Estimating

There is a posting on Gantt Head (www.gantthead.com) titled "Estimation Blues" in which the author describes an approach to estimating project durations using the PERT method and provides a spread sheet to compute the estimated duration for a project. The tool that accompanies the text describes how to capture three point estimates and use PERT to compute the characteristics of a project. The sample project contains 21 "scope items" of varying durations. The Minimum, Most Likely, and Maximum duration for each item are entered into the spread sheet. The PERT Mean is then summed for a total duration of all items.

Background on probabilistic estimating?

For those not familiar with PERT, each task in the project network is assigned three durations:

• Optimistic duration
• Most Likely duration
• Pessimistic duration

These durations can be acquired through a variety of means ranging from interviews to historical statistical samples. The term "most likely" in the statistical sense means the mode of the underlying probability distribution. The "most likely" value drawn from the collection of values in the set of random variables represented by the population of all possible values.

So What's the Problem Here?

The article appearsto present a useful approach to estimating the total duration of a project, using a spread sheet and gathering "estimates" that are then used to calculate to total duration using PERT.

The mathematics and the general approach are however wrong. I haven't spoken to the author (but hope to) so I can't say what audience he was writing to or what background he has in working on these types of problems. Anyone reading the article should not apply this approach. There are numerous problems, let me name two:

• The "most likely" values of PERT are the mode (the most recurring) of an underlying probability distribution for an activity's duration. This distribution has a "shape" over the range of all possible values. This shape may or may not be symmetric. The symmetry is important because, if the probability distribution function (pdf) is NOT symmetric then the mean (the average value), the median (the middle most value) and the mode (the most likely value) are not the same. If they are not the same, then the arithmetic addition described in the Gantt Head article can not be performed. It is highly unlikely a probability distribution of completion times for an activity will be symmetric. Beta or Log Normal, yes, symmetric no.
• The spread sheet in the article allows the user to enter the three point estimates but it does not describe the means to identify the dependencies on these activities. These dependencies are not only critical to the assessment of the total duration - critical path being one example. But they are critical to defining the correlations between the activities from a statistical analysis point of view. This correlation significantly impacts the total duration of the project in statistical ways not visible when the values are simply added.

Since space is limited, I'd start by directing the reader to "Estimating Probable System Cost," Stephen A Book, Crosslink, Winter 2000/2001, Aerospace Corporation and "Probablistic PERT," Arthur Nadas, IBM Journal of Research and Development, Volume 23, Nuumber 1, May 1979. These papers have further references and many more can be found on the web using the key words in the paper.

The Bottom Line Problem

Not only is the Gantt Head article incorrect in its technical approach, it is also flawed conceptually. Estimating schedule duration and cost is a probabilistic process not an arthmetic process. PMBOK makes this error, PM texts make this error, the common practices of PM make this error.

Without a better understanding of how our tools work, projects managers will be doomed to be late before they start. If you apply PERT without the probablistic adjustments, that is exactly what will happen.

Afterword

There are several approaches to estimating schedule and cost. Monte Carlo is one. Another is "Risk and Cost Management" (RACM). This approach has a nice survey of the problem and the solution of estimating cost.

Even if you don't apply any of this information, reading through the materials will show how not to use PERT and not to simply add the durations (and costs) to get a total. That total will ALWAYS be significantly less than the probablistic value and significantly less than "reality."