Probability, more or less

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……….more to follow…………………………………….

the power curve

Monte Carlo methods (the atom bomb program; Feynman, Taleb, etc)

Practical Applications


Cost Estimates (typically) use “expert” analysis as an “overlay” to an estimate. Based on interviews, industry/ proprietary data, and/or analysand’s experience to generate (a) most likely, (b) minimum and (c) maximum values- then distribute using formulae such as (a) triangular or (b) PERT (used in the graphs at the top of this post).

For Cost, @Risk and Crystal Ball the top commercial programs… can also “roll your own” in Excel, such as Sam’s or RiskAmp…

Scheduling is a little tougher than cost because of the interaction between activities (start of a successor based on the completion or some milestone in its predecessor).

For Primavera, Pertmaster used to be the one, but support may have been discontinued… Primavera has their own Monte Carlo add in.For Microsoft Project, @Risk has a Monte Carlo engine, among others…

Bottom Line:

Probability studies and Monte Carlo simulations are tools which help leverage expert judgments.

At their best, they can add detail and extend analysis .

At their worst, they can serve as a poor mechanized substitute, and as such have led more than one project astray.

An Alternate Visualization

Hair Chart

Another way of visualizing probabilities, is with a “hair chart” as shown above. This would track one hundred possible scenarios within a typical range for an endeavor. The optimistic lines chart multiple events at the optimum end of the range (30% point bounded in yellow); the most common, densest number of lines being when things go mostly as planned, or with equal plusses and minuses (the green 50% line); and of course more lines and another yellow for the pessimistic range of possibilities.

Deep Background

For a fun intellectual romp; to broaden one’s perspectives in this area, it would be hard to beat the brilliant, eccentric, derivatives Hall of Famer/ author Nassim Taleb. (the image links below open to Amazon, for used copies of the same books click here and here).

Fooled Black Swan1

For the academically rigorous (e.g. “boring”) stuff, or if you feel the need to drop the phrase “Central Limit Theorem”, or if you want to show off your old German 10-Deutschmark with Gauss’s curve on it, consider the following:

probability MIT Open

MIT Open Courseware: Introduction to Probability and Statistics (click on image)

probability AMS

American Mathematical Society: Introduction to Probability (pdf book)

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