speak their mind and contribute to the discussion. This is to identify as many risks as possible and to stimulate creativity. Which of the following tools and/techniques will help the risk manager the most (choose two)?
I’m a certified PMP since 2020.
To continue with your earned PMP credential, one needs 60 PDUs, which I
had very little of as of 2022 end. I reached out to Satya to know how
best to get these PDUs and with best possible learning.
Satya
asked which one do I use the most in my profession, to which I
informed: Risk Management! Satya advised me to go with RMP 30 contact
hours, which I immediately followed, made the payment and subscribed to
the RMP 30 Contact Hours Online course within hours.
Four
months down the line, I not only achieved all the needed PDUs 114 days
before my PMP renewal date, in the process I also learned a lot, which
includes learning from Satya’s Management Review sessions.
Indeed, I met all my goals with which I started.
My review of this online course is outlined below.
Why this Course – ManagementYogi’s RMP 30 Contact Hours
Risk
Management is vital for a Project Manager as it will be the
responsibility of a Project Manager to mitigate the risks throughout the
project life cycle.
Risk Management should be known in depth by the Project Managers, otherwise it affects the deliverables.
This
course outlines the need for better Risk Management and enables us to
appear for PMI-RMP exam as it is mandatory to have 30 contact hours.
I
work as a Program Manager, and I see a lot of interlocks between the
projects, and this would increase the risk multiple times.
Satya’s
Management Review Sessions: It is very unique. With Satya, we get an
opportunity to ask our questions and he doesn’t mind explaining the
concept in detail which supports osmotic learning. For example,
recently, I requested Satya to explain ‘Probability Distribution’ and he
covered it exhaustively for 2 hours. This is something what we will NOT
get with others.
Course – ManagementYogi’s RMP 30 Contact Hours: Key Features
The course gives a bird’s view of PMI-RMP certification, and it is very crisp.
It covers areas of Advance Risk Management as well, e.g., Probability Distribution, Hybrid-Agile management etc.
The
lesson end questions and three full length question sets are very
challenging. It’ll improve your understanding by leaps and bounds.
The
50-question assessment that will be finally taken is of very high
quality. Post the assessment, I received the 30 RMP Contact Hours
Certificate in 2 days.
Satya’s
course content will ensure that we read Risk Management Standards
(Foundational and Practice), PMBOK Guide 7th edition and PMBOK Guide 6th
edition.
In the Management Review Sessions, you will learn many aspects of Agile and Hybrid in detail.
Another unique thing about the course is that the course is constantly updated as needed, and updates are shared free of cost.
RMP Formula Gold Cards are very helpful as they can be downloaded for our reference.
Personally,
I like the Risk Monitoring lesson the most. In addition, practical
hands-on demonstrations will be shown in Management Review Sessions with
various tools. I liked the course as it made me read a lot and there is
a lot of learning too.
Lessons in the Course – ManagementYogi’s RMP 30 Contact Hours
First
and foremost, I want to inform you that the questions in this course
will be very tricky and unless the concepts are clear it will be
difficult to answer. These are high quality questions.
Next, I’ve outlined the following high-level information for the various lessons of the course.
Lesson – 1: Welcome: It enumerates the Course Structure.
Lesson – 2: Introduction: It explains the PMI-RMP exam in detail.
Lesson – 3: Fundamentals of Risk and Risk Management: It explains Performance Domains and Life Cycles.
Lesson
– 4: Risk Management Framework and Life Cycle: You’ll learn in detail
about Processes in Risk Management and framework. Emphasis is given on
flow and interactions.
Lesson
– 5: Risk Management and Other Knowledge Areas: This the most important
Lesson which explains the impact of Risk Management on other Knowledge
Areas and vice-versa.
Lesson – 6: Risk Management Planning: It explains Process and ITTOs.
Lesson – 7: Risk Identification: I primarily focused on the Data gathering and Data Analysis Technique in this lesson.
Lesson – 8: Qualitative Risk Analysis: This lesson goes into much more detail when compared to the content we had for PMI-PMP.
Lesson
– 9: Quantitative Risk Analysis: This lesson also goes in more detail
when compared to the content we had for PMI-PMP. In fact, it’s far
advanced.
Lesson – 10: Risk Response Planning: This lesson explains Process and ITTOs with other needed information.
Lesson – 11: Risk Response Implementation: It explains the process, ITTOs and various unknown areas before.
Lesson – 12: Risk Monitoring: I like this lesson the most as I can co-relate to my regular work at the Program Level.
