To ensure the successful completion of a project, it is of utmost importance for the project manager to find ways to handle uncertainties that can pose potential risks for a project. Risk management is an iterative process. Risks can relate to any aspect of the project – be it the cost, schedule, or quality. The key to managing risks is to identify them early on in the project and develop an appropriate risk response plan.
To develop a Risk Response Plan, you need to quantify the impact of risks on the project. This process is known as quantitative risk analysis wherein risks are categorized as high or low priority risks depending on the quantum of their impact on the project. The Project Management Body of Knowledge (PMBOK) advocates the use of Monte Carlo analysis for performing quantitative risk analysis.
Monte Carlo analysis involves determining the impact of the identified risks by running simulations to identify the range of possible outcomes for a number of scenarios. A random sampling is performed by using uncertain risk variable inputs to generate the range of outcomes with a confidence measure for each outcome. This is typically done by establishing a mathematical model and then running simulations using this model to estimate the impact of project risks. This technique helps in forecasting the likely outcome of an event and thereby helps in making informed project decisions.
While managing a project, you would have faced numerous situations where you have a list of potential risks for the project, but you have no clue of their possible impact on the project. To solve this problem, you can consider the worst-case scenario by summing up the maximum expected values for all the variables. Similarly, you can calculate the best-case scenario. You can now use the Monte Carlo analysis and run simulations to generate the most likely outcome for the event. In most situations, you will come across a bell-shaped normal distribution pattern for the possible outcomes.
Let us try to understand this with the help of an example. Suppose you are managing a project involving creation of an eLearning module. The creation of the eLearning module comprises of three tasks: writing content, creating graphics, and integrating the multimedia elements. Based on prior experience or other expert knowledge, you determine the best case, most-likely, and worst-case estimates for each of these activities as given below:
| Tasks | Best-case estimate | Most likely estimate | Worst-case estimate |
| Writing content | 4 days | 6 days | 8 days |
| Creating graphics | 5 days | 7 days | 9 days |
| Multimedia integration | 2 days | 4 days | 6 days |
| Total duration | 11 days | 17 days | 23 days |
The Monte Carlo simulation randomly selects the input values for the different tasks to generate the possible outcomes. Let us assume that the simulation is run 500 times. From the above table, we can see that the project can be completed anywhere between 11 to 23 days. When the Monte Carlo simulation runs are performed, we can analyse the percentage of times each duration outcome between 11 and 23 is obtained. The following table depicts the outcome of a possible Monte Carlo simulation:
| Total Project Duration | Number of times the simulation result was less than or equal to the Total Project Duration | Percentage of simulation runs where the result was less than or equal to the Total Project Duration |
| 11 | 5 | 1% |
| 12 | 20 | 4% |
| 13 | 75 | 15% |
| 14 | 90 | 18% |
| 15 | 125 | 25% |
| 16 | 140 | 28% |
| 17 | 165 | 33% |
| 18 | 275 | 55% |
| 19 | 440 | 88% |
| 20 | 475 | 95% |
| 21 | 490 | 98% |
| 22 | 495 | 99% |
| 23 | 500 | 100% |
This can be shown graphically in the following manner:
What the above table and chart suggest is, for example, that the likelihood of completing the project in 17 days or less is 33%. Similarly, the likelihood of completing the project in 19 days or less is 88%, etc. Note the importance of verifying the possibility of completing the project in 17 days, as this, according to the Most Likely estimates, was the time you would expect the project to take. Given the above analysis, it looks much more likely that the project will end up taking anywhere between 19 – 20 days.
Whenever you face a complex estimation or forecasting situation that involves a high degree of complexity and uncertainty, it is best advised to use the Monte Carlo simulation to analyze the likelihood of meeting your objectives, given your project risk factors, as determined by your schedule risk profile. It is very effective as it is based on evaluation of data numerically and there is no guesswork involved. The key benefits of using the Monte Carlo analysis are listed below:
Now that you are aware of the Monte Carlo analysis and its benefits, let us look at the steps that need to be performed while analysing data using the Monte Carlo simulation.
