6 Sigmais a quality management program to achieve “6 sigma” levels of quality.

6 Sigma is a highly disciplined process that helps to focus on developing and delivering near-perfect products and services.
Why “Sigma”? The word is a statistical term that measures how far a given process deviates from perfection. The central idea behind 6 Sigma is that if you can measure how many “defects” you have in a process, you can systematically figure out how to eliminate them and get as close to “zero defects” as possible.

To achieve 6 Sigma quality, a process must produce no more than 3.4 defects (defect=failing to deliver what the customer wants) per million opportunities. An “opportunity” is defined as a chance for nonconformance, or not meeting the required specifications. 6 Sigma focuses first on reducing process variation and then on improving the process capability (process capability=what your process can deliver).

6 Sigma was pioneered at Motorola in the mid-1980s by Bob Galvin, who succeeded his father and Motorola

founder, Paul Galvin, as head of the company, and by Motorola engineer Bill Smith. It has since spread to many other manufacturing companies, including Ford, GE, Honeywell, Raytheon, Seagate Technology, and Microsoft. However, it can be applied wherever the control of variation is desired. In recent years, it has begun to branch out into the service industry, and in 2000, Fort Wayne, Indiana became the first city to implement the program in a city government. Some, claiming that 6 Sigma impact has not yet been fully realized, advocate an open source approach so that the principles of 6 Sigma might be more widely adopted.

Why 6 standard deviation?
According to the graph of the standard normal distribution, only two billionths of the normal curve falls beyond 6 standard deviations, in contrast to the value of 3.4 millionths publicized by 6 Sigma promoters. Confusingly, that value corresponds to precision within 4.5 standard deviations, reflecting a 1.5 standard deviation “shift”.

Introduced by Mikey Harry around 1980, its magnitude was based on observations and personal experience, not empirical data.
It is used to account for model inaccuracies, since defects in manufacturing processes do not always correspond to the normal distribution. Instead, processes tend to “drift” with time, causing the majority of error to fall on one side of the normal distribution and as a result, a higher defect rate than 3.4 DPMO if no shift were used.

With 6 Sigma methodology, however, if the process drifts by 1.5 standard deviations, the level of quality will remain within 3.4 DPMO.

However, the 1.5 sigma shift assumption is not without its critics. Donald J. Wheeler, a respected quality professional, labels it “goofy”, arguing that it is misapplied in practice and that it is probably inaccurate anyway. Often, implementers of 6 Sigma simply add 1.5 “sigmas” to their sigma calculation, transforming a 4.5 sigma process (3.4 DPMO) into a 6 sigma process. But this reflects a misunderstanding of the nature of the shift. If short-term data is used (data that does not reflect potential process drift), 1.5 sigmas should be subtracted from the final sigma calculation to account for the potential drift.

Thus, achieving 3.4 DPMO using short term data reflects a three sigma process, not 6 sigma, when used to reflect the long-term failure rate. Alternatively, if long-term data is used to make the sigma calculations, the process drift will have already been accounted for, and no additions or subtractions to the sigma calculation are necessary.

The other common objection is that the choice of a shift of 1.5 sigma is too arbitrary and probably inaccurate.

Some suggest that the 1.5 sigma shift was implemented for marketing reasons, so that the program could be named 6 Sigma  instead of “4.5 Sigma” without setting the unrealistic goal of two defects per billion. However, according to original training material used at Motorola in 1985, the point at which a shift became detectable with a sample size of 4 was 1.5 standard deviations, suggesting that the number was not arbitrarily selected.

In practice, the principle of 6 standard deviations of quality between the upper and lower specification limits is often not applied with mathematical rigor.

Instead, 6 Sigma is seen as a methodology or mindset with the goal of minimizing defects. It is used in this way in non-manufacturing environments, where it serves as an analogy to manufacturing processes and is not used for statistical distributions. Similarly, the frequent misuse of the 1.5 shift assumption in manufacturing processes is a reflection of a similar attitude in industrial applications as well.

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