Monte Carlo Analysis

Posted on March 31, 2010 by

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“What is that Monte thing in the PMBOK®?” is probably one of the most common questions I receive from those studying for their PMP® exam. Monte Carlo Analysis is not explicitly listed as a tool and technique in the PMBOK, but it is mentioned as being part of two tools and techniques.

The What-If Scenario Analysis tool and technique is part of the Develop Schedule process. This tool and technique can include performing a Monte Carlo Analysis to help provide an overall project duration estimate. Quantitative Risk Analysis and Modeling Techniques is a technique of the Perform Quantitative Risk Analysis process. Monte Carlo Analysis can be applied here to develop a probability distribution for completion times or total project cost.

How does Monte Carlo Analysis work? Monte Carlo Analysis is a family of algorithms, whose calculations are best suited for a computer. We must first know the distributions of the possible inputs. Next, we iteratively draw from these distributions many times to create models. Lastly, these results are aggregated to form an overall model. Project managers are likely to use cost or duration estimates of individual activities to obtain an overall cost or duration.

For example, Annie’s activity is expected to take 10 days with a standard deviation of 1 day. Becky’s activity, which starts when Annie’s activity is complete, is expected to take 20 days with a standard deviation of 3 days. To calculate how long it will take to complete both these activities, the expected number of days they will take are randomly drawn from the two distributions. If Annie’s activity duration estimates are normally distributed, then about two-thirds of the time 8, 9, or 10 will be drawn since they represent the mean and one standard deviation above and below the mean (in a normal distribution about two-thirds of the data falls within one standard deviation above and below the mean). For the first iteration, 9 days may be randomly selected for Annie’s activity and 22 days may be selected for Becky’s activity. This is repeated many times until we have a distribution of how long we expect both activities to take.