dice of foam: a fuzzy, mundane perspective on project performance statistics

eXtra Dynamic Critical Path Method


..is a re-engineered project management methodology that helps make the impossible possible. It works even if one doesn’t have a computer; I’m not suggesting to discard technology. Just know XDCPM is that significant.

If you manage projects or produce most anything you’re aware of CPM —the critical path method of project planning and its companion Lean manufacturing processes in JIT, Kanban, Six Sigma etc.

CPM has its standard charts and techniques made by industrial and military science in the 1950's including the Gantt chart, PERT and it’s uncle GERT chart, and Earned Value Management (EVM). They help control authoritarian projects and strict manufacturing processes. Planners stuff and strain everything about a project into a structured model of standardized equations and processes that describe any project essentially as a finely tuned robot army. You can’t blame them. Practitioners have had to rely on estimates based on mathematical equations. Any available computers were not powerful enough to deviate completely from accepted pen and paper techniques.

If you have an army of robots, you know the greatness of the utility of Gantt, PERT/GERT, and EVM. If not, chances are, you’ve run into a few limits of these strict engineering techniques applied with today’s ever faster, complex and higher capacity systems. Computers now allow practitioners to use performance data instead of mathematical estimates and models. Computers have opened up new possibilities.

eXtra Dynamic CPM (XDCPM) is a practical, holistic interpretation of activity network analysis. It offers more utility to project management and expands possibilities of applying Six Sigma to diverse sustainable practices in an ever changing world.

XDCPM converges techniques in statistics, discrete numerical analysis and visual display. It manifests in three distinct ways: pie charts, Cobbler charts, and PRETTI charts. Estimating the cost or time it takes to complete each task is important for project management. XDCPM builds on EVM estimating concepts.

Pie chart histograms

Pie charts have well known advantages when representing cyclic information or parts of a whole. Some games use a spinning pointer with dial face instead of dice to represent chance. Memorable ones include the roulette wheel, Twister’s spinner, and the large carnival wheel in the TV game show “Wheel of Fortune”. Basically, a pointer arrow is fixed to the axis of a dial face. When the arrow (or wheel) is struck, it spins around slowing, until it stops at some chance point. If the dial face is in equal segments, it’s expected that the chance is equal that the pointer stops in any one.

A Pie Chart Histogram representing a discrete numeric probability distribution. In this example, the last value is about 10 times the first value and values are sorted in increase amounts clockwise.

The spinner dial face is a probability distribution represented as a pie chart. For the purposes of XDCPM, the value of any segment is proportional to the radial length of a segment; A segment twice the length is twice the value. Within each segment, the value is a constant.

The size of each segment can be different to represent different probability ranges. If a segment has twice the angle, it’s assumed a spinner will land in it twice as often.

An unbiased random number generator emulating a spinner in this configuration can emulate most any combination of dice. A small distribution of probabilities can represent most any result of chance, such as task duration and cost. Working with a list of probabilities is an advantage over finding and manipulating distribution curve equations with traditional techniques. Some uniquely loaded dice are difficult to create or represent as equations.

Examples of loaded dice, where one or more dice may represent task performance.

The probability distribution for duration and cost of any task is the list of results from prior cases that have the same operational parameters. For probability, divide each case by the total number of cases. The total probability of all previous results is one. The Pie chart is useful to mimic dimensions of task performance.

Is this exact? No, but the larger the sample, the greater the accuracy of the probability distribution. It takes only a few samples to begin to reflect the unique probability of most any task.

Pie chart histograms extend the EVM concept. Buried behind paywalls is knowledge in statistics that probability curves of a sequence of events are additive. Unique task probability curves (or the distributions that represent them) do not need to resort to computational and time-burdened Monte Carlo simulations and other statistical simulations used by Event Chain Methodology (ECM).

Cobbler charts

Cobber charts are an extension of Pie chart histograms. Histograms are sometimes used to represent numerical probability distributions. They are rectangular with an x and y axis, and tend to fit better in many types of published media such as paper or viewing screens. Pie chart histograms add a natural cycle constraint of 0 to 1 probability limits to the histogram. To keep this representation when using Cartesian graphed bar charts, it seems appropriate to give the rectangular Pie Chart Histogram an apropos name: the Cobbler Chart.

A Cobbler Bar Chart or Histogram representing a discrete numeric probability distribution. In this example, the last value is about 10 times the first value and values are sorted in increase amounts from left to right. This example shows non-uniform probabilities.

For the most part, it’s just a roulette wheel or The Wheel of Fortune’s wheel transformed into a rectangle. The bottom is the center of the wheel. The top is the value at each point on the wheel.

