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Triangular Distribution

The Triangular distribution is a continuous distribution bounded on both sides. It starts at the minimum value, increases linearly to peak at the mode, and then decreases linearly to the maximum value.

The Triangular distribution is often used when no or little data is available; it is rarely an accurate representation of a data set (see Law & Kelton). This distribution is generally employed in the first stage of building a model, when time is critical and a basic understanding of the system is being developed.

The information needed for the this distribution can be captured by asking three questions:

  1. What is the least amount of time it has ever taken to complete this activity?
  2. How long does it usually take to complete this activity?
  3. What is the longest it has ever taken to accomplish this activity?

If example if the result of your questions were:

  1. One
  2. Three
  3. Seven

The distribution would be formatted T(1,3,7). The result would be entered into a time field and would produce a result of the output shown graph below:

 triangular distribution used for process simulation triangular distribution used for business process simulation
traingular distribution used in process improvement

This distribution can take on very skewed forms, as shown above, including negative skewness. For the exceptional cases where the mode is either the min or max, this distribution becomes a right triangle.

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About the Author:

Scott Baird has been president of ProcessModel for more than 15 years. His focus has been to teach others how to improve processes dramatically. He has been successful in transferring these skills to over 200 companies, including ESPN, NASA, GE, Nationwide, Cendant, SSA and many more. Specialties: Group facilitation for process improvement, process design and simulation, simulation modeling, business management and training others to see opportunities. Scott loves to teach process improvement and has often been heard to say, “Of all the things I do, training others to improve processes is my favorite.” Scott is a father of four and a grandfather of eight. He is an avid woodworker, designing and creating presentation boxes. In his spare time, he volunteers in a college preparation program.