Sigma, σ, is the Greek character we use to represent standard deviation. 6 σ represents the spread of data about the mean. For data with a normal distribution 6 σ includes 99.7% of the data.

The 6 σ design approach incorporates knowledge of the variation that will occur within the design such that the design has is unlikely to fail.

According to Mikel J. Harry, the foundation of excellence in product quality rests on achieving six sigma product quality. [1]

## What is 6 σ product quality

Quoting Mikel J. Harry again:

In general, when we say that a product is 6 σ, what we are really saying is that any given product exhibits no more than 3.4 npmo at the part and processes set levels. This number (3.4) takes typical sources of variation into account.

Note: npmo or nonconformities per million opportunities is interchangeable with ppm or part per million.

The design and manufacture of the product result in a very small amount of variation that is outside the specifications.

The values outside the specifications while they may not cause immediate product failure, do tend to reduce the functionality and/or shorten the useful operating duration of that item.

The intent is not to create impossibly tight specifications. Rather the idea is to create specifications that allow the parts, materials, and assembly practices to vary and remain well within the design specifications.

The emphasis is on uses wider specifications and working to reduce part, material, and assembly related variation, or standard deviations.

The minimum target for any element of a design is to have 6 /sigma of separation between mean and the specification limits. At least 12 σ units between the upper and lower specification values.

The 3.4 dpmo value includes the expected 1.5 σ shifting of the mean as part of natural variability. For example, if a part is well centered and remains so, along with 6 σ relationship with the specifications, it would only enjoy 0.002 npmo.

Allowing the mean to shift up to 1.5 σ in either direction increases the expected defect rate to 3.4 npmo.

## 6 Sigma and scale

You may recall that for a normal distribution roughly 68% of the data is within +/- 1 σ of the mean. Furthermore, 99.7% is within +/- 3 σ.

Achieving 3 σ quality and a perfectly centered and stable process will produce approximately 2.7% nonconformities. Add the to-be-expected 1.5 σ shift of the mean and this number rises to 66.8%. More than half of your product will have nonconformities.

Achieving 6 σ quality results in 0.000002% in a stable and centered case. With the expected shift in mean, this changes to 0.0034%.

Since the percentages become very small when dealing with 6 σ we make use of npmo or ppm. The 0.0034% becomes 3.4 npmo.

These are small numbers and difficult to image.

To provide a sense of scale Mikel J. Harry uses a few examples. The first is considering a set electronic circuit boards with a total of 10,000 solder joints.

If 99% of the solder joint were good, that suggests each system would have 100 bad solder joints. If the solder joints have 6 σ quality that implies 99.999966% of joints are good. This means only 3.4 solder joints are bad in 100 systems.

Another set of examples, concerning the scale involved with different sigma levels of quality, is in figure 4. Comparison of Various Characteristics Using the Sigma Measurement Scale. [1] Here the table data without the associated images.

PPM | Sigmas | Area | Spelling | Distance |

0.000003 | 7 σ | Point of a sewing needle | 1 misspelled word in all of the books contained in several large libraries | 1.8 of an inch |

0.002 | 6 σ | Size of a typical diamond | 1 misspelled word in all of the books contained in a small library | 4 steps in any direction |

0.57 | 5 σ | Size of the bottom of your telephone | 1 misspelled word in a set of encyclopedias | A trip to the local gas station |

63 | 4 σ | Floor space of a typical living room | 1 misspelled word per 30 pages (about one chapter in a book) | 45 minutes of freeway driving (in any direction, of course) |

2,700 | 3 σ | Floor space of a small hardware store | 1.5 misspelled words per page in a book | Coast-to-coast trip |

45,600 | 2 σ | Floor space of a large supermarket | 25 misspelled words per page in a book | 1 1/2 times around the world |

317,400 | 1 σ | Floor space of an average factory | 170 misspelled words per page in a book | From here to the moon |

The PPM along with example use the defect rates for a centered and stable system. The idea is to provide a sense of scale for change in defect rate as quality improves.

The rest of the short book defines standard deviation, variance, and processes capability measures. The emphasis is on both the number of defect opportunities and the calculation of the expected number of nonconformities.

The work relies on the use of the normal distribution, yet the same principles apply for any underlying continuous distribution.

The concept described here is to design in robustness to the variation that will naturally occur, plus control a stable process to minimize variability.

## The evolution of 6 Sigma programs

In large part based on the work done at Motorola in the 1990’s and the emphasis on 6 /sigma design quality the quality community embraced 6 σ programs.

The programs included tools for teams to work together to solve issues causing unwanted or necessary variation within processes. Some programs dropped the focus on the data and statistics to emphasize the teamwork and problem-solving skills.

6 σ is a mathematical (statistical) concept. In my opinion, today’s 6 σ programs avoid the rigors of doing the math. To be successful implementing 6 σ concepts you must embrace the need for data analysis, statistics, and design of experiments.

Reducing and controlling variation will always be important. The real value of 6 σ programs is in the creation of a 6 σ quality product, which starts in design.

How’s your 6 σ program going? Add a comment and let me know if your program includes the math or not.

[1] Harry, Mikel J, University University Motorola. The Nature of Six Sigma Quality. Schaumburg, IL: Motorola University Press, 1997.

Hilaire Perera says

Six Sigma is a set of techniques and tools for process improvement. It was introduced by engineer Bill Smith while working at Motorola in 1986. Jack Welch made it central to his business strategy at General Electric in 1995. Black Belt & Green Belt groups originated from this concept. Today, it is used in many industrial sectors.

https://en.wikipedia.org/wiki/Six_Sigma