Distribution Intervals
In addition to specifying exact values for certain fields in your model (such as process and move times, quantities in arrivals, and other settings) you may also use distribution intervals. Distribution intervals add variances to your model, which can help them be more realistic in cases where amounts or times are unlikely to be exact and constant.
There are many types of distribution intervals available for use in ProModel AutoCAD® Edition. The following section explains the three most common types of distribution intervals: Exponential, Uniform, and Triangular. See the Full Table of Distribution Intervals for all available distribution intervals.
Exponential
The Exponential distribution is a continuous distribution bounded on the lower side. Its shape is always the same, starting at a finite value at the minimum and continuously decreasing at larger x. It is frequently used to represent the time between random occurrences, such as the time between arrivals at a specific Location or the time between failures in reliability models. It’s also used to represent the service times of a specific operation.
To use an Exponential distribution interval, use the syntax E(mean), where mean is the average amount for your interval. For example, E(10) minutes in the Arrival frequency indicates that a new Entity arrives about every 10 minutes, since 10 is the mean. However, Entities could arrive in less or more time.
Uniform
The Uniform distribution is sometimes called the rectangular distribution. It is a continuous distribution bounded on both sides. Note that the end points do NOT occur, the probability of either the minimum or maximum value occurring is zero.
To use a Uniform distribution interval, use the syntax U(mean, half range), where mean is the average interval amount and half range is the variance, (i.e., amount less or more than the mean that can occur). For example, U(9,1) minutes in the Arrival frequency indicates that a new Entity could arrive anywhere between 8.1 and 9.9 minutes after.
Triangular
The Triangular distribution is a continuous distribution bounded on both sides. It is often used when not a lot of data is available. The Triangular distribution may be used when the minimum value, the most likely value, and the maximum value for a numeric element are estimated. It is rarely the most accurate distribution, but is usually a good estimation.
To use a Triangular distribution interval, use the syntax T(minimum, mode, maximum), where minimum is the smallest amount in the interval,mode is the amount that occurs most often (note that this is not the same as the mean), and maximum is the largest amount in the interval. For example, T(1,8.6,11) minutes in the Arrival frequency indicates that a new Entity could arrive anywhere between 1 and 11 minutes after, and most often arrive 8.6 minutes after.
Full Table of Distribution Intervals
| Distribution | Syntax | Individual Components |
|---|---|---|
| Beta | B(a,b,c,d) | a=shape value 1, b=shape value 2, c=lower boundary, d=upper boundary |
| Binomial | BI(a,b) | a=batch size, b=probability of “success” |
| Erlang | ER(a,b) | a=mean, b=integer shape parameter |
| Exponential | E(a) | a=mean |
| Gamma | G(a,b) | a=shape value, b=scale value |
| Geometric | GEO(a) | a=probability of “success” |
| Inverse Gaussian | IG(a,b) | a=shape value, b=scale value |
| Lognormal | L(a,b) | a=mean, b=standard deviation |
| Normal | N(a,b) | a=mean, b=standard deviation |
| Pearson5 | P5(a,b) | a=shape value, b=scale value |
| Pearson6 | P6(a,b,c) | a=shape value 1, b=shape value 2, c=scale value |
| Poisson | P(a) | a=quantity |
| Triangular | T(a,b,c) | a=minimum, b=mode, c=maximum |
| Uniform | U(a,b) | a=mean, b=half range |
| Weibull | W(a,b) | a=shape value, b=scale value |
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