In XDCPM, a Cobbler chart represents historical performance as a probability distribution approximation of a curve that is unique to each task. With the Cobbler, it’s easier to compare relative values of variance than with the Pie.


A Project Reporting Evaluation and Track Task Interpretation (PRETTI) chart is a digest of PERT/GERT/CPM/Gannt network diagrams. These network diagrams highlight critical paths and help rank tasks that might affect a project’s schedule. PRETTI chart is a table of a network’s paths, where each column is a sequence of tasks called a path or track. Each cell is a task. There are no lines connecting tasks. Regardless of the complexity of a network, PRETTI charts are a stable rendition.

PRETTI charts identify the CPM and paths close to CPM duration by ordering paths from longest to shortest, left to right. The CPM and long paths are to the left. The shorter paths are on the right.

The color of each task indicates relative rank on affecting a project’s schedule. The colorization helps prioritize management-level interventions. Colorization adjusts to relative contrasts for grayscale displays. The CPM tasks are yellow. Tasks close to CPM are pink. The more an activity’s color is closer to green the less likely it is to affect a project’s schedule. These color combinations reduce issues with color-blindness.

Legend of PRETTI Chart task colors

The color and sorted columns show attributes of a task network without having to interpret a complicated diagram of specialized symbols. The larger a project, the more value a PRETTI chart offers.

Example PRETTI chart

Each cell in a PRETTI chart represents a task. Since paths can share the same task, shared tasks will be in multiple columns of the chart. Their color and network statistics remain the same regardless. If a task in the middle of the chart is yellow or a strong pink, you know it is on or near the CPM even if the rest of the tasks on a path are low priority green.


Processes at the heart of the pie, Cobbler and PRETTI charts have features worthy of highlighting.

Discrete probability distributions are a special, natural case for pie charts and computers. Project Management statistics tend to use beta distribution curves instead of discrete distributions, because curves are ideal distributions represented by equations. Discrete distributions are made of a finite set of data. If all distributions can be represented by a few ideal equations, then a mathematical statistics approach would work really well for CPM/EVM. Experience shows many dice are loaded and no two are loaded exactly the same; Task performance also tend to deviate from ideal estimates. Probability distributions based on historical performance adjust for unique circumstances as the number of cases increase. Discrete distributions are a practical compromise between ideal expectations and experience.

Every task has its own performance data. Some may have a significant history, but some may be speculative. That’s okay. The XDCPM process converts EVM minimum, maximum and median estimates into numerical probability distributions that represent normal distributed probability curves of EVM. XDCPM uses the best available information for each task.

Each task cell includes path related information as well as common network node values. The “waypoint” data include the largest amount of slack that precedes a task, which may be more representative than conventional EVM float and slack calculations.

XDCPM can use the EVM “time expected” calculations for estimates by converting probability distributions to min/med/max values. A fine grained or strict, three segment probability technique is possible. The backwards compatibility of the XDCPM is handy to check calculations between estimates and other EVM calculator results etc.

A strength of Critical Chain Project Managment (CCPM) is a focus on including resource dependencies in the task network. In XDCPM, resource dependencies are dependent tasks. Using material order lead times as duration keeps resource dependencies represented in the task network. To insert a milestone on a path, create a task with no duration or resource change.

Network analyses, such as GERT, include looping and various decision branch processes. XDCPM uses a simple rule set. If a path can branch, include all branches in the network description, or create separate networks to avoid redundant resource calculations. If a task repeats or loops, define it once and include a multiplication factor.

Product manufacturing and common Theory of Constraints practices sometimes need special handling for repeated tasks. In XDCPM, constraints are available for repetitive tasks, such as maximum number of repetitions without a break, maximum time before a forced break, maximum amount of overlap of two sequential tasks, and maximum number of current runs of the same task. XDCPM cost estimating has a complement discount feature available for all but the first task in a batch run.

The output of XDCPM can create a probability distribution of a network for use as an aggregate task in other network analysis thereby completing a fractal-like repeatable process that is capable of generating estimates by building complex configurations from a pool of other estimates.

Software App

XDCPM is more than a process paradigm. It is a proof-of-concept app that adapts to your project no matter how it grows. The app uses a smart input form that detects standard delimiters; Most data can be moved about with copy and paste via a web browser. Audit tables allow you to check the output and export your data for use in other apps.

If you’re a web developer, the app is published as open source under the GNU GPLv3 License. You can operate it with your own computers, change it for your own use, or distribute copies in compliance with the license. The app works on OpenACS, a mature multi-platform compatible web framework. It’s flexible parameters make it a good fit for private workgroups, social networking and private use.

To learn more about the process and app availability, visit the project at http://or97.net