Ever tossed a fair coin? I’d bet you have! At least in your childhood days while deciding which team would bat first in a baseball or a cricket match, or who would serve first in a badminton or tennis game. Every kid agrees to it because it’s unbiased. When you toss a fair coin, the chances of getting a head is 1/2 (0.5) or 50%. This is the division between the favorable outcome, which is a head and all possible outcomes (head and tail).
A coin toss is perhaps is the simplest introduction to probability, which informs chance or likelihood of occurrence of a random variable.The random variable here is getting a head. Let’s note the random variable as X and probability as P(X). Mathematically put:
Probability (Getting head) or P (X)
= Favorable number of outcomes of the event / Total number of possible outcomes
= 1 / 2 = 0.5 = 50%
Now, what’s the chance of getting a head when you toss a pair of coins together? In this case, the total number of possible outcomes is four: tail (first coin) and tail (second coin), tail and head, head and tail, and finally head and head. The values that the random variable can take are many, as shown in the below table:
As you can see, the possible values of X range from 0 to 2 (i.e., 0 head, 1 head, or 2 heads). This leads to the concept of distribution. Looking at the above table, we can see the frequencies of this random variable’s occurrences are 1, 2, and 1. This is distribution or frequency distribution. One could say: distribution is the possible values a random variable can take and how frequently these values occur.
Now, if I add probabilities to this random variable’s values, we get a probability distribution. This is depicted in below:
As shown in the above table:
We have all favorable outcomes for 0, 1, or 2 heads. These are represented in the first and second columns.
All possible outcomes are obviously four, and that’s shown in the third column.
P(X) is shown in the final column, and the probabilities are 25%, 50%, and 25%, respectively for 0, 1, or 2 heads. This is probability distribution. Summed up, it equals one.
Hence, we can say thatprobability distribution for a random variable describes how probabilities are distributed over the values of the random variable.
Discrete and Continuous Distribution
Distribution can be discrete or continuous. Discrete means you are getting an integer number (1 head or 2 heads). You don’t say that you will get 0.33 head! Considering another example of counting the number of children in households of a locality, you will come-up with results such as 0 child, 1 child, 2 children, etc. You won’t get 0.57 child!
You may be laughing now – what’s 0.33 head or 0.57 child!? Good to see you smiling. Smiling lessens stress and helps in understanding.
All random variables; however, are not discrete. For example, let’s say you are determining the distribution of age, weight, or height of people in a locality. Considering height, it can be anything: 5 feet, 5.5 feet, 5.85 feet, 6.1 feet, and so on. In such a case, the distribution is continuous. So, this distinction is important: at a high-level, there are two types of random variables – discrete and continuous and respective probability distributions – discrete probability distribution and continuous probability distribution.
Now, combining all, i.e., probability, distribution and probability distribution, I've the following consolidated tip.
But, how does all of this fit into Risk Management? Risk Managers don’t toss coins or calculate heads/tails in an experiment. That’s kids’ games and not for grown-up men or women! Perhaps; although, child play teaches the basics neatly.
Probability Distribution and Risk Management
With the above basics, let’s consider another example to understand probability distribution from the perspective of risk management. You are going to a friend’s house. It may take you one hour to reach your destination if you encounter no obstacles. If there is heavy traffic, it’s possible that you may not get there for three hours. With less traffic, it’s more likely to take 2 hours. Hence, you can say there are three possibilities:
Minimum (or Optimistic) travel duration = 1 hour
Most likely travel duration = 2 hours
Maximum (or Pessimistic) travel duration = 3 hours
In this case, the random variable (X) is the “travel duration.” Can you conclusively say which one of the estimates is correct? Unlikely, because other factors such as traffic conditions are involved. Now, if I add chances to these numbers, then we get probability distributions. I’ve prepared the below video to explain in more detail [Duration: 05m:33s]. For better audio-visual experience, you may want to go full HD and plug-in your earphones.
Importance of Probability Distribution *** UPDATED ***
In project risk management, the concept of probability distribution is applied to estimation. Continuing with our previous example, when we estimate, we take the most likely outcome of two hours, which is not correct because we’ve forgotten to consider other possibilities.
We can (and should!) consider possible scenarios, not just the most likely one. In other words, instead of saying an activity in a project is going to take “X” number of days, we also can consider other days using a distribution. For each duration in the distribution, there is a probability available.
This can be done for all the activities or tasks of the project, which in turn impacts the project schedule and cost. This enables us to build a more realistic plan.
Now that we have understood the basics of probability, distribution, and probability distribution, let’s look at the various types used in risk management.
Triangular Distribution *** UPDATED ***
Triangular distribution is the most common type of distribution used. Named triangular because of the shape of the curve, this refers to there being no pre-existing data, but only expert opinions or judgment.
Symmetrical Triangular Distribution
The below distribution is triangular and symmetrical.
