Tag 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.

New Version, New Edition of Statistical PERT

Statistical PERT – Normal Edition, New Version 2.0

I’m excited to announce that early in 2017, I will be releasing a new 2.0 version of the original Statistical PERT Excel workbooks and templates that I began creating in 2015.  Version 2.0 will introduce one-point, probabilistic estimation by letting estimators choose a heuristic to calculate both the minimum and maximum point-estimates in a three-point estimate.

A heuristic is well-defined on Wikipedia as, “any approach to problem solving, learning, or discovery that employs a practical method not guaranteed to be optimal or perfect, but sufficient for the immediate goals. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision.”

What I’ve learned in the two years that I and others have used Statistical PERT is that sometimes people just don’t want to go through the mental work of figuring out a 3-point estimate for an uncertain outcome.  Sometimes, it’s easier to start with a single estimate value and have the rest of the bell-shape curve implicitly created for you.  And although that may not be as precise and optimal as specifying all three points of a 3-point estimate, using a heuristic to create two of the three points in a 3-point estimate may be “good enough” for project planning purposes.

In the 2017 release of Statistical PERT, estimators may choose to employ a simple heuristic that takes a single point-estimate — the most likely outcome — and reduces it by a specified percentage to create the minimum point-estimate, and increases the most likely outcome by a specified percentage to create the maximum point-estimate.  SPERT estimators can choose separate heuristics for the minimum and maximum calculations.

For example, if I specify a value of 100 for the most likely outcome (the unit of measure doesn’t matter), I can say that the minimum point-estimate is 25% less than the most likely outcome, and the derived minimum would be 75.  Then I can say that the maximum point-estimate is 50% greater than the most likely outcome, and the derived maximum would be 150.  The resulting three-point estimate used to model the uncertainty would be (75, 100, 150).  I only had to set the minimum and maximum heuristics once for the entire worksheet, and all my subsequent one-point estimates will use heuristics to automatically create the minimum and maximum point-estimates.  Obviously, the math formulas involved are exceedingly simple, so the innovation here is mostly just about ease-of-use in creating three-point estimates, rather than technical innovation.

Estimators will be able to override heuristically-derived minimum and maximum point-estimates by just entering an actual, numeric value in place of the formula used to create minimum and maximum point-estimates.  All SPERT download files will still offer a separate worksheet to enter 3-point estimates without using heuristics, too.  Heuristics, then, are in addition to what is available in a Statistical PERT worksheet, not a replacement of anything currently available.

All existing Statistical PERT Excel downloads will be re-labeled as “Statistical PERT – Normal Edition” to reflect that all the currently-available downloads use Excel’s built-in normal distribution functions, NORM.DIST and NORM.INV.

Which brings me to the other exciting change for 2017….

Statistical PERT – Beta Edition, New Version 1.0

It’s been one year since I began a new quest to create a simple way to create probabilistic estimates using the more-flexible beta distribution, which handles skewed uncertainties more accurately than the normal distribution does.  I wanted to use Excel’s two beta distributions, BETA.DIST and BETA.INV in a spreadsheet that was just as easy to use as the original SPERT Excel spreadsheets, which hid the complexity of creating a standard deviation that the normal distribution functions require.

Excel’s beta distribution functions use two shape parameters, alpha and beta, which determine the precise shape of the beta curve.  Specifying alpha and beta shape parameters is not at all intuitive, however, so the goal was to create a technique that figures out a good approximation of alpha and beta based solely upon the estimator’s three-point estimate and the estimator’s subjective opinion about how likely the most likely outcome really is (just like the original Statistical PERT spreadsheets using the normal distribution!).

The details behind Statistical PERT – Beta Edition are too much to include in this blog post, but you can see a development build of the forthcoming version 1.0 that will be released in early 2017, along with the version 2.0 of Statistical PERT – Normal Edition.

Together, both editions of Statistical PERT will let anyone easily make estimates using Excel’s built-in, statistical functions.  And all Statistical PERT versions and editions will continue to be freely licensed under the GNU GPL, so you can download, use, modify and share any SPERT file like you’ve always been able to do.

Download a development-only build of Statistical PERT – Beta Edition here.