## Monte Carlo Simulation for Dummies

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.

### 2 Responses to “Monte Carlo Simulation for Dummies”

1. Glen B. Alleman Says:

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.