From Beta distribution to PERT model estimating technique |

Beta Distribution |

Regardless of the technique you use for estimating tasks, each estimate has to be quantified into a number. There are different ways for estimating project tasks, for example:

__Use of Historical Data__- "similar" projects categorized in a knowledge database system can be retrieved and consulted when making estimates.__Use of Experienced Resources__- estimating is a team effort, and the contribution from experienced resources in making estimation is very valuable.__Use of Estimating Databases__- make use of industry databases made available by organizations.

In many cases estimates can be made more accurate by applying a simple PERT (Program Evaluation and Review Technique) model. PERT is an estimating technique that uses a weighted average of three numbers to come up with a final estimate.

The PERT distribution comes out of the need to describe the uncertainty in tasks during the development of a complex project having thousands of tasks. Estimates were needed to be made intuitively, quick and consistent in approach. The PERT distribution is a probabilistic model based on Beta Distribution, and it derives its estimates based on the probability of occurrence. A version of this four-parameter Beta distribution is called a PERT distribution and makes the assumption that the MEAN = (MINIMUM + 4*MOST LIKELY + MAXIMUM) / 6. The default value of 4 scales the height of the distribution. This extra equation allows the four parameters to be determined from three input values: the minimum, most likely and maximum, which makes it ideal for modeling expert opinion of the uncertainty of a variable.

- E = Expected Value = (O+4M+P)/6 (this is the "weighted" average equation)
- P: Pessimistic value (this value is maximum, because it describes the case when things go wrong)
- O: Optimistic value (this value is minimum, because it describes the case where things go right)
- M: Most Likely value (this value describes the case given normal problems and opportunities)

For example, let's suppose we want a more accurate estimate of a task duration that is collocated in a Project Network Diagram, given the following values:

- P = 20 programmer days (pessimistic value when everything goes wrong)
- M = 15 programmer days (most likely)
- O = 10 programmer days (optimistic value where everything goes right)

__Use the following interactive form to get the expected task duration (mean value) for the above example.__

*(Similar tasks can be categorized to create a histogram and it's possible to use the last chart below to highlight the mean value*

*graphically,*

*as stepped area across all other values).*

Input Data (M,O,P)

Output Data Table (PERT Estimate)

*(refresh rate every 10 seconds)*

Output Data Graphically (PERT Estimate)

*(refresh rate every 10 seconds)*