The series of steps followed in the Monte Carlo analysis are listed below:
Each of the above listed steps of the Monte Carlo simulation is detailed below:
Sensitivity analysis is used for determining the most critical variables in a project. To identify the most critical variables in the project, all the variables are subjected to a fixed deviation and the outcome is analysed. The variables that have the greatest impact on the outcome of the project are isolated as the key project risk variables. However, sensitivity analysis in itself might give some misleading results as it does not take into consideration the realistic nature of the projected change on a specific variable. Therefore it is important to perform uncertainty analysis in conjunction with the sensitivity analysis.
Uncertainty analysis involves establishing the suitability of a result and it helps in verifying the fitness or validity of a particular variable. A project variable causing high impact on the overall project might be insignificant if the probability of its occurrence is extremely low. Therefore it is important to perform uncertainty analysis.
Monte Carlo simulation is a valuable technique for analyzing risks, specifically those related to cost and schedule. The fact that it is based on numeric data gathered by running multiple simulations adds even greater value to this technique. It also helps in removing any kind of project bias regarding the selection of alternatives while planning for risks. While running the Monte Carlo simulation, it is advisable to seek active participation of the key project decision-makers and stakeholders, specifically while agreeing on the range values of the project risk variables and the probability distribution patterns to be used. This will go a long way in building stakeholder confidence in your overall risk-handling capability for the project. Moreover, this serves as a good opportunity to make them aware of the entire risk management planning being done for the project.
Though there are numerous benefits of the Monte Carlo simulation, the reliability of the outputs depends on the accuracy of the range values and the correlation patterns, if any, that you have specified during the simulation. Therefore, you should practice extreme caution while identifying the correlations and specifying the range values. Else, the entire effort will go waste and you will not get accurate results.
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The first part of this series (Project Management – Statistics for dummies (part 1)) focused on the meaning of the Mean, Median and the Mode.
Today’s installment will try to make sense of the Variance and the Standard Deviation.
The variance is a measure of how spread out a data distribution is. It is computed as the average squared deviation of each number from its mean. Sounds a bit complicated so let’s try and work it out.
Using mathematical symbols, the above equation will look as follows:
Where:
is the VarianceFor example:
A project schedule consists of 10 tasks, with the following estimated durations:
| Task ID | Estimated Duration (days) |
| 1 | 3 |
| 2 | 4 |
| 3 | 5 |
| 4 | 6 |
| 5 | 3 |
| 6 | 7 |
| 7 | 4 |
| 8 | 5 |
| 9 | 2 |
| 10 | 4 |
Based on the above:
Now let’s calculate the Variance:
The sum of the squares of the difference between the individual values and the Mean =
(3 – 4.3)2 + (4 – 4.3)2 + (5 – 4.3)2 + (6 – 4.3)2 + (3 – 4.3)2 + (7 – 4.3)2 + (4 – 4.3)2 + (5 – 4.3)2 + (2 – 4.3)2 + (4 – 4.3)2 = 22.333
With N = 10 the Variance = 22.33 / 10 = 2.2333
The Standard Deviation (
– pronounced Sigma) is the square root of the Variance which, in the example above will be 
= 1.494434
So what does it actually mean?
Like the Variance, the Standard Deviation is a measure of how spread out a data distribution is around the mean (average) of the set. While the mean only provides an indication of the average result, it lacks the ability to indicate how widely spread all items in the set are. The Standard Deviation provides this additional dimension by indicating how spread the data items are from the average. A set of values that are closely clustered near the mean will have a low standard deviation, a set of numbers that are widely separated will have a higher standard deviation and a set of numbers that are all the same will have a standard deviation of zero.
The Program Evaluation and Review Technique (PERT) stipulates the use of Standard Deviation as a reflection of each tasks estimation’s uncertainty as it is calculated as the difference between the pessimistic and optimistic duration divided by six. A small Standard Deviation would be interpreted as a smaller uncertainty compared with a larger Standard Deviation. It should be noted, however, that although it would be theoretically correct to determine the level of uncertainty for each task by determining the tasks’ duration Standard Deviation; determining the project’s standard deviation require a more rigor approach which will involve the use of “Monte Carlo Simulation“.
