Six Sigma: what it is, what the sigma level means and how it is calculated

In one line

Six Sigma is a data-based improvement methodology that seeks to reduce the variation of a process until it produces at most 3.4 defects per million opportunities.

What it is

The MIT course (translated by the Pontificia Universidad Católica de Chile) defines a "defect" as any process output that does not meet the customer's specifications, and explains that improving quality means reducing defects per million opportunities (DPMO). There are two ways to bring that number down: reduce the opportunities (fewer steps, handoffs and chances for error) or reduce the defects at each stage. Six Sigma is defined as 3.4 defects per million opportunities, that is, a first-pass yield of 99.9997%. It also points out that, with a Six Sigma process, even a significant shift of the mean results in very few defects.

"Sigma" is the standard deviation: the sigma level counts how many standard deviations fit between the process mean and the customer's specification limit. The higher it is, the fewer defects.

The handbook from the Council for Six Sigma Certification gives the table used as a reference:

Sigma level	Defects per million opportunities (DPMO)
1 sigma	690,000
2 sigma	308,000
3 sigma	66,800
4 sigma	6,200
5 sigma	233
6 sigma	3.4

To see what each jump means, the MIT course compares 99% accuracy (3.8 sigma) with 99.99966% (6 sigma): with the first, 20,000 pieces of mail would be lost per hour, versus seven per hour with the second; drinking water would be unsafe for almost 15 minutes per day, versus one minute every seven months; there would be 5,000 incorrect surgical procedures per week, versus 1.7; and electricity would be missing for almost seven hours per month, versus one hour every 34 years.

How it is calculated

The Council proposes calculating the yield first and then looking up the level in the table:

• Yield (%) = (opportunities − defects) ÷ opportunities × 100
• DPMO = defects ÷ opportunities × 1,000,000

Calculate your sigma level

Real example

A marketing process inserts letters into pre-filled envelopes. A mix-up between envelope and letter is suspected; 1,000 letters from the week's batch are checked at random and 5 with an error are found, which, extrapolated to 150,000 letters per week, gives about 750 defects. The yield is (150,000 − 750) ÷ 150,000 = 99.5%: according to the Council's abbreviated table, the process is between 4 and 4.1 sigma. That is the value the calculator comes preloaded with.

The Ciudad Juárez case shows the same calculation on an assembly line: 130 defective parts out of 1,130 (DPMO of 115,044) gave a sigma level of 2.6 according to the paper (standard tables put it close to 2.7). After the improvements, 33 out of 1,250 (DPMO of 26,400) brought the level to 3.4. The details of the case are in Lean Six Sigma.

How it is organized: DMAIC and belts

Six Sigma's working cycle is DMAIC (define, measure, analyze, improve, control), which is explained in the DMAIC article. The Council also describes a hierarchy of roles:

• White belt: knows the basic principles; does not usually join improvement teams.
• Yellow belt: introduction to the method, with a basic grasp of DMAIC and data collection.
• Green belt: works within teams, normally supervised by a black belt; does a good part of the data collection and analysis, and sometimes leads small projects.
• Black belt: leader of improvement projects, with intermediate or advanced statistics and knowledge of Lean and total quality.
• Master black belt: the highest level; usually directs the black and green belts and provides training.

Where it comes from

According to the Council's handbook, the method was born at Motorola, whose engineers wanted to measure defects against one million opportunities; Motorola reported savings of more than 16 billion dollars in 12 years. It then passed through ABB and Allied Signal and reached General Electric, which, when Jack Welch adopted it, was operating at between three and four sigma; the estimated saving from moving up to six sigma was between 7 billion and 10 billion dollars. Niebel and Freivalds also place it as Motorola's total quality program.

Benefits

• A common, numerical language for talking about quality.
• An orderly method (DMAIC) for solving problems with data.
• It links improvement to financial results.

Limitations to keep in mind

• The sigma level of different processes is not always comparable: the Council's own handbook warns that a sigma level is not a final indicator.
• It requires reliable data and statistical training; in processes with few parts or that are not very repetitive, it is hard to apply.
• It is worth knowing whether a table includes the 1.5 sigma shift: it is what explains why "six sigma" equals 3.4 defects per million and not a much lower figure. Comparing numbers from tables that apply it with others that do not leads to errors.

In summary

Six Sigma turns quality into a number (DPMO, sigma level) and into a method (DMAIC). It is more powerful when combined with the flow perspective of Lean, as in Lean Six Sigma.