The three-point estimation technique is used in management and

information systems An information system (IS) is a formal, sociotechnical, organizational system designed to collect, process, store, and distribute information. From a sociotechnical perspective, information systems are composed by four components: task, people ...

applications for the construction of an approximate

probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomeno ...

representing the outcome of future events, based on very limited information. While the distribution used for the approximation might be a

normal distribution In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu i ...

, this is not always so. For example, a

triangular distribution In probability theory and statistics, the triangular distribution is a continuous probability distribution with lower limit ''a'', upper limit ''b'' and mode ''c'', where ''a'' < ''b'' and ''a'' ≤ ''c'' ≤ ''b''. ...

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: * ''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 There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set. For a data set, the '' ari ...

, standard deviation or

percentage points A percentage point or percent point is the unit for the arithmetic difference between two percentages. For example, moving up from 40 percent to 44 percent is an increase of 4 percentage points, but a 10-percent increase in the quantity being me ...

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 that a

PERT distribution In probability and statistics, the PERT distribution is a family of continuous probability distributions defined by the minimum (a), most likely (b) and maximum (c) values that a variable can take. It is a transformation of the four-parameter beta ...

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 In statistics, an L-estimator is an estimator which is a linear combination of order statistics of the measurements (which is also called an L-statistic). This can be as little as a single point, as in the median (of an odd number of values), or a ...

s, where: : ''E'' = (''a'' + 4''m'' + ''b'') / 6 : SD = (''b'' − ''a'') / 6 ''E'' is a

weighted average The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The ...

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

for

Monte Carlo Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino i ...

simulations. The

is also commonly used. It differs from the 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 In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a ...

) is then: : ''E'' = (''a'' + ''m'' + ''b'') / 3. In some applications,Ministry of Defence (2007
"Three point estimates and quantitative risk analysis"
/ref> the triangular distribution is used directly as an estimated

, 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 A work-breakdown structure (WBS) in project management and systems engineering is a deliverable-oriented breakdown of a project into smaller components. A work breakdown structure is a key project deliverable that organizes the team's work int ...

* Estimates the expected value E(task) and the standard deviation SD(task) of this estimate for each task time * Calculates the expected value for the total project work time as

\operatorname(\text) = \sum

* Calculates the value SD(project) for the standard error of the estimated total project work time as:

\operatorname(\text) = \sqrt

under the assumption that the project work time estimates are

uncorrelated In probability theory and statistics, two real-valued random variables, X, Y, are said to be uncorrelated if their covariance, \operatorname ,Y= \operatorname Y- \operatorname \operatorname /math>, is zero. If two variables are uncorrelated, there ...

The E and SD values are then used to convert the project time estimates to

confidence interval In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated ''confidence level''; the 95% confidence level is most common, but other levels, such as ...

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 × SD(project) * The 95% confidence interval for the true project work time is approximately E(project) ± 2 × SD(project) * The 99.7% confidence interval for the true project work time is approximately E(project) ± 3 × SD(project) * Information Systems typically uses the 95% confidence interval for all project and task estimates. 68–95–99.7 rule These confidence interval estimates assume that the data from all of the tasks combine to be approximately normal (see

asymptotic normality In mathematics and statistics, an asymptotic distribution is a probability distribution that is in a sense the "limiting" distribution of a sequence of distributions. One of the main uses of the idea of an asymptotic distribution is in providing ap ...

). 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.

References

External links

Risk and duration estimates: 3 point estimating
from www.4pm.com {{DEFAULTSORT:Three-Point Estimation Statistical approximations Informal estimation

Estimation

Project management

See also

References

External links