Interested to explore this topic a bit further? – check out the following books
The mantra for clearing the PMP certification exam is practice and even more practice. The more you reinforce your learning by attempting mock tests, the better prepared you will be for the exam. Various researchers have emphasized on the importance of reflective learning. Learning is an ongoing process and reflecting on whatever has been learnt by means of practice is one of the best ways of perfecting the learning. After you have completed an in-depth study of a particular process group or a knowledge area of the PMBOK, attempt as many practice questions as you can. The practice will not only highlight your strengths and weaknesses, but it will also go a long way in boosting your morale for the exam. Set every score you attain as a benchmark and try to improvise on it the next time. Practicing reinforces your learning.
While preparing for the PMP exam, make sure that you have a complete understanding of the PMBOK – all the knowledge areas, process groups, tools and techniques, inputs and outputs. Even if you consult other books for your preparation, the PMBOK Guide should still be your first reference material. Some highly recommended resources that you could refer to for your preparation (and which I myself used as part of my preparation for the PMP exam) are:
PMP Exam Prep, Sixth Edition: Rita’s Course in a Book for Passing the PMP Exam
The PMP Prepcast by Cornelius Fichtner, PMP
No doubt all your preparation and hard work will come in handy while preparing for the exam, but here is a list of do’s and don’ts that you should adhere to:
Get enough sleep prior to the exam and go for the exam with a relaxed mind, confident of getting PMP-certified by the end of it. All the best!
“I know you’ve heard it a thousand times before. But it’s true — hard work pays off. If you want to be good, you have to practice, practice, practice. If you don’t love something, then don’t do it.” Ray Bradbury – 1920-, American Science Fiction Writer.
Affiliate program disclosure: Links to external products and/or services published in this post could earn me (should you decide to purchase them) some referral commission. Please note that I take my referrals seriously and under no circumstances would I recommend something I don’t genuinely believe is of high quality and of high professional value.
Note: PMI®, PMP®, and PMBOK® are registered trademarks of the Project Management Institute, Inc.
Although, generally speaking, project managers are not expected to demonstrate complicated mathematical and / or statistical capabilities, there are some aspects of both these disciplines where basic knowledge and understanding of some basic concepts can enhance the project managers’ ability to perform fundamental project management duties – primarily around risk management.
The Project Management Body of Knowledge advocates the use of “Monte Carlo Simulation” within the context of performing quantitative risk assessment analysis. Although in most cases, executing such analysis will require the invocation of some sort of automated software tools, it is important for the project manager to understand the key principles behind the mathematical and statistical analysis performed by this sort of tools.
Today’s post will focus on three basic concepts (all of which, funnily enough, start with the letter ‘M’):
The mean (or average) of a set of data values is the sum of all of the data values divided by the number of data values. That is:
Using mathematical symbols, the above equation will look as follows:
Where:
is the sum of all x values in the setFor example:
A project schedule consists of 10 tasks, with the following estimated durations:
| Task ID | Estimated Duration (days) |
| 1 | 3 |
| 2 | 4 |
| 3 | 5 |
| 4 | 6 |
| 5 | 3 |
| 6 | 7 |
| 7 | 4 |
| 8 | 5 |
| 9 | 2 |
| 10 | 4 |
Based on the above:
The median of a set of data values is the middle value of the data set after it has been arranged in an ascending order.
Median = ½ (n + 1)th value in a set, where: n is the number of data values in the set
Note: If the number of values in the set is even, the median is calculated as the average of the two middle values.
For example:
The above task list, ordered in an ascending order, will look as follows:
| Task ID | Estimated Duration (days) |
| 9 | 2 |
| 1 | 3 |
| 5 | 3 |
| 2 | 4 |
| 7 | 4 |
| 10 | 4 |
| 3 | 5 |
| 8 | 5 |
| 4 | 6 |
| 6 | 7 |
Given that there are 10 tasks in this list, the then ½(10+1) = 5.5.
