6 Sigma vs. 3 Sigma Methods & Use | What are 6 and 3 Sigma? | Study.com

Explore 3 sigma and 6 sigma methods. Learn the important differences between 3 sigma and 6 sigma percentages and understand their similarities with various examples. Updated: 11/25/2022

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Sigma Levels Overview

Business today requires an understanding of quality control history and principles. Sigma levels, including 3 sigma and 6 sigma, reflect the science of statistics applied to quality control.

Modern probability methods and uses began in the 18th century when Carl Friedrich Gauss, (1777–1855), a German mathematician and physicist, introduced the normal curve. Walter A. Shewhart (1891–1967), an American physicist, engineer, and statistician, created a system where statistical methodology could be applied to industrial systems. The system was published in his book Economic Control of Quality of Manufactured Product in 1931. W. Edwards Deming (1900–1993), an American engineer, statistician, author, and management consultant, created the Deming Cycle, his own quality control cycle for organizational processes. Deming further created fourteen leadership principles for leadership to manage people and processes for optimal efficiency.

Sigma is a symbol reflecting population standard deviation. The Sigma levels from 1 to 6 give us a level of confidence for a given set of desired outcomes.

The sigma levels show that for a number of opportunities, the defects per million of these opportunities yield for a specific level of productivity. For a million opportunities, sigma level 1 creates 691,462 defects or errors, with a productivity rate of 30.85. For those same opportunities, 3 sigma creates 66,807 defects and a 3 sigma percentage of 93.319%. For those same million opportunities, 6 sigma offers 3.4 defects or errors; 6 sigma percentage creates a 99.9997% success rate.

3 sigma and 6 sigma are statistical tools used for quality control. They are used to inspect a random sample of process output, to validate whether or not the output is within an acceptable range, and to evaluate and improve production and service processes. Both 3 sigma and 6 sigma percentages are markers on the range of possible outcomes:

Sigma Performance Levels: 1 to 6 Sigma

Sigma Level
Defects/Errors Per Million Opportunities (DPMO)
Yield %

1
691,462
30.85

2
308,538
69.146

3
66,807
93.319

4
6,210
99.379

5
233
99.9767

6
3.4
99.9997

What is 3 Sigma?

3 sigma is a statistical calculation showing data 3 standard deviations from the mean, and is used to measure the predictability of expected outcomes. The 3 sigma percentage yields a quality standard of 93.319%, and allows the organization to both examine deviation causes and determine whether those causes can be known or unknown. 3 sigma assumes there is no underlying systematic cause for errors, and if errors are found outside the 3 sigma percentage range, it is assumed the process itself is the cause for errors and must be revised before it can be further analyzed.

What is 6 Sigma?

6 sigma is a statistical calculation showing data 6 standard deviations from the mean, and results in a 99.9997% quality standard rate. It was created by Motorola engineer Bill Smith in 1986 as a means of reducing process defects with a much higher quality standard than 3 sigma. In addition to identifying and eliminating manufacturing defects, the 6 sigma methodology:

• Provides a means for improving business capability by identifying and eliminating process defects and improving profitability
• Provides a vehicle for cultural change and continuous process improvement within an organization
• Provides specific guidelines for continuous improvement
• Focuses on customer desires and satisfaction
• Identifies the value stream and eliminates variations in the stream that do not serve it well
• Includes a diverse group of employees and other stakeholders
• Creates an agile, responsive environment in which to execute change