How to Calculate Six Sigma Quality

The term Six Sigma comes from the statistical basis of the approach and methodology used to address quality concerns: the roll-up of characteristic behaviors and the natural increase in variation in each characteristic over the long term.

The sigma scale is a universal measure of how well a critical characteristic performs compared to its requirements. The higher the sigma score, the more capable the characteristic. For example, if a critical characteristic is defective 31 percent of the time, you say that this characteristic operates at two sigma. But if it runs at 93.3-percent compliance, you say that it operates at three sigma.

Sigma Percent Defective Defects per Million
1 69% 691,462
2 31% 308,538
3 6.7% 66,807
4 0.62% 6,210
5 0.023% 233
6 0.00034% 3.4
7 0.0000019% 0.019

If a characteristic operates at three sigma, that means the variation in its performance exceeds acceptable levels 6.7 percent of the time. This breakdown may be an invoicing process that goes longer than the company’s allowed time limit. Whatever the critical characteristic may be, if it’s three sigma, it’s defective 6.7 percent of the time, or 66,700 times out of a million.

What the originators of Six Sigma discovered is that when they worked to have each critical characteristic in the system — the product, the service, the transaction — perform at a Six Sigma level, the risk of the individual characteristics being incorrect was small enough (0.00034 percent or 3.4 defects per million opportunities) that the overall system still performed at an exceptional level when all the parts were assembled together.

And even when long-term effects inevitably entered into each characteristic, the overall system performance remained high. These companies then had a method for competing at a whole new level on the global market. That’s why six is the magic number.

So why six and not five sigma? The complex products for which this method originated had enough characteristics rolled together and enough long-term degradation that only six would do. Four or five sigma just didn’t provide enough relief from these two constraints.

The systems and environments of transactional and service companies now adopting Six Sigma are often less complex; they don’t have as many critical characteristics coming together, so they don’t necessarily need to have each critical characteristic operating at Six Sigma. In these cases, four or five may actually do.

But the magnitude of the earlier success of Six Sigma has made the name stick. And almost all companies, regardless of their size or complexity, recognize the benefits of aiming for a Six Sigma goal. Even if the milestone of Six Sigma is never reached, the act of working toward that goal drives breakthrough changes.

In some instances, great companies are able to produce Six Sigma quality in their final products, services, and transactions — especially when safety or human life is involved. For example, did you know that you’re about 2,000 times more likely to reach your destination when you fly than your luggage is? That’s because airline safety operates at a level higher than Six Sigma, while baggage reliability operates at about four sigma.

99% Good (3.8 Sigma) 99.99966% Good (Six Sigma)
20,000 lost articles of mail per hour 7 articles of lost mail per hour
Unsafe drinking water for almost 15 minutes per day 1 unsafe minute of drinking water every seven months
5,000 incorrect surgical operations per week 1.7 incorrect surgical operations per week
2 short or long landings at major airports every day 1 short or long landing at major airports every five years
200,000 incorrect drug prescriptions each year 68 incorrect drug prescriptions each year
No electricity for almost 7 hours each month One hour without electricity every 34 years
11.8 million shares incorrectly traded on the NYSE every day 4,021 shares incorrectly traded on the NYSE every day
3 warranty claims for every new automobile 1 warranty claim for every 980 new automobiles
48,000 to 96,000 deaths attributed to hospital errors each year 17 to 34 deaths attributed to hospital errors each year
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