Three-point estimation

The three-point estimation technique is based on statistical methods, and in particular, the normal distribution. Three-point estimation is the preferred estimation technique for information systems (IS) projects. In the three-point estimation there are three figures produced for every estimate:

• a = the best-case estimate
• m = the most likely estimate
• b = the worst-case estimate

Estimation

Based on the assumption (possibly unwarranted) that a double-triangular distribution governs the data, several estimates are possible. These values are used to calculate an E value for the estimate and a standard deviation (SD) where:

E = (a + 4m + b) / 6

SD = (b − a)/6

E is a weighted average which takes into account both the most optimistic and most pessimistic estimates provided. SD measures the variability or uncertainty in the estimate. In Project Evaluation and Review Techniques (PERT) the three values are used to fit a Beta distribution for Monte Carlo simulations.

The triangular distribution is also commonly used. It differs from the double-triangular by its simple triangular shape and the mode does not have to coincide with the median. The mean (expectation) is then:

E = (a + m + b) / 3.

In some applications,^[1] the triangular distribution is used directly as an estimated probability distribution, rather than for the drerivation of estimated statistics.

Project management

To produce a project estimate the project manager:

• Decomposes the project into a list of estimable tasks, i.e. a work breakdown structure
• Estimates each the E value and SD for each task.
• Calculates the E value for the total project work as E (Project Work) = Σ E (Task)
• Calculates the SD value for the total project work as SD (Project Work) = √Σ SD (Task) ²

The E and SD values are then used to convert the project estimates to confidence levels as follows:

• Confidence level in E value is approximately 50%
• Confidence level in E value + SD is approximately 85%
• Confidence level in E value + 1.645 × SD is approximately 95%
• Confidence level in E value + 2 × SD is approximately 98%
• Confidence level in E value + 3 × SD is approximately 99.9%
• Information Systems uses the 95% confidence level, i.e. E Value + 1.645 × SD, for all project and task estimates.

These confidence level estimates assume that the data from all of the tasks combine to be approximately normal (see asymptotic normality). Typically, there would need to be 20–30 tasks for this to be reasonable, and each of the estimates E for the individual tasks would have to be unbiased.

See also

• Five-number summary
• Seven-number summary

References

1. Ministry of Defence (2007) "Three point estimates and quantitative risk analysis" Policy, information and guidance on the Risk Management aspects of UK MOD Defence Acquisition

External links

• It Takes Three to Make Good Estimates from Visionary Tools
• Three-Point Estimate Approximations from www.super-business.net
• Risk and duration estimates: 3 point estimating from www.4pm.com