Cursory discussions with young project managers reveal a simple yet concerning fact. Most project managers are aware of the need to identify and manage project risks and most will be aware of the need to establish and publish a project risk register. That’s the good news. Where most inexperienced project managers fail is in their lack of understanding of the need to rigorously manage project risks arising inherently from their project schedule.

A short example can illustrate the issue quite clearly. Assume your project has 5 tasks, each estimated with a confidence level of 90%. Based on the above, would you say that your overall chances of meeting your project target delivery date are 90%? You might intuitively say ‘Yes’ but then you’ll be wrong. The correct answer is actually less than 60% (being the product of the following calculation: 0.9 x 0.9 x 0.9 x 0.9 x 0.9 = 0.59). So, in this example, if you were confidently managing your project, expecting a very high chance of meeting your deadline, you could be up for a surprise when some of the odds start playing against you.

The initial lesson from this example is that as a project manager you need to understand and manage the risks inherently built into your schedule. These risks require the least brainstorming or group discussions as they are directly and explicitly jump out of your project schedule and as such should be the most apparent ones.

The reality of most projects is that they will have a substantially larger number of tasks about them than the example above. Not only will the average project have substantially more tasks, each task is likely to have varying degrees of confidence levels, such that establishing an overall project scheduling risk factor will be far more complicated.

A simplistic approach for taking scheduling confidence into account is the PERT (also known as Three Point Estimate) technique. This technique uses three estimates to define an approximation of the activity’s duration (and cost). This technique works as follows: Determine your Optimistic (O), Pessimistic (P) and Most Likely (M) estimates for each activity. Having determined these parameters calculate the expected activity duration using a weighted average of the three parameters, based on the following formula:

Expected activity duration = (O + 4M + P) / 6.

The reason I referred to this approach as being “simplistic” is because despite its elegant look, it is statistically incorrect, due primarily to the fact that it assumes that the duration of each activity can be determined independently from all other activities, which is hardly ever the case.

This is the point where using Monte Carlo Analysis can come handy. Rather than using the simplistic approach suggested by the PERT technique, the Monte Carlo Analysis technique utilizes the three estimates to repeatedly simulate the project’s completion date, while taking into account the statistical likelihood that each activity’s duration will be somewhere on the continuum between the three estimates. The result of this analysis will not be a definitive answer, i.e. the answer will not be in the form of “based on the individual activity duration estimates, the project is expected to finish of date X”. Rather, the answer will be in the form of “based on the individual activity duration estimates, there is X% chance that the project will be complete on or before date Y”.

The chart below was produced using a Monte Carlo Simulation software, and highlights the type of outputs that such a tool will produce. Let’s examine the chart and understand its content. The overall purpose of the chart is to present the likelihood (or a better term – probability) of the project completing on any particular date. The left axis (Hits) can be used to review the number of times, during the simulation, that a particular date was identified as a potential completion date. The right axis (Cumulative Frequency) shows the total accumulative times that the project was determined to complete on or before a particular date. The bottom axis (Distribution) shows the identified potential completion dates, while the height of the bar associated with that date is determined by the number of times that the date has been identified by the simulation as being the project’s completion date.

In this example, having analyzed the project activity durations, the following statements can now be made:

  • Based on the individual activity duration estimates, there is 80% chance that the project will be complete on or before 21/05/02.
  • Based on the individual activity duration estimates, there is 50% chance that the project will be complete on or before 15/05/02.

By the way, if you notice the yellow arrow, pointing at 08/05/02, this is the date shown as the project completion date on the project plan. Now that we’ve performed the risk analysis we can determine that our chances of actually finishing the project on or before that date are just 15%!

As the name of this post suggests, there is much more to Monte Carlo Simulation software than what I’ve presented here. The above, however, highlights the fundamental need to consider project scheduling risks as if you don’t they WILL come back to haunt you.

Can you see how this type of analysis can help you better manage your project risks?

I value your comments, if you have any thoughts on the above please join in and share with others!

Here is a list of relevant articles you might want to read:

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  1. Shim,

    Great overview. Just a couple of details.

    1. The five tasks you describe have to be in series for the math to work. In series, the 90% confidence level must also have a level probability distribution, so the 90% has a 10% uncertainty.

    2. The term “confidence” should be replaced with “variability.” Confidence is a scalar measure that does not describe the underlying statistical behavior of the task duration. This variability is described by the means and standard deviation of the probability distribution function – the shape of the statistical function that generates the random variables of the duration.

    3. The PERT approach not only assumes independence, more importantly the standard deviation is predefined and the distribution is symmetric. Neither of which are true in practice.

    4. The actual phrase for the probability of completion is “there is an 80% confidence of completing on or before at date.” Since the PDF shown in the example is a cumulative distribution function. What it says – in the sampling population, 80% of the random completion dates finish on or before a date.

    5. The 3 point samples can be used for the Monte Carlo Simulations as well. The MCS can also used a Most Likely (the mode) and the statistical upper and lower limit for a specific probability distribution function (pdf). The triangle distribution is a common one for projects that don’t have historical information.


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  17. Carl Cunningham

    Hi Shim,

    Thank you for your very informative and concise articles about Monte Carlo simulation, they have really helped with this fairly abstract subject. Just to satisfy my own curiosity, I asked members of various Project Management forums if they use Monte Carlo simulation during their project planning – the resonance was . What would you attribute this to?



    • Hi Carl, happy to respond but I suspect you’ve missed out one word from your comment: “the resonance was….”?

      Cheers, Shim


      • Carl Cunningham

        “you’ve missed out one word from your comment…”
        How right you are – I meant to write “zero”, as in “resonance was zero”. In the meantime, I have posed my original question (“Do you use MCS? If no – why not? If yes – what are your experiences?”) to several different PM forums. I received about ten responses, and out of the 10, nobody said that they regularly use MCS. Several respondents maintain that their scheduling and duration estimates are so well founded and accurate that they have nothing to gain by using MCS, and several others responded that they would use an MC simulation only as a negotiating tool when dealing with the Project Sponsor.

        What are your thoughts on this? Do you use MCS regularly during project planning?


        • Hi Carl, this is an interesting predicament, one I cannot easily explain.

          First of all, in answer to your last question, No, I do not use MCS regularly during project planning and for the following simple reason. I work as a contractor at different organizations and I hardly ever have the luxury of selecting my own tool set or the methodology. The best I was able to do was to ‘push’ the introduction and incorporation of Earned Value. I have recently worked on the development of an Earned Value Management Guide for my consulting company and I was resolved, at the end of that exercise, to create another guide that will tie in the control introduced by the use of EVM with the Planning rigor introduced by using MCS – alas, I am yet to get this under way.

          Like EVM, the use of MCS is predicated on substantial organizational education. You have to show the benefits in order to gain momentum and buy-in. I have attempted in the past to take an existing project and demonstrate the inherent risks in the schedule using MSC but the decision to incorporate such approach needs to be taken way before the project has started. Bear also in mind that for many project managers the concept of using MSC is a foreign concept many of which have not come across or have ever seen in operation. This, too, calls for greater education and awareness raising, which I tried to elicit through the use of my blog.

          Happy to hear of your thoughts on this matter.

          Cheers, Shim


  18. Carl Cunningham

    Hi Shim,
    thanks for your input – I understand what you mean when you say that substantial organizational education is needed prior to introducing EVM and MCS. I’m trying to sneak both in at least for my own projects.



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