Given that in this case n = 10, the median will be calculated as the average between the two middle values (being tasks 7 & 10) = (4 + 4) / 2 = 4 days.
The mode represents a data value that appears most frequently within a set of values. Obviously if one or more values appear in exactly the same frequency, all such values will be considered to be part of the set Mode.
For example:
Given the following set of numbers: 1, 2, 3, 2, 3, 4, 1, 3; the number 3 appears the most times and is therefore the Mode.
Stay tuned for the next installment as things will get slightly spicier.
The Project Management Body of Knowledge (PMBOK)
The PMBOK, published by the PMI, is a compilation of the project management guidelines to be adopted as a best practice for the successful execution of a project. It serves as a guiding principle for achieving the scope, cost, schedule and quality constraints of a project and is rigorously followed by numerous organizations throughout the world. The PMBOK establishes five process groups for any project, irrespective of the type of industry. These process groups are: Initiating, Planning, Executing, Monitoring and Controlling, and Closing. Each of these process groups has its own inputs, tools and techniques, and outputs. The inputs for a process group include the list of documents that are required to be in place before starting off a particular process.
For instance, before starting the scope planning process, you need to have the project charter and the list of assumptions and constraints for the project. The tools and techniques for each process group include the mechanism or the procedure that should be applied to the inputs to attain the desired outputs. During the scope planning process, you need to perform a benefit/cost analysis and use expert judgment to derive the scope statement for the project. The benefit/cost analysis and expert judgment in this example are the tools and techniques to be applied whereas the scope statement is the output of the scope planning process.
There are nine knowledge areas recognized by the PMBOK. These include the processes that need to be completed for the successful execution of a project. The nine knowledge areas are: Project Integration Management, Project Scope Management, Project Time Management, Project Cost Management, Project Quality Management, Project Human Resource Management, Project Communications Management, Project Risk Management, and Project Procurement Management. Each of these knowledge areas go through the initiation, planning, execution, monitoring and control, and closure phases.
The following table represents the matrix of the knowledge areas vs. the process groups:
check out the final article (The Secret to Clearing the PMP Certification Exam (Part 3)) which will include practical ideas on how to prepare and what resources to use in preparation for the exam.
Note: PMI®, PMP®, and PMBOK® are registered trademarks of the Project Management Institute, Inc.
You have read enough about the PMP certification and the benefits associated with it. You have also been toying with the idea of getting PMP-certified for quite some time but do not know where to begin with. You have often pondered how to clear the PMP certification exam. This article aims to throw some light on the PMP certification, its benefits, the eligibility requirements, the examination structure, reference material, and some practical tips for clearing the exam.
Before you resolve to get PMP-certified, you must understand that the secret for clearing the exam (apart, obviously, from having good practical experience in Project Management) is lots and lots of revisions and exam practices. If you are game for it, then half the battle is already won. So, let’s get cracking!
Project Management is increasingly becoming popular as a profession. More and more organizations have realized the benefits of following a disciplined methodology for executing their projects successfully. To become a successful project manager, it is imperative to have a thorough understanding of the different processes to be followed at each and every stage of the project. The Project Management Professional (PMP) certification is a universally recognized benchmark that validates an individual’s expertise and knowledge in the field of project management. The PMP certification is offered by the Project Management Institute (PMI) (http://www.pmi.org). It demonstrates your knowledge of all the aspects of project management. Once obtained, the certification will become a testimony to your understanding of how to manage and lead projects and project teams.
