Three-point estimation
Encyclopedia
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, 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:
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 percentage points
of the distribution. The accuracy attributed to the results derived can be no better than the accuracy inherent in the 3 initial points, and there are clear dangers in using an assumed form for an underlying distribution that itself has little basis.
(SD) where:
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:
In some applications, the triangular distribution is used directly as an estimated probability distribution
, rather than for the derivation of estimated statistics.
The E and SD values are then used to convert the project estimates to confidence levels as follows:
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.
Information systems
Information Systems is an academic/professional discipline bridging the business field and the well-defined computer science field that is evolving toward a new scientific area of study...
applications for the construction of an approximate probability distribution
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
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, 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:
- 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
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
, standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
or percentage points
Percentile
In statistics, a percentile is the value of a variable below which a certain percent of observations fall. For example, the 20th percentile is the value below which 20 percent of the observations may be found...
of the distribution. The accuracy attributed to the results derived can be no better than the accuracy inherent in the 3 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-triangular distribution governs the data, several estimates are possible. These values are used to calculate an E value for the estimate and a standard deviationStandard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
(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, the triangular distribution is used directly as an estimated probability distribution
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
, 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 structureWork breakdown structureA work breakdown structure , in project management and systems engineering, is a deliverable oriented decomposition of a project into smaller components. It defines and groups a project's discrete work elements in a way that helps organize and define the total work scope of the project.A work...
- Estimates 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 typically use 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 summaryFive-number summaryThe five-number summary is a descriptive statistic that provides information about a set of observations. It consists of the five most important sample percentiles:# the sample minimum # the lower quartile or first quartile...
- Seven-number summarySeven-number summaryIn descriptive statistics, the seven-number summary is a collection of seven summary statistics, and is a modification or extension of the five-number summary...
- Program Evaluation and Review TechniqueProgram Evaluation and Review TechniqueThe Program ' Evaluation and Review Technique, commonly abbreviated PERT, is a statistical tool, used in project management, that is designed to analyze and represent the tasks involved in completing a given project...
(PERT)
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