A Statistical Approach to Estimating

Another simplistic promo.

Developing range estimates is a valuable process but you either need data or a range of views to get a useful 'optimistic - pessimistic - most likely' (or other distribution).  One person’s view is subject to his/her personal biases.

Having developed a viable set of range estimates, simply using the data to calculate an 'expected value' and then doing a summation typically results in a 20% UNDER ESTIMATE. This was the basic flaw with PERT, see: http://www.mosaicprojects.com.au/WhitePapers/WP1087_PERT.pdf

The only sensible way to use three point estimates is a Monte Carlo analysis.  Monte Carlo will provide you with a lot of useful data to help manage the project and predict a realistic range of completion outcomes. 

You might also use Monte Carlo Simmulation in estimating you project

Patrick: I missed the reference to the 20% under-estimate in the cited paper. There is no 'basic flaw' with the PERT methodology, other than its simplicity. The PERT PDF compares favorably (IMO) with the PRA trigen distibution. It is does not afford you the option to select your risk preference (confidence level). It will give as valid an expected finish/final cost as any other PDF without knowledge of the 'actual' distribution. Absent any other mechanism, PERT is far superior to doing nothing to account for uncertainty. PERT is still a useful tool.

• http://www.goodplan.ca/2010/03/pert-loses-at-monte-carlo.html
• http://www.austprojplan.com.au/merge-bias-in-schedule-risk-example/
• http://www.prmyazilim.com/docs/riskanalysissimplified.pdf

While many of today's managers still cling tenaciously to "flat earth" ideals, the innovators are abandoning averages and facing up to uncertainty.

There are many who still believe that because they can get an average using a formula or even real data they can imput thier single average number on their calculations and this makes it a real probabilistic calculation. Probabilities is more than just averages.

• https://hbr.org/2002/11/the-flaw-of-averages 

Rafael; I was surprised by the output from Marc's example. It's been a while, but I recall getting better results. Note: This was prior to any stochastic capability. Schedules were bar charts with no logic. Mid-80s aerospace.

Using PERT the expected finish duration is 221 days v. 215. Even with this simple network there is only a 6% chance of meeting the 215 day finish (only 17% chance meeting the 221 day target). This is better than not trying to account for uncertainty, but not much. Still, a surprise.

Marc provides a good example but with the austprojplan.com example it is easier to visualize the difference.

There can be a huge difference when you have many chains competing to determine the schedule duration, the Merge Bias do matter.

In the example, for 1 activity the probability of making it in less than 108 days is  ~85% , for 2 is ~70% for four is ~50%. For PERT the probability distribution would be equal for all cases. There is a huge difference between 85% and 50% success probabilities.

People do not waste time with Monte Carlo just for fun. In lack of enough historical data you might estimate the individual activity duration distribution assuming a PERT distribution [as many Monte Carlo users do], but adding these durations along deterministic critical path with absolute disregard to the merge bias is too much into wrong statistical calculations.