Let’s examine the difference between a Statistical PERT estimate using the normal distribution and a PERT estimate (which is a special form of the beta distribution) using the RiskPERT function in Palisade’s @Risk Excel add-in. Only this time, lets look at an even more skewed probability curve. This time, the range between the most likely outcome (12000) and the maximum point-estimate will be four times greater (40000) than the range between the minimum point-estimate (5000) and the most likely outcome.
If you crack open the spreadsheet, below, you’ll see that, at the worst, the difference between SPERT estimates and RiskPERT estimates is off by up to 5%. The gap is worst around the top of the curve (naturally), and continues to shrink as you approach the right-side tail. At the 80th percentile, the difference is around 3%, and at the 90th percentile, the difference is less than 2%.
I don’t advise using Statistical PERT (using the normal distribution — a new edition of SPERT is forthcoming using the beta distribution) where the range difference on one side of the curve is more than four times greater than the other side. To me, when you approach a difference of 5% or more, then this technique may give estimates which could be misleading, depending on where along the probability curve you’re looking. When I release the first stable version of Statistical PERT – Beta Edition this winter, the new edition, using the beta distribution, will do a better job modeling skewed uncertainties.
Also, another point I want to make is that there is nothing sacred about the RiskPERT results. They provide one probability shape which may or may not be a good fit for the uncertainty you’re trying to model. Don’t think that RiskPERT estimates are “right” and any deviation from them is “wrong.” RiskPERT is one way to model risk. Statistical PERT, using the normal distribution, is another way. Whether one way is better than the other is an arguable point, and it mostly depends upon hard-to-identify properties associated with an uncertain outcome.
All that said, if your uncertainty has bell-shaped properties, and the skewing is no worse than 4x greater either to the left or to the right, than Statistical PERT will give good results provided you can accept estimation errors related to using a normal probability curve in place of a different probability distribution.