By looking at the graph above, we can say: There is approximately a 30% chance of the duration being 6 days, a full chance of the duration being 8 days’, and also a 30% chance of the duration being 10 days.”
Asymmetrical Triangular Distribution
Do note that the triangle shown need not be symmetric. Asymmetrical diagrams are shown below:
From here, you can calculate the durations with respective chances or probabilities.
Let’s take another example of a project, once with a task of Product Requirement Documentation (PRD) Preparation with an estimated 5 days duration. This is the most likely estimate, but we do not have the minimum and maximum value.
By using the Primavera Risk Analysis (PRA) software tool, the triangular distribution is depicted as below:
The durations can be 4, 5, or 6 days (shown in the X-axis). The respective chance for minimum, likely, and maximum values are entered when you perform a duration risk analysis. This is demonstrated in a video in the later part of this article.
While building the schedule model, this triangular distribution can be noted as Triangle (4, 5, 6) or Triangle (4; 5; 6).
Uniform Distribution
In rectangular distribution, you can use a maximum value and a minimum value, but not any most likely value. In the below example, we have a uniform (or rectangular) distribution.
Looking at it, we might say: The task has a minimum duration of 4 days, but a maximum duration of 12 days
You can use Uniform Probability Distributions when you specify the extremes of uncertainty of the activity under consideration and when the intermediate values have equal chances of occurring. It is also possible when you cannot draw any inference on the possible distribution shape.
Taking our previous example of the PRD Preparation task, which is estimated to be 5 days, using PRA, we have the following values for Uniform distribution:
Like Triangular distribution, while building the schedule model, this distribution can be noted as Uniform (4, 6).
Beta Distribution*** UPDATED ***
Beta distribution, like triangular distribution has also three possible values – worst case, most likely, and best case. Like the triangular model, it also gives more weightage to the most likely case. We have seen one example of Beta distribution in the earlier video.
Unlike the triangular distribution, the shape for beta distribution is smoother and the tails in Beta distribution taper off less quickly. A sample beta distribution curve is shown below:
Beta distribution can also be symmetric or asymmetric in shape. The notations happen like Beta (6, 8, 10). As you can see above, there can be many values close to the most likely values, and it slowly tapers off towards the minimum or maximum ends.
Using the PRA software tool, for our task, PRD Preparation, a Beta (or BetaPert) distribution will come out as below:
Do note that along with the triangular distribution, beta distribution is another frequently used probability distribution.
Normal Distribution
Normal distribution is defined by the mean of a planned (or remaining duration) activity for an activity and standard deviation (SD) of the activity.
This distribution is used if there is historical information available. Normal distribution also has a bell-shaped curve like Beta, but considers SD to calculate the worst (and best) case scenarios.
For our example (task of PRD Preparation with a duration estimate of 5 days), we note the normal distribution as Normal (5,1), where 5 is the mean and 1 is the SD.
Discrete Distribution
In a discrete distribution model, the duration of an activity under consideration can have a number of integer values, but without any intermediate values. In other words, the distribution is discrete, rather than continuous like in a triangle, beta, or uniform.
In the above sample, the activity has discrete distribution of values 6, 10, 18, and 20.
Considering our task of PRD Preparation, the discrete distribution will be seen as below with the PRA tool. The distributions are 2, 3, 4, and, 5 with respective weighting factors of 10, 20, 30 and, 50, respectively. This can be noted as Discrete ({2, 3, 4, 5}, {10, 20, 30, 50}).
Practical Example and Demonstration
With this understanding, let’s take a practical look using MS Project and Primavera Risk Analysis. The video [Duration: 05m:42s] demonstrates a project plan with fixed activity estimates. It’s next imported to the PRA tool and analyzed with various probability distributions for the activities of the project.
Conclusion
Probability distribution is very important when you use quantitative risk analysis, which involves a number of mathematical modeling and sampling. Managers or planners can also deploy advanced probability distributions such as lognormal distributions, cumulative distributions, general distributions, among others. The above video explains a few of these.
We have come a long way and seen a number of examples. I propose just one more exercise. I promise it won’t be difficult, provided you have read the content sincerely. Going back to our first examples of coin tosses, can you answer these:
What’s the probability distribution of getting a head when you toss three coins?
What are the values that the random variable can take?
If you are getting four values for the random variable of getting a head and when all your probability distributions are summed-up to equal one, then you have well understood the concept.
I welcome your thoughts, feedback, and suggestions in the comment section below.
* This article is dedicated to the memory of my father, the late Harendra Nath Dash, who passed away three years ago on June 11, 2019. He first introduced me to the concept of probability and statistics. It was mesmerizing then, and I still remember it. I wish this article to be a tribute to him and his teachings.
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