Three-point estimation: Difference between revisions

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

{{Article issues|wikify =January 2009|unreferenced =January 2009|context =March 2009|cleanup =March 2009}}

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. For 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:

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

These are then combined to yield either a full probability distribution, for later combination with distributions obtained similarly for other variables, or summary descriptors of the distribution, such as the [[mean]], [[standard deviation]] or [[percentile|percentage points]] of the distribution. The accuracy attributed to the results derived can be no better than the accuracy inherent in the three initial points, and there are clear dangers in using an assumed form for an underlying distribution that itself has little basis.

==Estimation==

Based on the assumption (possibly unwarranted) that a ''double''-[[triangularPERT 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) as [[L-estimator]]s, where:

: ''E'' = (''a'' + 4''m'' + ''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 [[ProjectProgram Evaluation and Review Techniques]] ([[PERT]]) the three values are used to fit a [[BetaPERT 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 (expectation[[expected value]]) is then:

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

In some applications,<ref name=MOD2007>Ministry of Defence (2007) [http://www.aof.mod.uk/aofcontent/tactical/risk/downloads/3pepracgude.pdf "Three point estimates and quantitative risk analysis"] [http://www.aof.mod.uk/aofcontent/tactical/risk/content/tpe.htm Policy, information and guidance on the Risk Management aspects of UK MOD Defence Acquisition]</ref> the triangular distribution is used directly as an estimated [[probability distribution]], rather than for the derivation 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 Eexpected value E(task) and the [[standard deviation]] SD(task) of this estimate for each task. time

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

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

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

* ConfidenceThe level68% inconfidence Einterval valuefor the true project work time is approximately 50%E(project) ± SD(project)

* ConfidenceThe level90% inconfidence Einterval valuefor +the SDtrue project work time is approximately 70%E(project) ± 1.645 &times; SD(project)

* ConfidenceThe level95% inconfidence Einterval valuefor +the 2true &times;project SDwork time is approximately 95%E(project) ± 2 &times; SD(project)

* ConfidenceThe level99.7% inconfidence Einterval valuefor +the 3true &times;project SDwork time is approximately 99.5%E(project) ± 3 &times; SD(project)

* IS{{Clarify|date=AugustInformation 2009}}Systems typically uses the 95% confidence level, i.e. E Value + 2&nbsp;&times;&nbsp;SD,interval for all project and task estimates.<ref>[[68–95–99.7 rule]]</ref>

These confidence levelinterval 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.

== See also ==

* [[Five-number summary]]

* [[Seven-number summary]]

* [[Program Evaluation and Review Technique]] (PERT)

* [[Triangular distribution]]

{{More footnotes|date=September 2010}}

{{DEFAULTSORT:Three-Point Estimation}}

[[Category:Statistical approximations]]

==References==

{{Reflist}}

{{Project cost estimation methods}}

{{Statistics-stub}}

{{DEFAULTSORT:Three-Point Estimation}}

[[Category:Statistical approximations]]

[[de:Drei-Zeiten-Methode]]

[[Category:Informal estimation]]