While hiring a project manager, most organizations are increasingly opting for people who are PMP-certified. The certification is becoming a distinguisher against the ever-growing competition and is a valuable tool for increasing your market value. With the PMP certification to add to your resume, you do not only stand a better chance of getting the coveted job, but are also in a position to negotiate for a higher pay package. Another key advantage of getting PMP-certified is that you establish a common language of communication with the project management fraternity. Organizations hiring a PMP-certified project manager are confident that the individual is well-versed with the various process groups and knowledge areas as prescribed by the PMI in its Project Management Body of Knowledge (PMBOK). Therefore, there is a higher probability that such an individual will easily gel with the organization’s project management methodology.
Considering the numerous benefits of getting PMP-certified, you would be wondering as to how to get PMP-certified? Well, to get PMP-certified, you need to combine substantial practice with a thorough understanding of the PMP examination structure and the concepts included in the PMBOK.
The PMP certification exam is conducted by the PMI. To be able to apply for the PMP certification examination, you need to have a bachelor’s degree with a minimum of three years (4500 hours) of demonstrable project management experience. In addition to this, you need to have 35 hours of project management education (which are referred to as Professional Development Units (PDUs)). More details about the PMP certification eligibility and the process for filling up the online application form can be obtained from http://www.pmi.org/PDF/pdc_pmphandbook.pdf. You must remember that filling up the application form is a time-consuming process and adequate care should be taken while filling up the form. At times, the application might be rejected, or audited to verify the correctness of the information provided by the applicant. On successful submission and approval of the application form, the PMI will send a notification for the same. After this, you can schedule your exam.
The PMP certification exam uses the computer-based testing method and you can schedule the exam at your convenience depending on your preparation. You have to appear for the exam within one year of successfully submitting the online application form.
The examination comprises 200 multiple choice questions that need to be completed within 4 hours. Out of these 200 questions, 25 questions are pretest questions which do not affect your overall score. The current passing score for the PMP certification exam is 61%.
The exam comprises a specific percentage of questions for each project management process group. The percentages of questions for each process group are: Initiating: 11%, Planning: 23%, Executing: 27%, Monitoring and Controlling: 21%, Closing: 9%, and Professional and Social Responsibility: 9%.
A visual representation of the distribution of the PMP questions across various process groups is given below:
All the PMP examination questions are based on the content included in the latest edition of the PMBOK (4th edition as of date). Therefore, it is important that you have a thorough understanding of all the concepts included in the PMBOK.
Click here for the second article in this series, titled ”The Secret to Clearing the PMP Certification Exam (Part 2)“. This article provides a closer look into the PMBOK.
Click here for the third article in this series, titled “The Secret to Clearing the PMP Certification Exam (Part 3)” which provides practical advise as to how to prepare and what resources to use in preparation for the exam.
As usual, your comments and suggestions will be appropriated.
Note: PMI®, PMP®, and PMBOK® are registered trademarks of the Project Management Institute, Inc.
If you live anywhere else in the world but Australia there is very little chance you will have heard of Donny Ryder.
Comes to think of it, even in Australia, you might have some difficulties remembering where and how you have come across his name.
I never met Donny Ryder. I live in Melbourne, which is (for those of you living in the Northern Hemisphere) in the southern part of Australia. Donny used to live in the Alice Springs area, which is in the Northern Territory of Australia.
‘Used to live’ is the operative word here. Donny was killed in July 2009 by five drunk, white Australians, who took it upon themselves to abuse and terrorize the local Aboriginal community.
I was hoping to be able to introduce these fine gentelmen to the world by publishing their photos on display here but alas their photos are no where to be found. Their names, however, are:
It is interesting to note that in delivering the sentences (of 12 months to six years), the Northern Territory Chief Justice Brian Martin in the Supreme Court in Alice Springs, made the following ludicrous statement, when he described Ryder’s death as at “the lower end of seriousness of the crime of manslaughter”.
I was hinting in an earlier post at the prevailing problem of intolerance, impatience and narrow mindedness that seem to occur, on a small scale in project spheres, but on a much larger scale in the general population.
We can’t change it but we damn sure can say we don’t like it.
And this is my small and insignificant contribution to the fight against intolerance and racial injustice.
Cheers mate.
