- While paging thought Rob Thomsett's site from the provious post I came across this presentation. Figure 8 describes the difference between a low risk profile and a high risk profile. Tomsett has is backward or at least has missed on important concept about the Most Likely value. At least he has confused those of us who earn our living doing probabilistic risk assessments.

... the higher the risk of the project the higher the estimation error

This is likely true - once all the qualifications are in place. But the "higher estimation error" is indicated by a higher standard deviation from the mean in the direction of a longer duration. This is NOT what is show in Figure 8.

First let's take a detour. Anyone wanting to understand risk management must buy and read (at least Chapter 6) *Effective Risk Management: Some Keys to Success 2nd Edition*, Edmund H. Conrow. Chapter 6 is titled "Some Risk Analysis Considerations." This book is tough sledding pretty much all the way through. Which is why it is important to read it. Risk Management is tough going almost all the time. As well download and read Probabilistic Risk Assessment Procedure Guide for NASA Managers and Practitioners

Back to Thomsett's curves. In the curve that is skewed to the left - that is the tail of the curve extends to the right, describes a higher risk situation. You read the curve in the following way. I'll assume that the right and left values on the x-axis are the 10%/90% confidence values of the probability density function (pdf). (This is a big assumption here, but I'll proceeed anyway)

But first let's point out a core problem. Thomsett states that these curves are for the same task in the same project. This can't be the case, since the Most Likely estimate is different between the two curves. It is that - a Most Likely estimate - the duration of the task that appears "most often" if the project and the task were executed a large number of times. If the Most Likely values are different - as shown in Figure 8 - then these are not the same tasks from the the same project. This is the basis of Monte Carlo simulation, where the values for the task duration are drawn from a large population of values described by the pdf.

I see how Thomsett could make the statement about the higher and lower risk descriptions - inverted in fact. BUT the statistics are flawed since the probability distribution functions for the task (the same task in the same project) must have to be changed in order to produce the results shown in Figure 8. This is "cooking the books" and not good statistics. This would work ONLY if you allowed the underlying statistics to change bewteen the High and the Low risk assessments. This approach provides no basis for assessment of the project since I can't even tie down the risk probability functions.

That said, let's look at the curves in another way...The first curve in Figure 8 states.

*The task will complete in 14 hours or less 90% of the time, in 8 hours or less 50% of the time, and in 5 hours or less 10% of time.*

The second curve can be read as...

*The task will complete in 24 hours or less 90% of the time (9 our of 10 times this task is performed it will complete in 24 hours or less), 20 hours or less 50% of the time, and 5 hours or less in 10% of the time (in only 1 out of 10 times will this task complete in 5 hours or less).*

It is very important to understand what these curves mean. They are probability densities of many occurances of the same activitiy. They represent a "population" of occurances of this activities. From this population of occurance you can derive inferences about the next occurance. This is why it is criticaly important to "calibrate" these curves with real data. This can be sample data or expert opinion data. But in all cases it must be calibrated in some way. See Chapter 6 of Conrow.

So the less risky plan is the second one, since the Most Likely completion time is very closer (in absolute duration) to the 90% confidence completion duration - that is if you tell me a completion time, it is LESS LIKELY that this time will be significantly longer than what you told me.

The first curve is riskier, since the Most Likely duration of 8 hours could be extended to 14 hours with a 90% confidence. This is a much longer extension of the task duration and therefore riskier for planning purposes.

So if I were provided to descriptions of the task duration the second curve would be less risky since the Most Likely estimate has a 90% confidence value closer (in percentage of overrun) than the first curve. Therefore it is less risky to produce disappointment.

BTW one should NEVER use the worst case term in these probability distributions. 10/90 is much preferred to the 0/100 for the end point descriptions. The worst case completion time might be infinite or near-infinite duration - espically in a BetaPERT distribution. For Traingles they have finite upper and lower limits, but the bias errors between 10/90 and 0/100 in a Triangle can be as much as 20% depending on the 2nd and 3rd momemnts of the pdf. ALWAYS use 10/90 estimates.

Now what does all this mean - to me personally and to the profession of project management.

If the conjecture that a methodology is somehow simplified - as is the case here - then the underlying facts need to be right. They need top represnt the statistical process describing the risk assessment of being late.

Some background on this topic can be found in

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