Category Archives: Beta Edition

Statistical PERT® Beta Edition Released!

Yesterday, on March 1, 2017, I released the first production release — Version 1.0 — of Statistical PERT® Beta Edition.  It was a long journey to get to that day!  Click here to download it now, or read the press release.

About two and one-half years ago, I pondered over how to model a risk uncertainty based upon expert opinion rather than historical data.  Very often, project managers estimate projects using expert opinion, so the question in my mind was highly relevant to my job.  In fact, in the 15 years I’ve worked as a project manager, and the 15 years I’ve worked as a software developer, I can’t remember any time where I did not rely on expert opinion to estimate the work activities on a project schedule.

At the end of that weekend in October, 2014, I had created something I called SPERT, short for Statistical PERT.  My work was rooted in PERT (Program Evaluation and Review Technique, which every PMI-credentialed project manager knows).  I started with PERT’s simple formula to estimate the mean of an uncertainty.  But the trouble is using the mean is that it only has about a 50/50 chance of being correct.  Most project uncertainties are bell-shaped risks, and the mean of a bell-shaped uncertainty lies at or near the top of the bell-shaped curve, where half the area is to the left of the mean, and half the area is to the right of the mean.

I wrestled with how to come up with a standard deviation for an uncertainty where there was no historical data.  That was the key problem that Statistical PERT cracked.  Once I came up with a way to do that, then it was simply a matter of using Excel’s two normal distribution functions, NORM.DIST and NORM.INV, to come up with probabilistic estimates.

But most project uncertainties aren’t symmetrically shaped.  Most often, things take longer than expected rather than less time than expected.  Most project uncertainties, then, are skewed to the right, where the area under the bell-shaped curve is greater to the right of the mode (and the mean) than to the left.  Using the normal distribution gave “good enough” results, but was there way to approximate a skewed uncertainty using just the built-in, statistical functions of Excel?

The answer was (and is), Yes.  The beta distribution, which is the distribution originally used with PERT, is a wonderfully flexible distribution that can model left-skewed, right-skewed and symmetrical uncertainties.  It does it all!  The challenge with using the beta distribution (and the reason almost no project managers even know about it, much less use it) is that it uses two shape parameters, or arguments in Excel, called alpha and beta, and nobody except statisticians and data geeks know how to choose the right combination of alpha and beta to get a bell-shaped curve that matches the risk nature of an uncertainty.

That was the nut to crack with Statistical PERT Beta Edition.  How could I create an easy-to-use, Excel template that employed Excel’s two beta distribution functions, BETA.DIST and BETA.INV, to model risk uncertainty?  How could the template know what combination of alpha and beta to choose from using as little input from the estimator as possible?

So, 18 months ago I started walking down that road.  I spent a long time using an approach which, later, I jettisoned because it resulted in bell-shaped curves with modes that didn’t match the estimator’s three-point estimate input.  The second approach, which in future blog posts I’ll try to describe, was the one I settled on because it was simple for the estimator to use, could be matched to similar results using SPERT Normal Edition and a regular Monte Carlo simulation, and required nothing new from the estimator than what the original Statistical PERT approach required:

  1. Create a three-point estimate for the uncertainty (minimum, most likely, maximum)
  2. Render a subjective opinion about how likely was the most likely outcome to occur
  3. Select a probabilistic estimate or make a risk-based, range forecast

Statistical PERT Beta Edition is really easy to use.  It has the distinct advantage over its older brother, the Normal Edition, of being able to more accurately represent skewed uncertainties.  Its main disadvantage is that, unlike the Normal Edition, it cannot be easily changed, and you can’t employ the approach to a blank spreadsheet like you can with the Normal Edition.  But as long as you live within those constraints, downloading and then using a SPERT Beta Edition example workbook or template is wonderfully easy for the estimator, who is shielded from having to interact directly with Excel’s statistical functions.  The template does that for you.

I look forward to sharing both editions of Statistical PERT with project managers, business analysts, educators and students throughout 2017 and beyond.  It’s my firm conviction that probabilistic estimates create better alignment among people on the nature of an uncertainty, and it fosters better decision-making among those responsible to make choices about future uncertainties, such as how long a project might take, or how much it might cost.

I welcome your feedback!  Feel free to reach out to me with any questions about Statistical PERT.

Statistical PERT Comparison with @Risk

From the very beginning of the creation of Statistical PERT, I have used Palisade’s excellent risk analysis Excel add-in program, @Risk, to compare Statistical PERT’s probabilistic results with those obtained by @Risk using, mostly, the RiskPERT function that comes with @Risk.  RiskPERT is a special form of the beta distribution that models the kind of probability curve traditionally associated with PERT.  I very often gauge Statistical PERT’s accuracy against the results from a Monte Carlo simulation using @Risk.

As I ready the release of Statistical PERT – Normal Edition Version 2 and Statistical PERT – Beta Edition Version 0.6, I wanted to compare the results of these new versions with what I would get using the RiskPERT function.  To make this comparison, I have to set Statistical PERT to use “Medium Confidence” in the Most LIkely outcome to obtain the closet match to a RiskPERT distribution curve.

In performing a sample of six different three-point estimates (only one of which implied a symmetrical bell-curve, one which implied a left-skewed curve, and four which implied right-skewed curves), I was very pleased with the results.

The Normal Edition, of course, extends the implied probability curve to infinity both to the left and to the right; hence, the comparison results with RiskPERT tends to be very different at the extreme ends (1%, 5%, 95% and 99%).  But the Normal Edition performed admirably even though it fits asymmetrical bell-curves to a symmetrical normal curve.

The Beta Edition, as expected, did very well tracking to RiskPERT even at the extreme ends, and it tended to track more closely to RiskPERT overall than what the Normal Edition could do.  This is, in fact, the key reason I wanted to develop a Beta Edition of Statistical PERT was to improve the implied fitting of a probability curve to a 3-point estimate that implied a skewed uncertainty.

Overall, the difference between an estimate from @Risk and a SPERT estimate was usually around 2% or less, and very rarely was it more than 3.5%.  SPERT-Beta’s average difference with RiskPERT was 1.6% across all the 3-point estimates I tested and never greater than 2.2% except when dealing with a perfectly symmetrical bell curve.  SPERT-Beta’s kurtosis for a normal curve is slightly lower than the kurtosis used by RiskPERT, which explains why SPERT-Normal did a better job tracking to RiskPERT for a normal bell-curve than what SPERT-Beta did.

Download an Excel spreadsheet showing a full comparison of @Risk’s RiskPERT function, Statistical PERT – Normal Edition, and Statistical PERT – Beta Edition.  And stay tuned:  these new releases of Statistical PERT happen on January 2, 2017!