Alistair Cockburn referred to a paper posted in PMForum. (Along with Alistair's site, PMForum is a MUST subscribe site for anyone claiming to be a project manager) The paper suggests the causal source of the "fat tails" for distribution of work effort. This paper possibly provides a theoretical source of the practice of using the Triangle distribution for the source of Monte Carlo simulations.

But several issues need to be addressed:

- The notion of infinite tails is not statistically sound. In practice triangle distributions represent bounded values for durations.
- The notion of infinite tails is not managerially sound. Models of duration and cost have management limits. In most cases these set at 125% of the baseline. After 125% overrun management intervention takes place and a new baseline established. In federal contracts Nunn McCurdy in breach is invoked. (There are numerous examples of this not being the case in commercial projects, but that's just BAD management).
- The notion of Linear Work is not used in any credible cost and scheduling model. The approach here in aerospace and defense is to bound the Work Packages with not cross more than one accounting period - usually 45 days. The allows the modeling of the Triangle distribution to be applied to a "not to exceed" duration within the two months around a single accounting period. This way the linear aspects are "forced" while the non-linear aspects are applied at a higher level. This does not prevent non-linear behavior but the lowest level is "linearized" and the macro level become tractable.
- Figure 2 of the paper is the most useful for our work. Modeling the difficulty of the work with the effort needed for that work is a Systems Engineering problem. Typically historical data is used. NASA has a extensive data base for "calibrating" work effort versus the technology. The issue of course comes when new work is needed - "inventing new physics" type work.
- The Stochastic behavior of humans is an interesting approach. The Monte Carlo simulations are driven by Probability Distribution Functions - Triangle is best used in the absence of underlying information. But true stochastic behaviors seem a bit extreme. Stochastic process are "true" random processes without correlation functions between internal variables and especially external coupling that evolve with time. This is unlikely in practice, but would make a great research topic if the historical data could be captured. But this paper is about the theory, so not an issue at this point. The author considers the task size, productivity, and task difficulty. A good starting point for this topic is
*Introduction to Stochastic Processes*, Lawler, Chapman Hall, 1995. I actually looked at it a few months ago when dusting the bookshelf.

Here's a graph we use to show the coupling of input variances to output variances for a single random variable. Random processes are assumed to be stationary and therefore not stochastic.

The challenge here is the define the coupling between work, productivity and difficulty. The paper does not speak directly to that. And unfortunately that is what is needed for any credible planning process. At the moment that information comes from subject matter experts.

On the cost side there is similar "coupling" models used on the programs we work. This picture is taken from a training presentation provided by MCR Corporation - a thought leader in this subject area - cost, schedule, and technical difficulty modeling.

My final - and constant - difficulty with the paper is the weak reference section. There is a wealth of material at the Association for the Advancement of Cost Engineering, INCOSE's Systems Engineering Journal, NASA's Cost Estimating Handbook site, and other "internal" cost and schedule modeling sites. The paper had two references.

The paper is a "must read," if only to start the conversation about the probabilistic nature of Cost, Schedule and Technical Performance Measures in the presence of probabilistic risk models.