Three-point estimation: Difference between revisions

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{{Short description|Technique used in management and information systems}}

The '''three-point estimation''' technique is used in management and [[information systems]] applications for the construction of an approximate [[probability distribution]] representing the outcome of future events, based on very limited information. While the distribution used for the approximation might be a [[normal distribution]], this is not always so. and, forFor example, a [[triangular distribution]] might be used, depending on the application.

In three-point estimation, three figures are produced initially for every distribution that is required, based on prior experience or best-guesses:

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''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 ProjectProgram Evaluation and Review Techniques ([[PERT]]) the three values are used to fit a [[PERT distribution]] for [[Monte Carlo Method|Monte Carlo]] simulations.

The [[triangular distribution]] is also commonly used. It differs from the [[Double-triangular distribution|double-triangular]] by its simple triangular shape and by the property that the mode does not have to coincide with the median. The mean ([[expected value]]) is then:

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

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To produce a project estimate the project manager:

* Decomposes the project into a list of estimable tasks, i.e. a [[work breakdown structure]]

* Estimates the expected value E(task) and the [[standard errordeviation]] SESD(task) of this estimate for each task time

* Calculates the expected value for the total project work time as <math>\operatorname{E}(\text{project}) = \sum{ \operatorname{E}(\text{task})}</math>

* Calculates the value SESD(project) for the standard error of the estimated total project work time as: <math> \operatorname{SESD}(\text{project}) = \sqrt{\sum{\operatorname{SESD}(\text{task})^2}}</math> under the assumption that the project work time estimates are [[correlation|uncorrelated]]

The E and SESD values are then used to convert the project time estimates to [[confidence interval]]s as follows:

* The 68% confidence interval for the true project work time is approximately E(project) ± SESD(project)

* The 90% confidence interval for the true project work time is approximately E(project) ± 1.645 &times; SESD(project)

* The 95% confidence interval for the true project work time is approximately E(project) ± 2 &times; SESD(project)

* The 99.7% confidence interval for the true project work time is approximately E(project) ± 3 &times; SESD(project)

* Information Systems typically uses the 95% confidence interval for all project and task estimates.<ref>[[68-95-9968–95–99.7 rule]]</ref>

These confidence interval estimates assume that the data from all of the tasks combine to be approximately normal (see [[Asymptotic distribution#Asymptotic normality|asymptotic normality]]). Typically, there would need to be 20&ndash;30 tasks for this to be reasonable, and each of the estimates E for the individual tasks would have to be unbiased.

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{{Reflist}}

==External links==

*[http://www.4pm.com/articles/PERT_program_evaluation_&_review_technique.pdf Risk and duration estimates: 3 point estimating] from www.4pm.com

{{Project cost estimation methods}}

{{DEFAULTSORT:Three-Point Estimation}}