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Interactive example using PERT estimating technique

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)

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