# Articles

## What is Beta Distribution?

In the 1950’s, the U.S. Navy was working on the Polaris nuclear submarine project. This project let to the development of a program known as PERT, Program Evaluation and Review Technique. PERT is a program that measures hundreds of ongoing tasks and predicts its requirements. These requirements include time estimations, future costs, and how much work effort you will need. Likewise, PERT lead to the usage of a three-point estimation technique, that categorizes these requirements into “optimistic”, “most likely”, and “pessimistic”. When calculated with other statistical data, a clear image of a project, its costs, and its timeline is easily seen. For Six Sigma, this three-point estimation technique is referred to as ‘Beta Distribution’.

## How Does It Work?

Like other statistical Six Sigma tools, Beta Distribution requires a condensed mathematical formula. However, before diving into the formula, we first need to define the variables needed. First, we calculate a, the “optimistic time”. This variable represents the minimum amount of time a project needs to be completed. Additionally, this factor assumes a small probability of less than 1%. Next, we calculate m, the “most likely time”. Unlike the first variable, m represents the time needed to complete a project based on historical data. Because of its higher probability, this factor is at the mode of the Beta Distribution curve. Last, we will calculate b, the “pessimistic time”. As the final variable, this represents the absolute maximum amount of time needed to complete the project. Like the first factor, b has a probability of less than 1%.

With all required factors now available, we input them into the Beta Distribution formula to give us: µ = a + 4m + b6. Where µ is the estimated mean, or average, of all variables. The next formula used for Beta Distribution is variance, which will show how wide the difference is in your variables. This equation is as follows: σ2 = (b-a/6)2. The greater difference in your optimistic and pessimistic values, the greater variance in your overall equation.

## How to Use Beta Distribution?

A tool is only helpful if you know how to properly use it. For Beta Distribution, the three-point estimation technique is a useful tool for optimal project management. With it, you can effectively visualize your project’s expected timeline, identify complicated or risky tasks, and provide confidence to your team. By knowing when to complete a project by, under specific circumstances, you will increase productivity and reduce errors. Likewise, calculating and isolating problematic tasks prepares your project team to handle situations accurately.

As a Six Sigma professional, your goal for every role is to decrease error, improve efficiency, and increase productivity. Using this tool, you will enhance your understanding of business process improvement and become a more advanced project manager.

For more information on our Lean Six Sigma courses and Root Cause Analysis Training, please visit 6sigma.us. 