Three-point estimation: Difference between revisions

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

{{Wikify|date=January 2009}}{{Unreferenced|date=January 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.

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 IS projects. In Three Point Estimation we produce three figures for every estimate:

* a = the best case estimate

* m = the most likely estimate

* b = the worst case estimate

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

These values are used to calculate an E value for the estimate and a Standard Deviation (SD) where:

* ''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==

E = a + (4*m) + b / 6<br />

Based on the assumption that a [[PERT 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:

SD = (b - a)/6

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

E is a weighted average which takes into account both the most most optimistic and pessimistic estimates provided and SD measures the variability or uncertainty in the estimate.

: SD = (''b''&nbsp;&minus;&nbsp;''a'') / 6

''E'' is a [[weighted average]] which takes into account both the most most optimistic and most pessimistic estimates provided and. SD measures the variability or uncertainty in the estimate.

To produce a project estimate the Project Manager:

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

* 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 [[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:

We then use the E and SD values to convert the project estimates to Confidence Levels as follows:

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

* Confidence Level in E value is approximately 50%

* Confidence Level in E value + SD is approximately 70%

* Confidence Level in E value + 2 * SD is approximately 95%

* Confidence Level in E value + 3 * SD is approximately 99.5%

* IS use the 95% Confidence Level, i.e. E Value + 2 *SD, for all project and task estimates

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.

== See also ==

==Project management==

To produce a project estimate the Projectproject Managermanager:

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

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

We then use theThe E and SD values are then used to convert the project time estimates to Confidence[[confidence Levelsinterval]]s as follows:

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

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

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

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

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

== See also ==

* [[Five-number summary]]

* [[Seven-number summary]]

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

{{More footnotes|date=September 2010}}

==References==

{{Reflist}}

{{Project cost estimation methods}}

[[Category:Statistics]]

{{DEFAULTSORT:Three-Point Estimation}}

[[Category:Statistical approximations]]

[[Category:StatisticsInformal estimation]]