Epilogue: The ABC’s Four Corners dedicated a program, titled “Dog Act” to Rony Ryder’s senseless killing. Thanks to that program I can now publish the pictures of Rony’s killers:
Check out the following articles for additional information:
I wrote in an earlier post about the tendency of some organizations to impose overly engineered processes in a (futile) attempt to increase quality.
The above was brilliantly demonstrated to me in an e-mail I received from a work colleague (thanks Doug) to which the following two recipes, for Chocolate Covered Brownies, were attached.
Have a look at the two recipes (follow the links) and, honestly, let me know which one of these two represents the way your projects are run?
“Our research shows that the Standish definitions of successful and challenged projects have four major problems:
- they’re misleading,
- one-sided,
- pervert the estimation practice,
- and result in meaningless figures.”
Source: J. Laurenz Eveleens, Chris Verhoef, “The Rise and Fall of the Chaos Report Figures,” IEEE Software, vol. 27, no. 1, pp. 30-36, January/February, 2010. http://www.computer.org/portal/web/csdl/doi/10.1109/MS.2009.154
Also check out the following article:
My good friend, Shane Clauson, which I highly respect, both as a person and a professional, made me realize that my previous post (“The Scientific Method and the IT Projects Failure Rate debate“) is incomplete as, although it highlights a certain problem, it stops short of defining the impact and consequential cost of that problem.
As I was thinking about Shane’s comments (directed to me via Twitter) I came across two articles which further helped me pinpoint my argument, as will be detailed below.
I first came across an article published in NewScientist, titled “Martin Gardner: Exposing fads and fallacies“. For those who are not in the know, Martin Gardner, who passed away just few days ago, wrote the “Mathematical Games” column for Scientific American magazine for 25 years and published more than 70 books. The NewScientist article is relevant to our discussion here as it 1) gave me the title for this post 
; and 2) demonstrated the need to tackle issues head on, irrespective of how complicated or ludicrous they seem.
I subsequently read an article in the Australian newspaper, “The Age”, telling the story of the ban put on the British doctor accused of conducting an unethical research leading to a world-wide fear that a common vaccine could cause autism.
It doesn’t require much explanation to argue the case that spreading a lie, when the subject of that lie is within a medical context, can have far reaching consequences. In the case of the vaccine-autism issue, the consequences were that many parents decided to abandon the vaccine and “Vaccination rates in Britain and other countries have not fully recovered since Dr Wakefield and his colleagues’ research was published in 1998, and there are measles outbreaks throughout Europe every year“.
I could have easily brought up a good number of other cases, from the medical arena, where the spread of inaccurate and misleading information has had far reaching impact on people and institutions.
So what about the current debate regarding the IT projects failure rate? Why does it matter? You say it’s 65%, he says it is far lower, I say it is %34.5 – at the end of the day who cares and why is it important?
Let’s talk for a moment about Life Insurance.
Few years ago I’ve come to appreciate the fact that having a life insurance in place will buy me the peace of mind I need, thinking about the financial hardship I might bestow on my family, should anything prematurely happened to me. I quite vividly remember my meeting with my insurance broker. As we were discussing the various options in which I could possibly injure myself or get myself killed, the realization daunted on me that as the risk of dying seemed to increase by the second, so did the price I was willing to pay to mitigate that risk (i.e. the insurance premium). In short, the scaring technique applied on me by the insurance broker resulted in my willingness to impart of greater sums of money in order to buy that illusive peace of mind.
Ok, back to the discussion about IT Projects’ failure rate.
The impact of the over elaboration on the risk of implementing projects in the IT industry is threefold:
The bottom line is that the scare campaign is costing someone-somewhere real $$$’s. These additional costs do not necessarily translate to better success rate as, these additional costs are spread across projects which did not require these additional costs to be spent on in the first place but, like my life insurance example, were sucked into spending more believing this will buy them a better peace of mind.
Don’t get me wrong, I did get myself a life-insurance policy; and companies should invest in proper methodical processes. These, however, need to be done based on factual statements, devoid of fads and fallacies while separating the science from the fiction.
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